Research Agenda 2017-07-24T04:36:20+00:00

The Research Agenda

Understanding Income and Wealth Inequality

Moritz Kuhn is Associate Professor at the University of Bonn. His research interests cover the macroeconomics of inequality, labor markets, and human capital. Kuhn’s RePEc/IDEAS profile.

Income and wealth inequality are at historical highs. 1.5 million sold copies of Thomas Piketty’s book “Capital in the 21st century” have demonstrated that inequality is the defining issue of our time. Today, economists, policymakers, and the general public are actively engaged in a discussion about the causes and consequences of high and rising inequality and its implications for reforming the tax and social security system, as well as labor and financial market institutions. Although the debate is often coined in economic terms, it touches very fundamental issues like social cohesion in democratic societies.

But our understanding of the driving forces of inequality is still hazy. Why do some people earn so much more than others? Why do some people possess fortunes while others have barely any wealth? Does income inequality lead to wealth inequality, or vice versa? More generally, what determines the joint distribution of income and wealth? Answering these pivotal questions about inequality in contemporary societies is paramount to understand its consequences and constitutes the focus of my research agenda. I approach these questions by exploring existing datasets but also compile new ones. Newly-compiled data allows me to adopt new perspectives on inequality. In existing data, I take a more granular view at differences along the income and wealth distribution. I use the resulting evidence to inform my model-building. While traditional work studied wealth inequality as the result of an exogenous stochastic income process, the guiding idea of my work is that the income and wealth distribution are determined jointly so that policy changes reshape both. Based on this idea, I develop new models to study policy reforms in unequal societies.

My research agenda builds on a long tradition in modern economic research. 100 years ago, at the 31st annual meeting of the American Economic Association, the then-president Irving Fisher said that “the causes and cures for the actual distribution of capital and income among real persons” is a subject that needs “our best efforts as scientific students of society.” This is the goal I have set myself, and it is a great pleasure for me to present my research agenda in this newsletter. Let me add at the beginning that my research relies on an extensive and invaluable collaboration with coauthors in Bonn and elsewhere.

In my discussion, I will focus on three specific topics. The first topic addresses the connections between income and wealth inequality. I will start with a brief discussion of my recent paper (Kuhn, Schularick and Steins, 2017a) in which we compile and analyze a new micro-level dataset spanning seven decades of U.S. economic history. Using this data, we document strongly diverging trends between income and wealth inequality. We demonstrate that house price dynamics and portfolio heterogeneity of households explain these diverging trends. Second, I will discuss my recent work on the sources of earnings inequality. In Bayer and Kuhn (2017a), we explore a unique matched employer-employee dataset from Germany to revisit a key question from human capital theory about the importance of employers, education, experience, and job characteristics in determining wage differences. We find that a job’s hierarchy level encoding responsibilities and independent decision making required in the job is the most important driver of wage differences. Third, I will discuss my work to develop models to explore how policy changes affect earnings dynamics and the distribution of earnings. I will focus on a life-cycle labor market model developed in Jung and Kuhn (2016) that is jointly consistent with facts on worker mobility and earnings dynamics, focusing in particular on large and persistent earnings losses after worker displacement. At the end of the discussion of each of the three main topics, I will briefly touch upon companion works that explores the link between rising inequality and household debt (Kuhn, Schularick and Steins, 2017b), heterogeneity in earnings dynamics (Bayer and Kuhn, 2017b), and the effects of changes in the unemployment insurance system on labor market dynamics (Hartung, Jung and Kuhn, 2017). I will also take the opportunity to briefly talk about related work with José-Víctor Ríos-Rull (Kuhn and Ríos-Rull, 2016) providing a comprehensive reference on facts of U.S. earnings, income, and wealth inequality, and with Tom Krebs and Mark Wright (Krebs, Kuhn and Wright, forthcoming in the RED special issue on human capital and inequality) exploring the interaction of human capital accumulation, financial markets, and inequality.

1. Connections between income and wealth inequality

In Kuhn, Schularick and Steins (2017a), we provide newly compiled micro data for the income and wealth distribution of U.S. households over the entire post-World War II period. Despite the popular perception that inequality is the defining issue of our time, the existing micro data to study inequality trends spanning several decades remains very limited.

The newly compiled data is based on historical waves of the Survey of Consumer Finances (SCF) going back to 1949. We cleaned and harmonized the historical data to build a new dataset that we refer to as harmonized historical Survey of Consumer Finances (HHSCF). We expect that this new micro data will offer also other researchers the opportunity to address important questions with respect to changes in the financial situation of U.S. households since WW2.

In Kuhn, Schularick and Steins (2017a), we use this data to complement existing evidence on long-run trends in inequality discussed by Saez and Zucman (2016) and Piketty and Saez (2003). Most of the debate about rising inequality focused -mainly due to data limitations- at income and wealth concentration among the richest households. HHSCF data allows us to complete the existing picture on rising inequality by providing a granular picture of inequality trends among the large group of the bottom 90% of households. Existing tax data can only draw the rough contours of the developments in these strata. The paper demonstrates a strong hollowing out of the middle class. The much-debated income and wealth concentration at the top was accompanied by losses concentrated among the middle 50% of the income and wealth distribution. In other words, the middle classes lost out.

We then contrast the evolution of income inequality to the evolution of wealth inequality over time. Conceptually such a comparison of changes in income and wealth inequality is intricate because changes in inequality measures like the Gini coefficient are hard to compare if wealth inequality exceeds income inequality initially. We construct what we call the “inequality gradient”. The inequality gradient measures growth differences along the distribution relative to a distribution of inequality-neutral growth, i.e. a situation when all groups grow at the same rate. When we compare changes of income and wealth inequality over time, we find an asynchronous and asymmetric increase. Income inequality increased earlier than wealth inequality and more so. We find the strongest increase of income concentration between 1970 and 1990; over most of this time period, wealth concentration decreased. We find almost the mirror image during the financial crisis and its aftermath when wealth concentration strongly increased while income concentration increased only little. Exploring the joint evolution of income and wealth inequality has the potential for important new theoretical insights. The canonical consumption-savings model keeps a tight grip on their joint evolution. It is therefore an open question if and in how far the trends we discuss pose a challenge to recent attempts to model trends in wealth inequality (Kaymak and Poschke, 2016, Hubmer, Krusell and Smith, 2016). At the very least, in Kuhn, Schularick and Steins (2017a) we provide an explanation for the documented asymmetric increase of income and wealth inequality that is not present in the canonical macroeconomic models of wealth inequality. We document substantial differences in household portfolios along the wealth distribution. The middle class holds most of its assets in housing (non-diversified portfolios) with substantial mortgage debt against this housing (leveraged portfolios). We also demonstrate that diverging trends between income and wealth inequality can be traced back to particular historical episodes when house price booms hit these highly non-diversified and leveraged household portfolios and led to large and concentrated wealth gains in the middle class. These in turn mitigated the rise of wealth inequality relative to the rise in income inequality. Put differently, rising house prices slowed down the increase in wealth inequality. Our results highlight the importance of asset price changes and differences in portfolio composition to understand trends in wealth inequality.

Companion and related work

In a companion paper (Kuhn, Schularick and Steins, 2017b), we provide new evidence on the distribution of household debt and its changes over time. Household debt is rarely studied by macroeconomists but has recently received increasing attention after the financial turmoil of the Great Recession. We use the HHSCF data to explore the changes in the distribution of debt underlying the six-fold increase in household debt relative to income in the U.S. since World War II. The causes and consequences of this phenomenon are much debated across the social sciences. We show that debt-to-income ratios have risen at approximately the same rate across all income groups and that the aggregate increase in household debt is predominantly linked to the accumulation of housing debt. Middle-class and upper-middle class households mainly accounted for the massive rise in aggregate debt–and not poor households financing additional consumption in the absence of income growth, as is often assumed.

In related work with José-Víctor Ríos-Rull (Kuhn and Ríos-Rull, 2016), we provide a comprehensive description of income and wealth inequality based on U.S. SCF data that we hope will serve as reference for other researchers. We provide most results from the paper for download at In the paper, we also address a recurring topic in the discussion of the sources of wealth inequality, namely, the intergenerational transmission of wealth through bequests. It is a widely-held belief that a lot of wealth is transmitted across generations through inheritance, yet, when looking at the micro data from the SCF, we find that in 2013, 80% of wealth in the U.S. economy is not inherited but acquired over a person’s lifetime. We show that this even holds for the wealthiest households. If anything, the share of inherited wealth is decreasing towards the top of the wealth distribution. A simple sanity check of this finding can be done by looking at the richest Americans from the Forbes 500 list. In 2015, 8 out of the Top 10 wealthiest Americans did not inherit their wealth but built it within their life-time. Most of them are entrepreneurs who created wealth through inventions or new ideas that they turned into fortunes by selling shares in financial markets.

2. Sources of earnings inequality

Understanding the sources of earnings inequality is the goal of an ongoing research project with Christian Bayer (Bayer and Kuhn, 2017a). We use data from the German Structure of Earnings Survey (SES), an administrative linked employer-employee survey, which provides exceptionally detailed information on job characteristics, employers, employees, their earnings and hours. In this data, observables can explain more than 80 percent of cross-sectional wage variation. Such an amount of explained cross-sectional variation is unheard of in existing data on individual earnings. The reason for this explanatory power is not that overall earnings variation is small but it is the unique information about job characteristics that delivers this result. The data allows us to shed light on a key question in human capital theory because we can quantify how important employers, education, experience, jobs and their characteristics are in determining wages.

We decompose cross-sectional wage inequality into an individual, a plant, and a job component. Among the three, the job component explains 40% of the age difference of average wages and almost all of the rise in wage inequality by age. The hierarchy level of workers is the most important information within the job component. Hierarchy encodes responsibility and independent decision making connected with a job. It captures therefore a functional concept and not a qualification concept so that hierarchy is correlated with formal education but is inherently job specific. In fact, we show that a substantial fraction of workers is employed on all hierarchy levels for virtually any level of formal education (with the exception maybe of extreme combinations) and that workers progress along the “hierarchy ladder” as they get older. Both results clearly indicate that formal education and hierarchy measure two distinct concepts. The plant component, differences between low-paying and high-paying plants, by contrast accounts for only 20% of the age variation of wage inequality. We interpret these results as showing that the ability to take responsibilities and to work independently are skills that are highly valued in the labor market and are required to climb the “hierarchy ladder” with large returns on wages.

The information on hierarchy (job responsibility) that we bring to speak is critical for the decomposition of earnings inequality. We show that when job characteristics are ignored, plant differences appear to be more important both in explaining average wage differences by age as well as the increase of wage inequality by age. In other words, high-paying plants are high-paying because of their job composition rather than some other intrinsic characteristics of the plant. Hence, the average human capital in the plant determines its average wage level. On top comes that even fundamentally high-paying plants have a larger fraction of jobs on higher levels of hierarchy, i.e. there is a positive correlation between plant effects in pay and the job composition of a plant.

Companion and related work

In ongoing companion work with Christian Bayer, we are compiling a long-run dataset on the evolution of the German wage and employment structure. The data has information on employment and wages across hierarchy groups, different industries and employment types, and by gender. The data is compiled from archived historical tabulations of the German Statistical Office. Comparing these detailed historical tabulations to microdata from the 2001 Structure of Earnings Survey (SES), we find that the tabulated characteristics explain 2/3 of the earnings variation in the cross-section. Our data digitalization effort is still ongoing. Once our data is complete, it will cover the entire time period from 1957 until today. The data will be pivotal for exploring the transformation of the German labor market over the past six decades. We will use the data to explore if changes in the employment structure (“quantities”) or in the wage structure (“prices”) are more important in accounting for the observed increase in earnings inequality over time. A related question is explored in Song, Price, Guvenen, Bloom and von Wachter (2015). They ask if changes in the wage structure within or between firms contributed to the rise in U.S. earnings inequality over the past decades. Yet in their dataset it is not possible to observe changes in the composition of jobs that explains most of wage differences between plants in the German data.

In other related work with Christian Bayer (Bayer and Kuhn, 2017b), we exploit high-quality administrative data from social security records of the German old-age pension scheme to explore how unequally distributed labor market risks are. The data has the unique feature that it is administrative and covers entire employment histories of workers from age 14 to 65. Using this data, we document a high concentration of unemployment and sickness episodes within worker cohorts, low-pay no-pay cycles for the typical unemployed, and stable employment with very low unemployment risk for the typical employed. While unemployment risk is prominently studied as a source of earnings risk, we document that also earnings risk on the job is highly concentrated among few workers. These results scrutinize the assumption of a homogeneous risk process and suggest that besides widely-documented and widely-studied earnings inequality, there is also large “inequality in earnings risk”. We are exploring the consequences of risk heterogeneity for the design of public insurance and transfer systems as part of this project.

3. Theoretical models of earnings dynamics and the distribution of earnings

Most macroeconomic models of inequality follow the path-breaking work of Aiyagari (1994), Huggett (1993), and Imrohoroglu (1989) on heterogeneous agents incomplete markets models. These models treat income dynamics and income inequality as exogenous; a single, stochastic earnings process is the driver of all heterogeneity. Macroeconomists rely on this workhorse model to study the consequences of pension or tax reforms, financial market liberalization, or technological progress. The model assumes that labor market and earnings dynamics remain unaffected by changes in the macroeconomic environment so that income inequality constitutes a policy-invariant fundamental of the model. For policy analysis, this poses a severe limitation because changes in labor market institutions, retirement policy, tax policy, social security programs might as well affect individual labor market behavior. The third topic on my research agenda is the development of models of income dynamics that are shaped by individual behavior. Since most income comes from the labor market, my research focuses on earnings dynamics in the labor market.

In Jung and Kuhn (2016), we develop a life-cycle general equilibrium labor market model. The model is jointly consistent with facts on worker mobility and earnings dynamics documented in the literature. The model can be seen as a human capital model with general and specific human capital accumulation where “human capital production” is the result of a frictional process that is explicitly modelled via labor market behavior. This implies that the human capital accumulation technology itself is endogenous to the labor market environment. With this model, we provide a new tool to study the effects of macroeconomic changes on earnings dynamics and close a gap in the existing literature. Existing labor market models provide very little guidance to explore earnings dynamics. They generate earnings dynamics that are highly transitory so that, for example, a job loss is a rather inconsequential event. By contrast, a large empirical literature following Jacobson, LaLonde and Sullivan (1993) has shown that workers who lose their stable job experience large and persistent earnings losses. Using our structural life-cycle model, we offer an explanation for the inability of existing models to account for the empirically observed earnings dynamics. Our model builds on the observation that an upward and a downward force prevent earnings shocks to loom large in existing models. The upward force is search. Workers who fall off the job ladder can search on and off the job trying to climb back up. Search frictions prevent an immediate catch-up, but, given the large job-to-job transition rates observed in the data, search is a powerful mean-reverting mechanism. The downward force is separations at the top of the job ladder. If separation rates are high even at the top of the job ladder, then the implied short job durations will make a worker, who is still at the top of the job ladder today, look quickly similar to a worker who just lost his job. These two forces governed by labor market mobility induce mean-reversion of earnings dynamics and make earnings shocks transitory and short lived in existing labor market models. Our paper is the first to uncover this tight link between labor market mobility and earnings dynamics. Put differently, existing labor market models provide little guidance to study earnings dynamics because they stay close to the representative-agent paradigm by imposing uniform exogenous separation rates across all jobs. Any differences from search wash out quickly in such models and all workers remain close to the average worker.

A further innovation of the paper is that we use information on worker mobility dynamics rather than wage dynamics to estimate the parameters of the skill accumulation process. Our model describes rich endogenous mobility dynamics over the life-cycle and in the cross-section conditional on age. Exploiting this variation, we develop a new approach based on ideas similar to Topel (1991) to estimate the skill accumulation process based on mobility differences of workers by age and job tenure.

We use the model to provide an explicit example of an investigation of changes in the labor market environment on earnings dynamics. We study the Dislocated Worker Program (DWP) and its effectiveness to mitigate earnings losses of displaced workers. We explore retraining and placement support as the two central pillars of the DWP. We find that the two policies are ineffective in reducing earnings losses. We explain this finding based on the insights from our structural analysis. Active labor market policy might help to remove frictions and foster mean reversion by making displaced worker look more quickly like the average worker but there will remain the gap between the pre-displacement job at the top of the job ladder and the average job in the labor market.

Empirically, we provide new evidence on heterogeneity in job stability for the United States. Going back at least to Hall (1982), there exists evidence that despite high average worker mobility rates there is also a large share of very stable jobs. We document that mean and median tenure increase almost linearly with age, so that at age 60 the average U.S. worker has been with her/his employer for 14 years. Our life-cycle model captures this heterogeneity in job stability. Abstracting from such heterogeneity limits what labor market outcomes can be explored because it severely distorts the decision to invest in human capital and the returns from search on and off the job. We argue that a life-cycle structure is the natural setup to deal with the inherent non-stationarity of job stability, the rising tenure with age. While life-cycle models are by now a standard tool in the macroeconomic literature to study topics on wealth inequality, our model highlights the importance of life-cycle variation for the study of topics on earnings dynamics and inequality.

Related work

In related work (Hartung, Jung and Kuhn, 2017), we investigate the effects of policy reforms on labor market dynamics. We study the unprecedented overhaul of the German unemployment benefit system as part of the so-called “Hartz reforms” in the mid-2000s. Most scholars attribute the German labor market miracle after the Hartz reforms to the cut in UI benefits based on a mechanism by which the cut in benefits incentivized the (long-term) unemployed to search harder for jobs. We provide new evidence that challenges this narrative. We document based on micro data from the employment panel of integrated employment histories (SIAB) that the bulk of the decline in unemployment rates is due to a change in inflow rates into unemployment. The Hartz reforms have mainly operated by scaring employed workers to separate into unemployment, not by prompting unemployed workers to search harder. Our analysis focuses therefore on the effects of labor market institutions on job stability. Job stability is, as I discussed above, a critical determinant of earnings dynamics. We show that a search model with endogenous separations and heterogeneity in job stability can quantitatively explain the German experience. The highlighted channel implies a large (macro)-elasticity of unemployment rates with respect to benefit changes. Our findings thereby add a new aspect to the current debate on the role of UI benefits on unemployment rates by highlighting the effects on job stability and unemployment inflows. A mechanism that we argue is particularly relevant in the European context.

In related work with Tom Krebs and Mark Wright (Krebs, Kuhn and Wright, 2017), we explore a consumption-saving model with human capital accumulation but without frictions in the human capital accumulation technology. The friction we focus on in this paper is limited enforcement of financial contracts. Households have access to a complete set of credit and insurance contracts, but their ability to use the available financial instruments is limited by the possibility of default (limited contract enforcement). We demonstrate that the model calibrated to the U.S. yields substantial under-insurance of consumption against human capital risk. In Krebs, Kuhn, and Wright (2015), we show that the degree of under-insurance in the model is quantitatively consistent with under-insurance in the U.S. life-insurance market. Key to generate this result are age-dependent human capital returns. High returns at the beginning of working life lead to high human capital investment of young households that are traded off against a lack of insurance against shocks. We find that the welfare losses due to the lack of insurance are substantial. We explore how changes in the macroeconomic environment affect life-cycle earnings dynamics via human capital investment and the resulting consequences for inequality.

4. Future work

My ongoing work will already provide important answers to the key questions of my research agenda. A lot of work still lies ahead. Some of the next steps emerge already clearly. The obvious next step is to embed a version of the described labor market model in a consumption-saving framework. Such a model will provide the framework to study the joint determination of the income and wealth distribution. Ongoing work is at early stages. A second step is to explore how well existing models of wealth inequality match the joint distribution of income and wealth. Preliminary results suggest that existing models face difficulties. We are exploring in ongoing work if incorporating closer links between the current labor market situation and financial decisions helps in bringing model and data closer together.


Aiyagari, S. R. (1994). Uninsured idiosyncratic risk and aggregate saving. The Quarterly Journal of Economics vol. 109(3), pages 659-684.

Bayer, C., and Kuhn, M. (2017a). Unequal lives: Heterogeneity in Unemployment, Health, and Wage Risk. Mimeo, University of Bonn.

Bayer, C., and Kuhn, M. (2017b). Which ladder to climb? Evidence on wages of workers, jobs, and plants. Mimeo, University of Bonn.

Hall, R. E. (1982). The importance of lifetime jobs in the US economy. The American Economic Review vol. 72(4), pages 716-724.

Hartung, B., Jung, P., and Kuhn, M. (2017). What hides behind the German labor market miracle? A macroeconomic analysis. Working paper, University of Bonn.

Hubmer, J., Krusell, P., and Smith Jr., A. A. (2016). The historical evolution of the wealth distribution: A quantitative-theoretic investigation. Working paper 23011, NBER.

Huggett, M. (1993). The risk-free rate in heterogeneous-agent incomplete-insurance economies. Journal of economic Dynamics and Control vol. 17(5), pages 953-969.

Imrohoroglu, A. (1989). Cost of business cycles with indivisibilities and liquidity constraints. Journal of Political Economy vol. 97(6), pages 1364-1383.

Jacobson, L. S., LaLonde, R. J., and Sullivan, D. G. (1993). Earnings losses of displaced workers. The American Economic Review vol. 83(4), pages 685-709.

Jung, P., and Kuhn, M. (2016). Earnings losses and labor mobility over the life-cycle. CEPR discussion paper 11572.

Kaymak, B., and Poschke, M. (2016). The evolution of wealth inequality over half a century: the role of taxes, transfers and technology. Journal of Monetary Economics vol. 77, pages 1-25.

Krebs, T., Kuhn, M., and Wright, M. L. (2015). Human capital risk, contract enforcement, and the macroeconomy. The American Economic Review vol. 105(11), pages 3223-3272.

Krebs, T., Kuhn, M., and Wright, M. L. (2017). Insurance in human capital models with limited enforcement. Review of Economic Dynamics vol. 25.

Kuhn, M., and Ríos-Rull, J.-V. (2016). 2013 update on the U.S. earnings, income, and wealth distributional facts: A view from macroeconomic modelers. Federal Reserve Bank of Minneapolis Quarterly Review vol. 37(1).

Kuhn, M., Schularick, M., and Steins, U. I. (2017a). Wealth and income inequality in America, 1949-2013. Mimeo, University of Bonn.

Kuhn, M., Schularick, M., and Steins, U. I. (2017b). The American debt boom, 1948-2013. Mimeo, University of Bonn.

Piketty, T. (2014). Capital in the Twenty-First Century. Belknap Press.

Piketty, T., and Saez, E. (2003). Income inequality in the United States, 1913-1998. The Quarterly Journal of Economics vol. 118(1), pages 1-41.

Saez, E., and Zucman, G. (2016). Wealth inequality in the United States since 1913: Evidence from capitalized income tax data. The Quarterly Journal of Economics vol. 131(2), pages 519-578.

Song, J., Price, D. J., Guvenen, F., Bloom, N., and Von Wachter, T. (2015). Firming up inequality. NBER working paper 21199.

Topel, R. (1991). Specific capital, mobility, and wages: Wages rise with job seniority. The Journal of Political Economy vol. 99(1), pages 145-176.

Mikhail Golosov and Aleh Tsyvinski on New Dynamic Public Finance

Mikhail Golosov is Professor of Economics at Princeton University. His research interests lie in the impact of taxation and optimal dynamic contracts. Aleh Tsyvinski is Arthur M. Okun Professor of Economics at Yale University. He is interested in optimal fiscal policy and the role of governement. Golosov’s RePEc/IDEAS profile and Tsyvinski’s RePEc/IDEAS profile.


One of the central questions in macroeconomics and public finance is how to design taxation and social insurance policy. Debates about how progressive taxes should be, how to reform the Social Security system, or how generous welfare programs should be, are consistently on the front pages of newspapers and at the top of policy agendas. The New Dynamic Public Finance (NDPF) is an approach to the design of optimal taxation and social insurance programs that lies on the intersection of macroeconomics and public economics, contributes to the theoretical understanding of how policy should be conducted, and provides practical recommendations that can be used by policymakers around the world.

Traditional approaches to optimal policy

We start with a short description of the NDPF approach and the main results derived with it. We will also contrast this approach with a Ramsey approach widely used in the macroeconomic literature and in policymaking.

The Ramsey approach studies the problem of funding a stream of government expenditures through taxation, operating under the assumption that only distortionary linear or proportional taxes can be used (see Chari and Kehoe 1999 for a comprehensive review). The main goal of the government is to minimize social distortions arising because of the assumed nature of taxes. If, instead, lump-sum taxes were allowed, then the unconstrained first-best optimum could be achieved. While Ramsey models have provided several insights into optimal policy (zero capital taxation result, tax smoothing, time inconsistency of taxation), their well-understood limitation regarding the ad hoc nature of tax instruments may make interpreting their prescriptions problematic. Moreover, the focus of Ramsey approach on funding government expenditures makes it less suitable for analyzing the important roles taxes and transfers play in a modern economy — provision of redistribution and social insurance.

The Mirrlees approach (pioneered by Mirrlees 1971) moves the question of social insurance and redistribution to the front of analysis. The starting point is that people in the economy differ in their income generating abilities or, more generally, face risks. These abilities may be I.Q., physical stamina, or health — we generally refer to these abilities as skills. Society would like to provide insurance for the people who are less advantaged than others by providing redistribution from the more fortunate ones. The problem with provision of such redistribution or insurance is that, if income generating abilities are private information, agents may pretend to be those to whom redistribution is directed. For example, a progressive income tax designed to redistribute to those who are poor because of low income generating ability would create a disincentive for agents with high skills to work as hard. Therefore, the optimal taxation or insurance program must balance the desire to redistribute with the provision of incentives.

The New Dynamic Public Finance

The New Dynamic Public Finance is a recent literature that analyzes the Mirrlees framework in dynamic settings. Many taxes, such as a capital tax or social insurance programs like Social Security in the U.S., feature incentive-insurance tradeoffs that are dynamic, or intertemporal. These dynamic tradeoffs are the focus of the NDPF. Specifically,: (1) NDPF focuses on social insurance and redistribution, an important goal of policymaking; (2) NDPF policy predictions do not rely on the ad hoc restriction of the taxes but on the fundamental tradeoffs between insurance and incentives; (3) The NDPF allows for a richer set of optimal tax instruments and social insurance benefits such as the ones used in practice (progressive taxes, means tested social insurance programs, etc).

In Golosov, Kocherlakota and Tsyvinski (GKT, 2003) we re-examine the two central conclusions of taxation literature, that capital should not be taxed, and consumption goods should be taxed uniformly, using dynamic model with a general process of private information. Each individual is subject to potentially serially correlated labor income shocks and wishes to obtain insurance against adverse realizations of these shocks. We establish a very general result that, if the evolution of skills is stochastic, the celebrated uniform commodity taxation theorem of public finance continues to hold, but the zero capital income taxation theorem does not necessarily apply. Because of the dynamic nature of the incentives that agents need to be provided with, incentive compatibility requires a wedge relative to the decentralized consumption plans and this translates into a positive implicit tax on capital.

The theoretical results in GKT not only answer some important questions, but also raise a number of issues. First, one would like to know how important these taxes might be in realistic social insurance problems. Second, it is necessary to consider methods of implementing these optimal policies in a simple manner. We address this question in Golosov and Tsyvinki (2006) by studying the problem of optimal disability insurance. We show that we can use the new methods developed in GKT and combine them with the data to answer questions about the design of optimal disability insurance. This is a relevant problem both because it provides a simple and tractable example of the general set up in GKT and also because disability insurance is one of the most important social programs, providing insurance against a very important and life-changing event. The disability insurance is one of the largest social insurance programs in the United States, considerably larger than, for example, unemployment insurance. We provide a simple decentralization scheme for implementing the optimal disability insurance policy. Our proposed implementation scheme involves an asset test in which a person receives a disability payment only if his assets are below a certain level. Many social programs use such asset tests, even though they are not currently used in Social Security Disability Insurance. We use the available data to show that the introduction an asset test would provide significant benefit to the economy.

We build on these results in Golosov and Tsyvinski (2007) to investigate the theoretically more challenging question of whether there is a role for the government in designing social insurance programs when individuals can also engage in private insurance using competitive markets. In dynamic optimal taxation environments with informational frictions it is often assumed that a government is the sole provider of insurance. However, in many circumstances, private insurance companies can and do provide insurance against various shocks, ranging from unemployment to health shocks and bankruptcy. The presence of competitive insurance markets may significantly change optimal policy prescriptions regarding the desirability and extent of social insurance policies. In this paper we allow a rich set of competitive insurance markets, the structure of which is endogenously affected by informational constraints and by government policy. This latter feature is particularly important, since it emphasizes that government and private provision of insurance are coupled and need to be studied together. We show that while the markets can provide a significant amount of insurance, there is still a role for welfare improving distortionary taxes or subsidies imposed by the government. The reason for this is that private insurance companies cannot fully internalize pecuniary externalities that arise from the dynamic nature of the incentive problems that they are facing.

Path forward: from theory to policy

This research agenda has now reached a stage at which it is able to analyze the design of social insurance programs and optimal taxation in rich environments that can be closely matched to microeconomic data.

In Golosov, Troshkin, and Tsyvinski (2016) we study a rich lifecycle economy with individuals who are ex ante heterogeneous in their abilities and experience idiosyncratic shocks to their skills over time.

We first derive a novel decomposition that allows us to isolate key economic forces determining the optimal labor distortions in lifecycle economies with unobservable idiosyncratic shocks and to provide their characterization. We show that the labor distortion in a given period is driven by two components: an intratemporal component that provides insurance against new shocks in that period, and an intertemporal component that relaxes incentive constraints and reduces the costs of insurance provision against shocks in the previous periods. The intratemporal component depends on the elasticity of labor supply, the hazard rate of the current period shock conditional on past information, and the welfare gain from providing insurance against that shock. The intertemporal component depends on past distortions, a specific form of a likelihood ratio of the shock realization, and the marginal utility of consumption.

This decomposition then implies that the behavior of the optimal distortion is quite different for the top and the bottom of the income distribution. The labor distortions for high-productivity shocks are determined by the labor elasticity and the higher moments of the shock process. The labor distortions for low shocks depend on the persistence, the past history, and the growth rate of consumption, and are generally increasing in age.

We then use newly available high-quality administrative data on labor earnings (see Guvenen, Ozkan and Song (2014) and Guvenen et al. (2015)) and the U.S. tax code to estimate the stochastic process for skills and quantify the implications for the optimal distortions. Similar to the earnings, the process for the shocks is highly persistent and leptokurtic. We find that the optimal labor distortions are approximately U-shaped as a function of current labor earnings, with the dip in the distortions around the level of earnings in the previous period. The optimal savings distortions generally increase in labor earnings. The distortions are fairly large in magnitude, especially in the right tail: the labor distortions approach 75 percent, while savings distortions approach 2 percent of return to savings. We also show that the welfare losses from using simple affine policies instead of the optimal policy are around 2 to 4 percent of consumption. Moreover, the optimal labor distortions differ significantly from those in a model with the lognormal shocks, both qualitatively and quantitatively, and imply higher welfare gains from non-linear, history-dependent policies. These findings (both the U-shaped and the relatively high welfare gains from nonlinear, history-dependent taxation) are largely driven by the high kurtosis found in the labor earnings process in the data. This suggests that a system of progressive taxes and history-dependent transfers that are being phased out relatively quickly with income can capture most of the welfare gains in this economy.

The discussion above shows that it is challenging to develop a theory of taxation that both allows for sufficiently rich tax functions and provides transparent, intuitive insights about the effect of taxes. In Golosov, Tsyvinski, and Werquin (2016) we develop an alternative variational approach to the analysis of the effects of taxation that both preserves the transparency of the Ramsey approach and allows us to handle more complicated, nonlinear tax systems. Instead of solving for a constrained optimal problem and then backing out the implied optimal taxes that decentralize the optimum, we develop a method to optimize with respect to the tax function directly. This method builds on the perturbation ideas that Piketty (1997) and Saez (2001) apply to a static economy. Our paper finds sufficient conditions for the more rigorous application of that approach and extends it to more general dynamic settings. First, we apply it to optimal taxation problems and show how it recovers the hallmark results on optimal linear commodity taxation of Diamond (1975) and non-linear labor taxation of static model of Mirrlees (1971), both of which are special cases of our general environment. Our formulas emphasize the insight that the same general principle underlies the two models, namely that more sophisticated (in this case, non-linear) tax instruments allow the government to better target the distortions associated with higher tax rates toward the segments of the populations that have either relatively small behavioral responses, or where relatively few individuals are affected. We then show that this fundamental principle can be generalized and applies to broader classes of environments. In particular, we derive several novel predictions such as the optimality conditions for the optimal non-linear capital income tax, or for the optimal labor tax on joint income of couples.

We also show how this approach can be used beyond optimal taxation, as we apply it to analyze tax reforms and welfare gains from increased sophistication of tax systems. We sequentially decompose the welfare gains of reforming existing, not necessarily optimal, tax systems as the tax instruments become more sophisticated. We show the effects of taking into account individuals’ intertemporal optimization decisions, of allowing for age- and history-dependence, and of joint conditioning of labor and capital income. This sequential decomposition of increasingly sophisticated tax systems shows that the welfare effects of general tax reforms depend on aggregate measures of three key elements: the government’s redistributive objective; the labor and capital income elasticities and income effect parameters with respect to the marginal income tax rates, which capture the behavioral effects of taxes; and the properties of the labor and capital income distributions, namely the hazard rates of the marginal and joint distributions. Finally, we show how one can use available empirical moments of income distributions and elasticities to quantify the welfare effects of small tax reforms. Unlike the traditional approach to measuring welfare gains, which requires solving often difficult maximization problems to find the optimum, our method is very transparent and can be done almost -Y΄by hand‘.

More broadly, the variational approach that studies the effects of the tax reforms is complementary to the New Dynamic Public Finance literature studies environments in which taxes are restricted only by explicit restrictions on government’s information set. If we restrict attention to the classes of taxes considered in the NDPF literature, we obtain an alternative characterization of optimality conditions in terms of elasticities. More generally, it is easy to use our approach to analyze the tax systems using restricted tax instruments, e.g., non-linear but separable from labor income taxes, and quantify welfare gains from switching to more sophisticated taxes, e.g. gains from introducing joint taxation of capital and labor.


The dynamic public finance literature achieved significant progress in a relatively short period of time. What started as an abstract optimal dynamic contracting framework now has become an active research agenda that delivers theoretical, quantitative, and empirical results that are increasingly relevant to policy. In our opinion, there are three primary directions in which the literature may move. First, most of the empirically and policy relevant problems still require major theoretical and quantitative effort to be analyzed. Progress in developing new tools is needed to ease the analytical burden and to lower the barriers to entry for more applied researchers. Second, in many cases, the problem of implementation with simple tax systems is as laborious (and hence interesting) as the problem of finding the optimum. We have discussed one alternative — a variational approach that starts with the tax system and changes it directly and hence does not need to separately consider the policy and implementation problems. Progress in developing a simple yet general tax implementation of the optimum in a variety of settings and connection to the variational approach is important. Third, a large number of more applied public finance and macroeconomic questions can be addressed with this framework — from the design of specific taxes or elements of the tax code to a variety of social insurance and redistribution programs.


V. V. Chari and Patrick Kehoe. 1999. “Optimal Fiscal and Monetary Policy,” in: John Taylor and Michael Woodford (editors), Handbook of Macroeconomics, vol. 1, ch. 26, pages 1671-1745.

Peter Diamond, 1975. “A Many-Person Ramsey Tax Rule,” Journal of Public Economics, vol. 4(4), pages 335-342.

Mikhail Golosov, Narayana Kocherlakota, and Aleh Tsyvinski, 2003. “Optimal Indirect and Capital Taxation,” Review of Economic Studies, vol. 70(3), pages 569-587.

Mikhail Golosov and Aleh Tsyvinski, 2006. “Designing Optimal Disability Insurance: A Case for Asset Testing,” Journal of Political Economy, vol. 114(2), pages 257-279.

Mikhail Golosov and Aleh Tsyvinsk, 2007. “Optimal taxation with endogenous insurance markets,” Quarterly Journal of Economics, vol. 122(2), pages 487-534.

Mikhail Golosov, Maxim Troshkin, and Aleh Tsyvinski, 2016. “Redistribution and social insurance,” American Economic Review, vol. 106(2), pages 359-386.

Mikhail Golosov, Aleh Tsyvinski, and Nicolas Werquin, 2016. “A variational approach to the analysis of tax systems,” Update of NBER Working Paper No. 20780.

Fatih Guvenen, Serdar Ozkan, and Jae Song, 2014. “The nature of countercyclical income risk,” Journal of Political Economy, vol. 122(3), pages 621-660.

Fatih Guvenen, Jae Song, Serdar Ozkan, and Fatih Karahan, 2015. “What do data on millions of US workers reveal about life-cycle earnings risk?” NBER Working Paper No. 20913.

James Mirrlees, 1971. “An Exploration in the Theory of Optimum Income Taxation,” Review of Economic Studies, vol. 38(2), pages 175-208.

Thomas Piketty, 1997. “La redistribution fiscale face au chômage,” Revue française d’économie, vol. 12(1), pages 157-201.

Emmanuel Saez, 2001. “Using Elasticities to Derive Optimal Income Tax Rates,” Review of Economic Studies, vol. 68(1), pages 205-229.

Jeremy Lise on Heterogeneity and dynamics in the labor market and within the household.

Jeremy Lise is currently Reader at University College London. He will be joining the University of Minnesota as Associate Professor in the Fall of 2016. His research interests lie in understanding labor markets and intra-household allocation. Lise’s RePEc/IDEAS profile.

I would like to take this opportunity to discuss some of the questions I am currently interested in and working on.

  1. What is the structure underlying the complex patterns we observe in earnings data? What is the relative importance of ability, effort, luck and frictions in explaining variation in labor market outcomes?
  2. Do frictions in labor markets affect low- and high-skilled labor differently?
  3. How is the allocation of heterogeneous workers to heterogeneous jobs affected by aggregate shocks?
  4. To what extent do cognitive, manual and interpersonal skills have differing returns in the labor market? How do these skills differ in the extent to which they can be learned on the job?
  5. What can economic theory tell us about how resources are shared within households? How might this change over the duration of a marriage? What light does the data shed on this?

My current work draws together and builds on developments in several branches of the literature: equilibrium labor search, matching and sorting; consumption and savings; estimating earnings processes; intra-household allocations; and equilibrium policy evaluation. These areas of the literature draw on a variety of complex data sets, including large-scale panel data, complex survey data, matched employer-employee data based on administrative records, and data generated by randomized control trials to understand various aspects of labor market and households dynamics. Economic theory provides a framework for how to approach measuring, aggregating and interpreting the data. My research combines the development of new theory or modeling approaches, detailed work with micro data, and the application of state of the art empirical methods.

1. Worker heterogeneity, uncertainty and labor market outcomes

In the labor market, we observe large cross-sectional differences across workers in terms of wages and employment rates, even after we condition on a large set of observable characteristics including measures of human capital such as education and experience. Much of this difference is likely due to remaining unmeasured differences in ability across workers. As such, unobserved heterogeneity will play a key role in any research that seeks to understand differences in outcomes. However, these fixed differences across individuals are not sufficient to explain several robust features of the age profile of dispersion in wages and consumption for a cohort of individuals: First, the variance of log wages (or earnings) increases approximately linearly with age for a cohort. Second, the variance of log consumption shows a similar linear increase, although the level and slope are less than for wages.

The observed pattern for wages is consistent with both the accumulation of permanent shocks to human capital as well as heterogeneity across workers in the slope of human capital accumulation. The pattern for consumption strongly suggests that individuals face substantial uncertainty during their working lives (either shocks to human capital or persistent uncertainty about their own human capital). Understanding the sources of this uncertainty is a major goal of my research.

Separating heterogeneity from uncertainty is difficult. It requires using jointly data that reflects shocks and data that reflects choices, combined with an economic model that provides a theoretical link. In Lise (2013) I developed a model of endogenous job search and savings to provide a link between the observed process of job mobility and job loss and consumption/savings decisions. The process of choosing to search for and move to better jobs, combined with the risk of job loss that resets this process, produces a wage process with strong asymmetries. Workers expect regular and moderate positive changes to wages as they move to better opportunities, while the down side risk (wage loss) becomes increasing large the higher up the job ladder. This asymmetry implies optimal savings behavior that produces substantial dispersion in assets and consumption, even across identical workers. The risk of falling off the job ladder when near the top gives workers a strong precautionary incentive to save.

Recently Arellano et al. (2015) and Guvenen et al. (2015) highlight a striking feature of earnings changes in the US data: most year-over-year changes are small, and the large changes are more often negative than positive (i.e. wage changes exhibit negative skewness and excess kurtosis), and this becomes increasingly true if you condition on higher and higher levels of previous earnings. Both sets of authors cite the model features of Lise (2013) as potentially useful to understanding this pattern and the consumption/savings behavior it would induce.

This anticipates my current work with Michael Graber (Graber and Lise, 2015) where we jointly model a stochastic process for human capital accumulation, job search and consumption/savings choices. The model incorporates heterogeneity across workers in fixed productivity, heterogeneity across workers in their ability to acquire human capital on the job, jobs that differ in terms of both productivity and how they facilitate human capital acquisition, and shocks to human capital as well as differences in the random opportunities to move to better jobs and job destruction shocks associated with the job ladder. While still very preliminary, our current results suggest that that pre-labor market differences across workers account for almost the entire initial cross-sectional dispersion; shocks to human capital account for almost the entire rise in wage and consumption variances; and the job ladder accounts for the entire profile of conditional skewness and kurtosis of wage changes. We find that the combination of permanent heterogeneity, stochastic human capital accumulation, and the job ladder are necessary ingredients in the model to jointly account for these patterns in the data.

2. Frictions and sorting in the labor market

An additional mechanism that has the potential to produce a rising variance of wages as a cohort of workers gains experience comes from the dynamic process of sorting of workers to jobs. To the extent that there are important complementarities in production between the skills of workers and the technology of firms, aggregate output is maximized under positive assortative matching (Becker 1973). Positive assortative matching also maximizes dispersion in wages across workers. If it takes time for the market to attain the fully assortative allocation (either because time and real resources must be devoted to the process or because individuals in the market have to learn about their best match) a cohort of workers may start out mismatched and only gradually become perfectly sorted. As a result, the variance of wages for this cohort will be low at the beginning when there is not much sorting and rise continuously until the variance is maximized with complete sorting.

In a recent paper with Costas Meghir and Jean-Marc Robin (Lise, Meghir and Robin, 2016 RED special issue in honor of Dale Mortensen) we analyze the wage and labor market outcomes for high school and college educated cohorts in the NLSY79 through the lens of a frictional sorting model. We find very different implications by education. We estimate that for the low-skilled workers skill and technology are essentially substitutes. Frictions are substantial and the decentralized allocation of workers to jobs is close to random, but this does not lead to a loss in output, as there are no complementarities in production. In contrast, we find substantial complementarities between skill and technology for the college educated; for this group positive sorting results in higher aggregate output. Here we find substantial positive sorting and the decentralized allocation is close to second best (a constrained social planner could only attain a very minor improvement) largely due to the speed of worker reallocation.

In Lise et al. (2016) we use the dynamic implications of sorting as a cohort ages to estimate our model using panel data on workers only. There has been continuous improvement as of late in the availability and usability of matched employer-employee data (constructed from administrative files) that will be particularly informative in furthering our understanding of the allocation of workers to jobs and sorting in the labor market. My current work with Thibaut Lamadon, Costas Meghir and Jean-Marc Robin (Lamadon et. al. 2015) provides an identification proof and develops an estimator to uncover the match specific production function using such matched employer-employee. A key contribution of this research is that we show that the model equilibrium and the implied wage and mobility dynamics are essential for identifying and interpreting any parameter estimates. This contrasts starkly with the widely adopted statistical approach (two sided fixed effects) which, while providing a convenient description of the data, requires identifying assumptions on mobility which are known to be inconsistent with most models of labor market mobility. This project relates closely to work that has been described in this Newsletter by Rasmus Lentz (2009), Jan Eeckhout and Philipp Kircher (2011), and Marcus Hagedorn and Iourii Manovskii (2014).

For a complete understanding of the interaction of heterogeneous workers and firms it is desirable to move beyond a scalar measure of skill. In current work with Fabien Postel-Vinay (Lise and Postel-Vinay, 2016) we develop and estimate a model in which jobs are defined by a vector of skill requirements and workers by a vector of human capital.  In particular we think of jobs (or occupations) as requiring various amount of cognitive, manual and interpersonal skills, and workers differing in the amount of these skills they currently possess. Our estimates indicate that the market treats these skills very differently. Cognitive skills have high returns and are difficult for workers to acquire on the job.  Manual skills have much lower returns, but are easily picked up on the job.  Interpersonal skills have moderate returns, and are approximately fixed over a worker’s lifetime.  We learn about the degree to which these skills can be acquired on the job by looking at workers who have the same measured skills at labor market entry, but start in different jobs that use these skills with differential intensity.  The extent to which these initial jobs differentially affect the types of jobs these workers do 5, 10 or 15 years later is informative about the extent to which skills can be adjusted as a function of the history of jobs the worker has had.

Accommodating correlated shocks in frictional labor market models with two-sided heterogeneity (either across industries, regions, or at the aggregate level) was generally thought to be intractable since the state space would then contain time varying distributions. This has limited the types of questions that researchers could address since it was necessary to assume a stationary environment from the start. Recently Guido Menzio and Shouyong Shi (2010a,b, 2011) showed that assuming that search is directed rather than random results in a block-recursive equilibrium that removes the distributions from the state space. It turns out that a related result can be proved for a class of random search models. In a recent project with Jean-Marc Robin (Lise and Robin, 2016) we develop an equilibrium model of random on-the-job search with ex-ante heterogeneous workers and firms, aggregate shocks and vacancy creation. The model produces rich dynamics in which the distributions of unemployed workers, vacancies and worker-firm matches evolve stochastically over time. We prove that the match surplus function, which fully characterizes the match value and the mobility decision of workers, does not depend on these distributions. This result means the model is tractable and can be estimated. We illustrate the quantitative implications of the model by fitting to US aggregate labor market data from 1951-2012. The model has rich implications for the cyclical dynamics of the distribution of skills of the unemployed, the distribution of types of vacancies posted, and sorting between heterogeneous workers and firms.

There are four key modeling assumptions that lead to the result. 1) Match formation and destruction are efficient, 2) utility is transferable, 3) the value of a vacancy is zero, and 4) firms make state contingent offers and counter offers to workers. The first three assumptions are standard. They simply mean that the worker and firm agree that the value of the match is the expected present discounted sum of output they can produce, and they should form a match (and remain matched) only if this exceeds the value of home production. The last assumption is exactly the wage determination process proposed by Postel-Vinay and Robin (2002). Firms make take-it-or-leave-it offers when hiring unemployed workers and engage in Bertrand competition with the other firm when hiring employed workers. The implication is that workers are always hired at their reservation value, which is equal to the value of remaining unemployed for those hired from unemployment and equal to the total match value with their current firm for those who are poached. A direct implication of this is that the value a worker receives when changing jobs does not depend on the type of firm she moves to. Bertrand competition between the poaching and incumbent firm always results in the worker receiving the total value of the match she leaves, independent of the match she goes to. When the worker leaves to another job the firm is left with a vacancy of zero value. Thus, the value to the current worker-firm pair is the same whether the worker stays and produces or leaves.

At parameters chosen to match aggregate time series for the US, the model implies that in booms a wider variety of vacancies are posted, unemployed workers find jobs more quickly (although they tend to be further from their ideal job on average), and workers receive alternative offers at an increased rate, reallocating quickly in the direction of jobs most suitable to their abilities. In contrast, in recessions unemployed workers find jobs more slowly (although they tend to be better matched for the jobs they do accept), employed workers receive offers less frequently and hence move more slowly toward their ideal job. As a result, workers tend to be more mismatched when transiting from unemployment in a boom, but quickly become well matched though on-the-job search. In recessions they are better matched when transiting from unemployment, but mismatched workers remain so longer due to fewer job-to-job transitions.

The model we developed in Lise and Robin (2016) works off comparing values. For the purposes of analyzing the dynamics of allocations it is not necessary to make any additional assumptions about the wage process used to deliver the value to the worker. This has the advantage of being robust to the particular wage determination one might assume, but has the disadvantage of not providing a mapping between model parameters and observed wages. Our current work in progress provides this mapping. With a little bit of additional structure on how wages relate to values we derive explicit expressions for the dynamics of the joint distribution of wages over worker-firm-type matches. The next step is to use this mapping, along with matched employer-employee data, to directly identify and estimate the underlying primitive heterogeneity across workers and firms, the match production function, and the structure that generates the observed cyclical patterns in the distribution of wages at the match level.

3. Intra-household allocations

In the models of the labor market described above, a worker-firm pair is the key unit of analysis. The skills of workers and the technologies of firms combine to produce output and local competition determines the transfers from firms to workers. Similarly in the marriage market, the productivity and preferences of women and men combine to produce marital surplus, and outside options allocate that surplus between spouses. In parallel to my work on the labor market, I have also been interested in better understanding the determinants of time and expenditure allocations within households (Lise and Seitz, 2011). In recent work with Ken Yamada (Lise and Yamada, 2015) we use particularly rich panel data from Japan that provides measures of the consumption expenditures allocated to household public consumption as well as the private consumption expenditures for each individual household member. Additionally, the data provides measures for time allocated by each household member to the market, home production and leisure. The fact that the data provides a complete description of allocations across individuals within the household and has repeated observations over time on the same households allows us to directly estimate and test between dynamic models of intra-household allocation. We find that information relating to relative differences between spouses in the level and growth rates of wages, which is known or predictable at the time of marriage, is strongly predictive of relative consumption and leisure allocations across households in the cross-section. Additionally, we find that new information about wages revealed during marriage predicts changes in within-household allocations in ways that are inconsistent with efficiency in the absence of renegotiation. The data strongly reject the hypothesis that households fully commit to state contingent allocations at the time of marriage. The results are consistent with a model of limited commitment in which new information about either partners’ market opportunities may require a renegotiation to prevent one of the spouses from being better off single. We are currently exploring further tests between models such as asymmetric information or complete lack of commitment (period by period renegotiation).

Our current agenda, which is in early stages, involves developing and estimating a dynamic model of household interaction with endogenous human capital and durable public goods (children). Clearly children are one of the key reasons for household formation. The tradeoff between time used in market production and time used investing in children’s development has complicated dynamic considerations when spouses cannot fully commit. Time spent with children will in general raise the value of the public good and hence the marital surplus; on the other hand, time spent away from the market may deteriorate a spouse’s human capital, and possibly their bargaining position. Given the importance of human capital formation, an open question is the extent to which households are able to attain the efficient level of investment in children.


Arellano, M., R. Blundell, and S. Bonhomme (2015): “Earnings and consumption dynamics: a nonlinear panel data framework.” Working paper, CeMMAP.

Becker, G. S. (1973): “A Theory of Marriage: Part I.” Journal of Political Economy, 81(4), 813-846.

Eeckhout, J. and P. Kircher (2011): “Sorting in Macroeconomic Models.” EconomicDynamics Newsletter, 13(1).

Graber, M. and J. Lise (2015): “Labor Market Frictions, Human Capital Accumulation, and Consumption Inequality.” Manuscript.

Guvenen, F., F. Karahan, S. Ozkan, and J. Song (2015): “What Do Data on Millions of U.S. Workers Reveal about Life-Cycle Earnings Risk?” Working paper, NBER.

Hagedorn, M. and I. Manovskii (2014): “Theory Ahead of Identification.” EconomicDynamics Newsletter, 15(1).

Lamadon, T., J. Lise, C. Meghir and J.-M. Robin (2015): “Matching, Sorting, Firm Output and Wages”. Manuscript.

Lentz, R. (2009): “Heterogeneity in the Labor Market.” EconomicDynamics Newsletter, 11(1).

Lise, J. (2013): “On-the-Job Search and Precautionary Savings.” Review of Economic Studies, 80(3): 1086-1113.

Lise, J., C. Meghir and J.-M. Robin (2016): “Matching, Sorting and Wages.” Review of Economic Dynamics, 19(1): 63-87. Special Issue in Honor of Dale Mortensen.

Lise, J. and F. Postel-Vinay (2015): “Multidimensional Skills, Sorting, and Human Capital Accumulation.” Manuscript.

Lise, J. and J.-M. Robin (2016): “The Macro-dynamics of Sorting between Workers and Firms.” Manuscript.

Lise, J. and S. Seitz (2011): “Consumption Inequality and Intra-Household Allocations.” Review of Economic Studies, 78(1): 328-355.

Lise, J. and K. Yamada (2015): “Household Sharing and Commitment: Evidence from Panel Data on Individual Expenditures and Time Use.” Manuscript.

Menzio, G. and S. Shi (2010a): “Block recursive equilibria for stochastic models of search on the job.” Journal of Economic Theory 145(4), 1453-1494.

Menzio, G. and S. Shi (2010b): “Directed search on the job, heterogeneity, and aggregate fluctuations.” American Economic Review: Papers and Proceedings 100(2), 327-32.

Menzio, G. and S. Shi (2011). “Efficient search on the job and the business cycle.” Journal of Political Economy 119(3), 468-510.

Postel-Vinay, F. and J. Robin (2002). “Equilibrium wage dispersion with worker and employer heterogeneity.” Econometrica 70(6), 2295-2350.

The changing nature of business cycles

Nir Jaimovich is Professor of Finance and Business Economics at the Marshall Business School at USC. He is an applied macroeconomics whose research interests are at the intersection of macroeconomics and labor economics. Jaimovich’s RePEc/IDEAS profile.

1. Introduction

The U.S. labor market has fared poorly since the Great Recession ended six years ago. The goal of my current research is to understand the reasons behind this lackluster performance. In this research overview, I summarize my recent work with my coauthors. I first describe my work with Henry Siu where we show how jobless recoveries in the aggregate economy relate to the disappearance of “routine occupations.” Next, I discuss my work with Arlene Wong and Sergio Rebelo in which we study how changes in consumption patterns account for a substantial fraction of the fall in U.S. employment in the recent recession.

2. Job Polarization and Jobless Recoveries

In the last three to four decades, many of the occupations that were once commonplace have begun to disappear as they have become obsolete. These occupations, which tend to be middle-skill occupations, involve tasks that are “routine” in the sense that they involve a limited set of tasks which are “rule based,” and can be performed by new technologies. This fact is documented in the “job polarization” literature (see a summary in Acemoglu and Autor (2011)) which shows how employment growth has been in the upper- and the lower-tails of the wage distribution.

During the same time period, in the three recessions (of 1991, 2001, and 2009) that coincided with the job polarization era, aggregate employment continued to decline for years following the turning point in aggregate income and output. These types of behaviors have been coined “jobless recoveries.” In contrast, prior to job polarization and advances in automation and computing, jobless recoveries did not occur.

In “Job Polarization and Jobless Recoveries” (joint with Henry Siu), we first show that the routine job loss is almost completely “bunched” during recessions. More importantly, we show that the root of jobless recoveries can be traced to the disappearance of routine jobs. This is a result of three facts. First, employment in routine occupations account for a significant fraction (about half) of aggregate employment. Second, essentially all of the recessionary contraction in per capita aggregate employment can be attributed to recessionary contractions in the middle-skill, routine occupations. Third, jobless recoveries are observed only in these disappearing, middle-skill jobs. The high- and low-skill occupations to which employment is polarizing either do not experience contractions, or if they do, rebound soon after the turning point in aggregate output. Finally we note that, jobless recoveries were not observed in routine occupations — nor in aggregate employment — prior to the era of job polarization. Hence, jobless recoveries can be traced to the disappearance of routine occupations in recessions.

2.1. The facts

In order to establish the link between job polarization and jobless recoveries, we first consider a simple counterfactual where we ask the following question: How would the aggregate labor market react if routine employment had recovered in the last three recession as it did before the job polarization era? This is an informative exercise since recessions in aggregate employment are due almost entirely to recessions in routine occupations. Our findings are clear: Aggregate employment would have experienced a fast turning with a significant recovery in the employment per capita. Importantly, we note that our emphasis on routine occupations is not simply a relabeling of dynamics in the cyclically sensitive goods-producing industries (manufacturing and construction) nor a relabeling of the dynamics of low educated workers.

2.1.1. U.S. cross-states analysis

To formally test for the relation between job polarization and jobless recoveries we analyze the labor dynamics across the 50 United States and the District of Columbia during the1982 (prior to job polarization era) and 2009 (during the job polarization era) recessions. Specifically, we show that since the onset of job polarization, regions in the US that were most susceptible to the disappearance of routine employment also experience the most jobless recoveries. In contrast, prior to the job polarization era this relation did not exist.

Specifically, to measure a state’s susceptibility to the disappearance of routine employment, we calculate the share of a state’s total employment held in routine occupations, prior to recession. That is, the greater this share, the greater the scope for a permanent drop in routine employment brought on by a recession, all else equal. Then, to measure the states’ strength of the recovery, we measure the per capita employment growth in the first four quarters following the recession’s trough. Given the timing of the variables relative to the recession, the estimated effect cannot be interpreted as due to reverse causality. Furthermore, to address potential omitted variable bias, we include a series of state-specific controls (all averaged at the periods prior to the recession) : (i) the share of goods-producing industries in each state’s output, and (ii) the state’s population share of individuals with low education. Our two key findings are as follows.

First, both in the pre and during the polarization era, states with higher routine employment shares experienced greater per capita employment loss during the recession. Hence, the relation between the routine share and employment loss during recessions has not changed. In contrast, the relation between the routine share and the joblessness of recovery has changed since the job polarization era. Specifically, prior to the long-run decline of per capita routine employment, states with higher routine employment shares exhibited stronger employment recoveries. In contrast, during the job polarization era, states that were more susceptible to polarization forces experienced more jobless recoveries. In other words, on average, in 1982, states with higher routine shares experienced larger employment losses during recession and stronger employment gains during recovery; in 2009, on average, states with higher routine shares also experienced larger recessionary losses but weaker employment recoveries.

2.1.2. Cross country analysis Our final piece of evidence builds on the fact that since the 1990s job polarization has also been observed in Western European countries (e.g. Goos et al. (2009) and Goos et al. (2014)). In our work we show that since the job polarization era, on average, there has been a marked fall in the recovery of employment following recessions. This is in contrast to that fact that prior to the job polarization era, employment would expand (on average) following recessions. Importantly, there has been essentially no change in the strength of output recoveries over time. Thus, the international data clearly indicates the emergence of jobless recoveries since the job polarization era (see also Gaggl and Kaufmann (2015)).

2.2. Theory

Having established these facts, we then study a simple search-and-matching model of the labor market linking the phenomena of job polarization and jobless recoveries. Specifically, our framework is a search-and-matching model of the labor market with occupational choice and a routine biased technological change. The search-and-matching framework of Diamond (1982), Mortensen (1982), and Pissarides (1985) is well-suited for our analysis since it emphasizes the dynamic, multi-period nature of employment and occupational choice.

The key mechanism in our model is that workers differ in their ability in performing occupational tasks, and this ability is reflected in the output in a worker-firm match. In the presence of a routine biased technological change, the surplus of matches for routine occupations eventually becomes negative generating a destruction of routine jobs. In our framework, a recession accelerates this disappearance. Moreover, once output recovers, employment does not. This is because workers who used to be suited to routine occupations are facing lower than usual job finding rates as they can no longer go back to their previous routine occupations.

Overall, the model gives rise to routine job losses being “bunched” in recessions despite a smooth routine biased technological change.. Moreover, the model gives rise to aggregate job losses in recessions being concentrated in routine occupations and that jobless recoveries are caused by the disappearance of routine employment. We furthermore demonstrate how the key mechanisms embodied in the model conform with data on transition rates across labor market states, and how these have changed across pre- and post-job polarization eras.

Moreover, the model’s explicit consideration of frictional unemployment also allows us to address the recent discussion of shifts in the Beveridge Curve as well as “mismatch” in the labor market (see, for instance Sahin et al. (2012)) since the end of the Great Recession. Specifically, we show how jobless recoveries caused by job polarization can cause an outward shift of the Beveridge Curve. Nonetheless, such an episode need not result in any increased mismatch between vacancies and unemployed workers.

2.3. Summary

In the last three to four decades, the US labor market has been characterized by job polarization and jobless recoveries. In our work we demonstrate how these are related. We first show that the loss of middle-skill, routine employment is concentrated in economic downturns. Second, we show that job polarization accounts for jobless recoveries. We then propose a simple search-and-matching model of the labor market with occupational choice to rationalize these facts, and we find that the model captures a number of key facts regarding labor market flows.

3. Consumption and the labor market

Over the Great Recession, many U.S. households have seen their real income fall. For instance, between 2007 and 2012, the real median household income fell by approximately 10%. Such changes in income naturally resulted in the adjustment of consumption expenditures. This adjustment led various researchers to argue that lower household demand was key to explaining the significant fall in employment during the Great Recession. These studies have focused on the decline in total household expenditures due to: (i) a decline in quantity consumed across all expenditure categories, (ii) postponement of purchases in some categories (such as large durables), and (iii) lower prices paid as households search more intensely for the lowest possible price (see for example Aguiar, Hurst, and Karabarbounis (2013), Kaplan and Menzio (2015), and Nevo and Wong (2015)).

In “Trading Down and the Business Cycle” (joint with Arlene Wong and Sergio Rebelo), we contribute to this literature as follows. On the empirical front, we combine several microeconomic datasets and document two facts; First, we show that a key way in which households have adjusted to lower incomes is by trading down, i.e. reducing the quality of the goods and services consumed. Second, we show that the production of low-quality goods is less labor intensive than that of high-quality goods. This suggests that as households trade down in the quality of goods and services they consume, the demand for labor falls. Indeed, through simple accounting exercises we find that the trading-down phenomenon accounts for about a quarter to a third of the fall in U.S. employment in the recent recession.

Motivated by these empirical patterns, we then study two business cycle models that embed quality choice, and we find that the presence of quality choice significantly magnifies the response of the economy to real and monetary shocks generating larger booms and deeper recessions. This amplification results from stronger shifts in both labor demand and labor supply which we discuss in detail below.

3.1. Motivating Example

Consider the case of food expenditures during the Great Recession. In real terms, food expenditures fell by about five percent during this period. Total food expenditures are composed of expenditures on “food at home” and “food away from home.” While the expenditures on food at home fell by four percent during this period, the expenditures on food away from home fell by about eight percent during this period. This naturally reflects the fact that the food away from home category is a “luxury” one.

However, the fall of about eight percent in the food away from home category is an average of a fall of about ten percent in expenditures at “full-services restaurants” (establishments with a relatively broad menu and a wait staff offering meals for consumption primarily on-premise) and a much smaller fall of about four percent at “limited-service restaurants” (establishments where food is purchased and paid before eating and there is generally no wait staff). In other words, as American households cut their expenses on dining out during the recession, the fall in consumption at full-services restaurants has been more than twice the fall at limited-service restaurants.

Consider now a common dining experience at an upscale restaurant vs. a fast-food establishment. While in the former, one tends to see many employees at the restaurant, the latter is characterized by a much smaller number of employees. Indeed, formally we find that in limited-service restaurants the number of employees per million dollar of sales is approximately half of that ratio at high end restaurants.

Thus, the shift in consumption expenses towards low end restaurants combined with the lower labor intensity at these restaurants results in a fall in the demand for workers. In what follows we discuss how this pattern was present in other sectors of the economy during the Great Recession.

3.2. Empirical findings

To understand the interaction between the quality of goods and services and the labor intensity used to produce them, we construct a new firm-level data set using several sources. Specifically, we obtain quality proxies from three sources: data scraped from the Yelp! website, the confidential micro data set used to construct the Producer Price Index (PPI), and the Census of Retail Trade. Then, armed with a quality measure for each firm, we merge this information with Compustat data to measure labor intensity per each firm in our data set.

3.2.1. The quality measure


Our first data set comes from Yelp!, a website where consumers share reviews about different goods and services. Specifically, for each store and location pair, Yelp! asks its users to classify the price of the goods and services they purchased into one of four categories: $ (low), $$ (middle), $$$ (high), and $$$$ (very high) (since there are few observations in the very-high category, we merge the high and very high categories into a single high-price category).

In order to construct a quality measure per firm, we first associate each firm (for example, Cost Plus, Inc.) with its brand names and retail chains (for example, Cost Plus owns the retail chain World Market). We find the Yelp! profile for each retail chain and brand in the 18 largest U.S. cities and collect the first match (for example, the first match for World Market in Chicago is the store on 1623 N. Shefield Avenue). We then compute the average price category across the first match for each of the 18 cities (to compute this average, we assign 1 to category low, 2 to middle and 3 to high and very high). We end up covering five North American Industry Classification System sectors: accommodation, apparel, grocery stores, restaurants, home furnishing.

PPI data

Our second data set uses the confidential micro data collected by the Bureau of Labor Statistics (BLS) to construct the “Producer Price Index” (PPI). The PPI data set measures producers’ prices for manufacturing, services, and all the other sectors of the economy.

In order to construct an indicator of quality for each firm, we proceed as follows. For each six-digit level product that an establishment sells we calculate its price relative to the median price in the industry for the same product. For single-product establishments, we use this relative price as the measure of the quality of the product produced by the establishment. For multi-product establishments, we compute the establishment’s relative price as a weighted average of the relative price of different products, weighted by shipment revenue. We then aggregate the establishment ranking to the firm level by taking a shipment-value weighted average.

Then, having a rank of firms by their relative price we assign the top 15 percent to the high-quality category, the middle 55 percent to the middle-quality category, and the bottom 35 percent to the low-quality category. This is the distribution of firms by quality tier that characterizes the firms included in the Yelp! data. We end up covering three manufacturing sectors ((i)Food, textiles, etc, (ii) Wood, chemical, etc., (iii) Computers, equipment., etc.) and the Retail trade sector.

U.S. Census of Retail Trade

Our third data set comes from the U.S. Census of Retail Trade, and it covers the General merchandise sector. The U.S. Census of Retail Trade splits firms into three price tiers that correspond to three different levels of quality: non-discount stores (high quality), discount department stores (middle quality), other general merchandise stores, including family dollar stores (low quality).

3.2.2. The labor intensity measure

We merge the quality information for each firm in our Yelp! and PPI data sets with data from Compustat on the number of employees and sales. The primary labor intensity measure we use is the ratio of employees to sales. The choice of this measure is dictated by data availability since less than 1/4 of the firms included in Compustat data report the share of labor in total cost, which is a natural measure of labor intensity. In the sample of firms that report the labor share in cost, the correlation between labor share and employees/sales is 0.94. Similarly for General merchandise, the U.S. Census of Retail Trade provides information about employment and sales for each of the three tiers. We use this information to construct labor intensity measures.

3.2.3. Findings

Based on the sales information from Compustat and the U.S. Census of Retail Trade our first finding is that between 2007 and 2012, firms that produce middle- and high-quality items lost market share relative to firms that produce low-quality items. Overall, based on the Yelp! and U.S. Census of Retail Trade data, we find that the low-quality segment gained a market share of about five percent during this period, while the middle-quality segment lost about four percent. Similar magnitudes are observed in the PPI data.

Our second fact is that our measures of labor intensity are increasing in quality. For example, the number of employees per million dollar of sales is 15.1, 9.2, and 6.5, for high-, middle- and low-quality apparel stores, respectively. So, other things equal, a shift of one million dollar of sales from a middle-quality to a low-quality apparel store eliminates roughly three jobs.

Overall, the low-quality segment employs around five workers per million dollars of sales, while the middle and high-quality segments employ around eight and eleven workers per million dollars of sales, respectively.

Having established the two facts, (i) the increase in the share of the low-quality categories, and (ii) their lower labor intensity measures,we then proceed to quantify the effects of trading down on employment by using a simple accounting method. For each sector we compute the change in employment accounted for by changes in market shares. That is, we ask how much would employment have fallen just from the observed changes in the market shares of the different quality segments. In other words, we do not change the “size of the consumption pie,” but rather change its composition across the different quality segments. We find similar results across the different data sets. Specifically, the mere change in the composition of consumption across the quality segments can account for between a quarter to a third of the fall in employment in the industries we analyze.

We then use the same framework, analyzing the role of movements from luxury categories to necessity categories. Specifically we first use the U.S. Consumer Expenditure Survey (CEX) to assign consumption into “luxuries and necessities” categories. This is done by estimating the elasticities of the category budget shares to total household expenditure (the use of Engel Curve slopes of the goods and services to classify the categories into luxuries and necessities is also used in Bils, Klenow and Malin (2012)). We then construct labor intensity measures for each expenditure category. To do so, we first match the CEX expenditure categories with the National Income and Product Accounts (NIPA) personal consumption expenditures categories (PCE). We then further match the PCE categories with the relevant commodities included in the PCE. This allows us to match the commodities to the Input/Output tables and using the Census we then construct a labor intensity measure for each commodity, and thus also for each of the consumption categories.

We find that there is a positive relation between how “luxury” a category is and its labor intensity measure. That is, we find that, on average, the more luxurious a category is, the higher its labor intensity measure is. This positive correlation suggests that recessionary shifts from luxuries to necessities can potentially affect aggregate labor because of variations in labor intensity across categories of luxuries and necessities. While this effect is present qualitatively, we find that quantitatively, category substitution, in stark contrast to the results of changes within categories, accounts for a negligible amount of the drop in aggregate employment.

Thus to summarize, our findings suggest that of the two forms of substitution, the adjustment of consumption towards low-quality products within categories is of a first-order importance for aggregate employment. Our simple accounting exercises suggest that this adjustment accounts for about a quarter to a third of the fall in aggregate employment during the Great Recession. In contrast, the movements from luxury categories to necessity categories, did not contribute to the fall in aggregate employment, from the perspective of the variation in labor intensity and observed changes in consumption patterns.

3.3. Theory

We view these empirical findings as indicative of the importance of studying the general equilibrium effects that quality-trade-down can have on the economy. To study the effects of trading down from a theoretical perspective, we embed quality choice into two otherwise standard models: a flexible-price model and a Calvo-style sticky-price model. We find that the presence of quality choice magnifies the response of these economies to real and monetary shocks. We begin by discussing the key ingredients of the model and then discuss our findings.

The Production Function

We are interested in a production function that is consistent with our key empirical facts. That is, that higher quality firms are characterized by higher labor intensity and that higher quality goods charge higher prices. A natural production function that delivers this result is a constant elasticity of substitution (CES) production function augmented with quality.

The Utility Function

Naturally, in order for households to consume a product with a higher quality (and for households to be willing to pay a higher price), there has to be a benefit. As such we need to introduce quality into the utility function. Moreover, a natural requirement is that quality be a normal good, so that higher income consumers choose goods of higher quality. While this condition seems natural, it imposes restrictions on the form of the utility function. Specifically in order for quality to be a normal good, the utility function must be non-homothetic in consumption. With this requirement in mind, we show that a utility function that is separable in consumption and hours worked and where quality multiplies the consumption function satisfies this condition. An advantage of this functional form is that it nests the usual separable utility in consumption and hours worked as a special case.

3.3.1. Findings

We first consider a flexible price model. Specifically, this is a simple extension of the basic two-sector real business cycle model with the modified production and utility function discussed above. This greatly simplifies the comparison of versions of the model with and without quality choice. We find that the presence of quality choice magnifies the response of our model economies to real and monetary shocks, generating larger booms and deeper recessions. Moreover, the model generates a relative variation of hours and output that is very close to the one observed in the U.S. data which is traditionally been difficult to achieve in RBC models (e.g. Rogerson (1988), Hansen (1985) and Benhabib, Rogerson, and Wright (1991)).

This amplification results from stronger shifts in both labor demand and labor supply. Consider the case of an expansion. In standard business-cycle models, the response of workers to an increase in the real wage is muted by the presence of decreasing marginal utility of consumption. As workers who supply more labor use the additional income to raise their consumption, their marginal utility of consumption declines. The possibility of consuming higher quality goods reduces this fall, resulting in a larger increase in the labor supply. At the same time, the production of higher quality goods requires more labor, generating a larger increase in the labor demand than in a model without quality choice.

The quality-augmented model has two other interesting properties. First, it can generate comovement between employment in the consumption and investment sectors, a property that is generally difficult to obtain (see Christiano and Fitzgerald (1998) for a discussion). Second, the model produces an endogenous, countercyclical labor wedge. As Shimer (2009) discusses, this type of wedge is necessary in order to reconcile business-cycle models with the empirical behavior of hours worked.

We are also interested in showing that the same mechanism that amplifies real shocks also amplifies nominal shocks. We do so by embedding quality choice in an model with Calvo style sticky prices. Similar mechanisms to the one discussed above generate an amplification of monetary shocks.

3.4. Summary

In our work we show that during the Great Recession consumers traded down in the quality of the goods and services they consumed. Since lower quality products are generally less labor intensive, this trading down reduced the demand for labor, accounting for between a quarter to a third of the decline in employment during the Great Recession. We then consider models where consumers change the quality of the goods they consume over the course of the business cycle. We find that introducing quality choice improves the performance of business cycle models.

4. References

Acemoglu, Daron, and David Autor, 2011. “Skills, tasks and technologies: Implications for employment and earnings,” in Orley Ashenfelter and David Card (Eds.), Handbook of Labor Economics, Volume 4B, Chapter 12, pp. 1043-1171, Elsevier.

Aguiar, Mark, Erik Hurst, and Loukas Karabarbounis, 2013. “Time use during the Great Recession,” The American Economic Review, vol 103(5), pages 1664-1694.

Autor, David, Frank Levy, and Richard Murnane, 2003. “The skill content of recent technological change: An empirical exploration,” Quarterly Journal of Economics, vol. 118(4), pages 1279-1333.

Benhabib, Jess, Richard Rogerson, and Randall Wright, 1991. “Homework in Macroeconomics: Household Production and Aggregate Fluctuations,” Journal of Political Economy, vol. 99(6), pages 1166-1187.

Bils, Mark, Pete Klenow, and Benjamin Malin, 2012. “Testing for Keynesian Labor Demand” in: Daron Acemoglu, Jonathan Parker, and Michael Woodford (Eds.), NBER Macroeconomics Annual, pages 311-349, Cambridge, MA: MIT Press.

Christiano, Lawrence, and Terry Fitzgerald, 1998. “The business cycle: it’s still a puzzle,” Economic Perspectives, Federal Reserve Bank of Chicago, vol. 22, pages 56-83.

Diamond, Peter, 1982. “Aggregate demand management in search equilibrium,” Journal of Political Economy, vol. 90(5), pages 881-894.

Gaggl, Paul, and Sylvia Kaufmann, 2015. “The cyclical component of labor market polarization and jobless recoveries in the U.S.,” University of North Carolina at Charlotte.

Goos, Maarten, and Alan Manning, 2007. “Lousy and lovely jobs: The rising polarization of work in Britain,” Review of Economics and Statistics, vol. 89(1), pages 118-133.

Goos, Maarten, Alan Manning, and Anna Salomons, 2009. “Job polarization in Europe,” American Economic Review: Papers & Proceedings, vol. 99(2), pages 58-63.

Hansen, Gary, 1985. “Indivisible labor and the business cycle,” Journal of Monetary Economics, vol. 16(3), pages 309-327.

Jaimovich, Nir, and Henry E. Siu, 2012. “The Trend is the Cycle: Job Polarization and Jobless Recoveries,” NBER working paper 18334.

Jaimovich, Nir, Sergio Rebelo, and Arlene Wong, 2015. “Trading down and the business cycle,” Federal Reserve Bank of Atlanta CQER working paper 2015-5.

Kaplan, Greg, and Guido Menzio, 2015. “Shopping externalities and self-fulfilling unemployment fluctuations,” Journal of Political Economy, forthcoming.

Mortensen, Dale T., 1982. “Property rights and efficiency in mating, racing, and related games,” American Economic Review, vol. 72(5), pages 968-979.

Nevo, Aviv, and Arlene Wong, 2015. “The elasticity of substitution between time and market goods: Evidence from the Great Recession,” NBER working paper 21318.

Pissarides, Christopher A., 1985. “Short-run equilibrium dynamics of unemployment, vacancies, and real wages,” American Economic Review, vol. 75(4), pages 676-690.

Rogerson, Richard, 1988. “Indivisible labor, lotteries and equilibrium,” Journal of Monetary Economics, vol. 21(1), pages 3-16.

Sahin, Aysegul, Joseph Song, Giorgio Topa, and Giovanni L. Violante, 2014. “Mismatch unemployment,” American Economic Review, vol 104(11), pages 3529-3564.

Shimer, Robert, 2009. “Convergence in Macroeconomics: The Labor Wedge,” American Economic Journal: Macroeconomics, vol. 1(1), pages 280-297.

Findings from Big Data on Income Inequality and Income Uncertainty, by Fatih Guvenen

Fatih Guvenen is Professor of Economics at the University of Minnesota. His research is concerned with the income risk and the income distribution of households. Guvenen’s RePEc/IDEAS profile

My research program focuses on income inequality and income uncertainty, two economic phenomena that are distinct from each other, yet also closely related. Both inequality and uncertainty are central to a broad range of social issues. Many questions of current policy debate are inherently about their distributional consequences. For example, heated disagreements about major budget issues–such as reforming the healthcare or the Social Security system–often revolve around the distributional effects of such changes. Similarly, a crucial aspect of the policy debate on taxation is “who should pay what?” It is therefore not surprising that inequality and uncertainty have garnered significant attention from economists (and social scientists more broadly) as well as from policy makers and the broader public.

The substantial rise in income inequality in the United States starting in the late 1970s has given additional urgency to questions surrounding inequality. The vast academic literature that has developed to understand inequality has produced a wealth of insights and ideas about possible mechanisms and proposed a range of policy remedies. As is often the case, the same research also raised more questions and uncovered further puzzling facts that need to be explained themselves.

My research explores a set of interrelated questions in this broad area. Three key themes run through the different projects I work on: (i) using rich data sets (some of which have become recently available) from both administrative and public sources, (ii) emphasis on higher-order moments–skewness, kurtosis, and tail behavior–of the data, and (iii) working non-parametrically so as not to assume away important nonlinearities that may be present in the data. The substantive questions I explore can be categorized under three headings: 1. Short-term (business cycle) phenomena: a. Variation in income volatility (risk) over the business cycle b. Variation in firm volatility over the business cycle 2. Long-term trends: a. Long-run trends in inequality b. Long-run trends in inequality and mobility of top earners 3. Life-cycle trends a. Deviations from lognormality of earnings shocks b. Variation in the higher-order moments over the lifecycle c. Variation in higher-order moments across income groups

1. The Data Sets

One data set my coauthors and I have used in several of these projects comes from the Master Earnings File (MEF) of the U.S. Social Security Administration. The MEF is a population sample of all US individuals with a Social Security Number. It currently covers years 1978 to 2013 and contains information on labor earnings (salary and wage earnings from W-2 forms), employers (unique employer ID for each job held in a given year), and 4-digit SIC (industry) codes of the employer. We draw various subsamples from the MEF ranging from 1% to 10% of the US population. The substantial sample size of more than 600 million individual-year observations (in the 10% sample) allows us to employ a fully nonparametric approach and take what amounts to high-resolution pictures of individual earnings histories. The relaxation of parametric assumptions is a key part of this research agenda.

In addition, we also use data from Swedish and German administrative records (i.e., LINDA and IAB) as well as from various surveys (PSID for the United States and GSOEP for Germany) and firm-level datasets (Compustat Global, OSIRIS, and ORBIS) as explained below.

2. Business Cycle Variation in Risk

2.1 Earnings Risk

A central question in business cycle analysis concerns what happens to idiosyncratic risk in recessions. Two types of idiosyncratic shocks have received special attention: (i) individual earnings shocks, and (ii) firm-level shocks. The conventional wisdom is that both types of shocks become much larger in recessions, and this property was typically captured by a rise in the variance of such shocks. In a first set of papers, my coauthors and I revisit this conclusion, using new data and a fully non-parametric approach, and reach some surprising conclusions.

How Does Earnings Risk Vary Over the Business Cycle?

The conventional wisdom in the earnings dynamics literature has long been that earnings shocks have countercyclical variance–or equivalently, the variance of shocks becomes larger in recessions. While this view is consistent with the plausible idea that many individuals experience large negative shocks in recessions, it also implies, perhaps less plausibly, that, with a larger variance, many more individuals experience larger positive shocks in recessions than in expansions.

In Guvenen, Ozkan, and Song (2014), we have documented two sets of results. First, we revisited the question of counter-cyclicality and found that the variance of idiosyncratic earnings shocks is not countercyclical at all–in fact, it is virtually flat over the business cycle. Instead, it is the left-skewness of shocks that is strongly countercyclical: that is, during recessions, the upper end of the shock distribution collapses–large upward earnings increases become less likely–whereas the bottom end expands–large drops in earnings become more likely. Thus, while the dispersion of shocks does not increase, shocks become more left skewed and, hence, risky during recessions.

A second question we address in this paper is whether there are any observable characteristics that can be measured prior to the recession that predict a worker’s fortunes during a recession. This would represent a different kind of risk than the purely idiosyncratic kind that receives most of the attention in macro/labor work. This is because such risks can be thought of as a “factor structure” whereby an aggregate shock translates differently to workers with different characteristics. Because we have panel data on individuals we can construct observable variables based on the work history of each worker and see if they predict his fortunes during a recession (and similarly during an expansion). We found that one such variable–the 5-year average earnings of a worker immediately prior to a recession–strongly predicts how much the worker will suffer during the recession. For example, prime-age workers that enter a recession with high earnings suffer substantially less compared with those who enter with low earnings. During the Great Recession, workers who were at the 10th percentile before the recession lost 18% more in earnings than workers who were at the 90th percentile before the recession. Interestingly, the Great Recession was not unique: the 1980-83 double dip recession displayed just as strong a factor structure. This implies a large expansion of inequality during the recession that results from a predictable factor structure.

Although this pattern is monotonic between the 10th and 95th percentiles (i.e., higher pre-recession earnings, less earnings loss), this pattern reverses inside the top 5% and even more strongly inside the top 1%. For example, workers who entered the Great Recession in the top 1% (as of 2006) on average lost 30% of their income between 2007 and 2009. Furthermore, those in the top 0.1% as of 2006 lost 50% of their earnings between 2006 and 2011 (a much longer horizon). As surprising as this may sound, the Great Recession was not the most severe recession for very top earners: earnings losses for the top 1% and 0.1% was more severe during the 2000-2001 recession and just as bad during the 1989-1994 period. (Clearly, earnings do not include capital income, but do include bonuses, restricted stock units at time of vesting, and exercised stock options.)

The findings in this paper owe much to the non-parametric nature of the analysis, which reveals facts that could have been obscured or hidden with parametric formulations.

Social Insurance Policy

The analysis in the preceding paper raises as many questions as it answers. Two questions are especially pressing. First, are the facts regarding the business cycle variation in higher-order moments (the acyclicality of variance, the procyclicality of skewness, and the factor structure) specific to the United States, or is it more broadly a feature of business cycles in developed economies? Second, how robust are these results (i) to considering household earnings instead of male earnings (as was done in Guvenen-Ozkan-Song (2014)) and (ii) to the introduction of social insurance policies, in the form of unemployment benefits, welfare system, and the tax system?

To provide a broad perspective on these questions, in Busch, Domeij, Guvenen, and Madeira (2015) we study panel data on individuals and households from the United States, Germany, and Sweden, covering more than three decades of data for each country. The data for the U.S. is from the PSID, and for Germany and Sweden they come from IAB (admin), GSOEP (survey), and LINDA (admin), and include earnings information on households as well as detailed tax and benefits information.

The answer to the first question is that the cyclicality of higher-order risk is remarkably similar across these countries that differ in many details of their labor markets. In particular, in all three countries, the variance of earnings shocks is virtually constant over the business cycle, whereas the skewness becomes much more negative in recessions. (For some variables–such as female earnings in Sweden–we actually find the variance to be procyclical, not countercyclical. This happens because the top end of the shock distribution collapses more than the expansion in the bottom end. Skewness is procyclical in all such cases.) Perhaps surprisingly, the skewness of shocks is even more strongly procylical in Germany and Sweden compared with the United States. Therefore, the fundamental forces driving skewness over the cycle seem to be pervasive across developed economies.

Second, moving from individual earnings to household earnings makes only a small difference to the results. However, government provided insurance–in the form of unemployment insurance, welfare benefits, aid to low-income households, and the like–plays a more important role in reducing downside risk in all three countries; the effectiveness is weakest in the United States and strongest in Germany. We calculate that the welfare benefits of social insurance policies for stabilizing higher-order income risk over the business cycle range from 1% of annual consumption for the United States to 5% of annual consumption for Germany.

2.2 Idiosyncratic Firm-level Risk

Just as idiosyncratic shocks to earnings can affect individuals’ decisions, shocks to firm-level variables can affect (or reflect) firm-level choices and outcomes. With this in mind, a series of papers have investigated the business cycle variation in firm-level variables and have shown that they display countercyclical variance. For example, going back to at least Schwert (1989), it is well-known that stock returns become more volatile in recessions; an important paper by Bloom (2009) has drawn attention to the fact that firm sales and profit growth variance is countercyclical in the US data; Berger and Vavra (2013) have shown that product price dispersion is countercyclical, among others.

Given the evidence above about the strong cyclicality of skewness in earnings shocks, it seems natural to ask if firm-level variables also have cyclical third moments.

In Bloom, Guvenen, and Salgado (2015) we use various datasets from the United States and others to examine the business-cycle variation in the higher-order moments of the growth rates of firm-level variables (sales, profit, and employment). For US publicly listed firms, we use Compustat from 1962 to 2013, and for firms in other countries, we use Compustat Global, OSIRIS, and ORBIS, which contain very rich data on sales, employment, profits, and so on. For many developed countries, the data is quite comprehensive, going back to the 1980s, and including both public and private firms. For others, the time horizon is shorter and only public firms are included.

A robust finding across countries and firm-level variables is that skewness is, again, strongly procyclical. In fact, this pattern–of lower tail greatly expanding during recessions–is also the main driver behind the countercyclicality of variance. Overall, procyclical skewness of firm growth variables holds across a broader set of countries and time periods than the countercyclicality of variance—which is countercyclical in some countries, but is acyclical or even procyclical in some other countries and sub-periods. These results are robust to different selection criteria, across firm size categories, and across industries.

To summarize, the results of these three papers draw attention to fluctuations in skewness over the business cycle as a robust feature–much more so than fluctuations in variance, especially for earnings risk–that can drive fluctuations in uncertainty over the business cycle.

3 Long-Term Trends in Earning Inequality

3.1 Firming Up Inequality

Another set of questions is raised by long-run trends in earnings inequality. In particular, while it has been well documented that earnings inequality has increased rapidly in the United States over the last three decades, little is known about the role of employers (i.e., firms) in this trend. (Notable exceptions are Dunne et al (2004), Barth et al (2014), and Card et al (2014).)

To put this question in context, labor economists have considered a number of observable characteristics–such as education, gender, race, experience, and so on–and examined how much of the rise in inequality happened across groups of workers that differ in these characteristics. Using these variables, one can decompose the rise in inequality into their “proximate causes” so to speak: inequality could be rising because, say, the premium for skills, proxied by education, increased over time, leading to an increased gap between those with high skill and those with low skill. Alternatively, inequality could be increasing because, keeping the skill premium constant, the fraction of workers who are skilled has increased over time leading to more inequality. Similarly, because earnings inequality rises with age (i.e., more inequality among older workers than among younger workers), a shift in the labor force composition toward older workers will increase inequality. While these decompositions do not get to the fundamental determinants of rising inequality, they are useful in pointing to variables that are closely linked to those determinants.

One observable characteristic that has not received much attention is the employer that an individual works for. For example, we can ask: how much of the rise in earnings inequality can be attributed to rising dispersion between firms in the average wages they pay, and how much is due to rising wage dispersion within firms? Similarly, how did rising inequality affect the wage earnings of different types of workers working for the same employer–men vs. women, young vs. old, new hires vs. senior employees, and so on?

To address questions like these, in Song, Price, Guvenen, and Bloom (2014), we begin by constructing a matched employer-employee data set for the United States using administrative records. This is possible thanks to the fact that the MEF is a population sample and for each job it records the unique employer identification number. So we can use worker side information to construct firm data on total wages, wage distribution by worker characteristics (age distribution, gender composition), employment, and so on. Using this matched dataset of all U.S. firms between 1978 to 2012, we show that virtually all of the rise in earnings dispersion between workers is accounted for by increasing dispersion in average wages paid by the employers of these individuals. In contrast, pay differences within employers have remained virtually unchanged. Remarkably, this result has a fractal-like quality: it holds true within 4-digit industries, within different geographical regions, for firms of different size classes, and so on. In cases where we do find a change in within-firm wage inequality, it is almost always a (small) decline over time.

This finding may seem a bit surprising in the face of claims often made in the media that the rise in CEO and executive pay is driving the rise in inequality (See for example, Piketty (2013, pp. 315, 332), Mishel and Sabadish (2014), among others.) Given the nature of our matched dataset, we can zoom in on the top of the earnings distribution within a firm and see if these claims are borne out in the data. Perhaps surprisingly, we find that the wage gap between the most highly paid employees and the average employee in a firm has increased by only a small amount. Specifically, whereas the earnings of workers in the 99.99th percentile are five times higher today than in 1982, their earnings relative to the average worker in their firm are only 20% higher. The flip side is that the average pay at the employers of these top earning workers is four times higher today than in 1982. Hence, even at the very top of the earnings distribution, the vast majority of rising inequality has occurred between rather than within firms.

3.2 Inequality and Mobility at the Top

The MEF provides a unique opportunity to study top earners, thanks to its uncapped earnings records and its panel structure that allows us to track individuals over long periods of time. Some of the earlier work on top earners relies on tracking “the share of earnings accruing to the top x%” each year to circumvent the lack of panel data on these individuals. While such analyses can provide useful insights, the changing composition of top earners from year to year can affect conclusions in ways that may be hard to predict.

In Guvenen, Kaplan, and Song (2014) we analyzed changes in the gender structure at the top of the earnings distribution in the United States over the last 30 years. We found that although females still constitute a small proportion of the top percentiles, they have made sustained gains throughout this period. Therefore, while the glass ceiling remains, it is thinner than before. A large proportion of the increased share of females among top earners is accounted for by the mending of, what we refer to as, the paper floor — the phenomenon whereby female top earners were much more likely than male top earners to drop out of the top percentiles. More generally, membership in the top earnings groups has become more stable for both genders: entry and exit rates have declined and top earners have become a more entrenched group in the population.

In ongoing work, we are estimating some parsimonious stochastic processes for earnings just for top earners, with the aim of providing input into quantitative research on top earners.

4 Lifecycle Earnings Risk

Another strand of my research is concerned with the evolution of earnings over the life cycle. This year about 4 million young Americans will enter the U.S. labor market for the first time. In the subsequent 40 or so years, each one of these individuals will experience a unique adventure involving surprises (finding an attractive career, being offered a dream job, getting promotions and salary raises, and so on) as well as disappointments (failing in one career and moving on to another, experiencing job losses, suffering health shocks, and the like). Workers’ perceptions of these unforeseeable events, which constitute idiosyncratic risks to labor income, are central to many personal economic decisions, as these risks are hard to insure. Therefore, such risks also lie at the heart of numerous economic policy questions: what determines the inequality of consumption and wealth? How effective is fiscal policy in alleviating effects of recessions? And what is the optimal way to tax earnings? Addressing these questions thus requires a sound understanding of the nature of earnings risk over a career.

For the most part economists have been content with modeling earnings dynamics in a rather parsimonious fashion. This usually involves a low order autoregressive process (e.g., AR(1)), an i.i.d. shock, and Gaussian innovations. It is also assumed that the parameters governing these stochastic elements are constant over the life cycle and across the population. (Notable exceptions of course exist, but this description fits the typical calibration experiments.) This parsimony is often defended on the grounds that the panel data available to pin down the parameters of such processes (e.g., the PSID) is not rich enough to identify richer specifications and that more complex processes would introduce additional state variables into dynamic programming problems, making solutions much harder. While both points are correct, in the last few years, larger and richer panel datasets have become available, and with the increasing speed of computers the second issue is also becoming a less binding constraint.

In Guvenen, Karahan, Ozkan, and Song (2015), we pose and answer three questions about earnings dynamics over the life cycle. First, how good an approximation is lognormality for earnings shocks, a common assumption made out of convenience? Second, how do the properties of earnings shocks–especially deviations from lognormality–change over the life cycle? Third, how do these properties change across the population? In our paper we aim to answer these questions using no parametric assumptions on the distribution of income changes. Rather, we use robust and non-parametric statistics that are reported in the form of figures and tables. This visualization of the data allows us to see some very non-linear patterns easily. Some of these patterns would have been difficult to even predict beforehand, so imposing a priori parametric assumptions would have obscured the patterns documented in this paper.

One of the main findings is that changes over time in earnings (over both short and long time horizons) display large deviations from log-normality. In particular, relative to a normal distribution with the same median and standard deviation, the histogram of earnings changes in the data has a much sharper peak in the center, little mass on the shoulders (the region around +- 1 standard deviation), and long and thick tails. These three features of an empirical density are best summarized by its kurtosis. A common measure of kurtosis is the fourth standardized central moment of the distribution. The empirical distribution of one-year earnings growth has a kurtosis of 18, much higher than a normal distribution, which has a kurtosis of 3.

To provide a more familiar interpretation of these kurtosis values, we calculate measures of concentration. If the data were drawn from a normal density, only 8 percent of individuals would experience an annual change in earnings of less than 5 percent (of either sign). Theis corresponding number in the data is 35 percent, showing a much higher concentration of earnings changes near zero. Furthermore, the probability that a worker will receive a very large shock (an fivefold increase or an 80 percent drop) is 12 times higher in the data than under log-normality. To put it differently, in a given year, most individuals experience very small earnings shocks, and a small but non-negligible number experience very large shocks.

Moreover, the average kurtosis masks significant heterogeneity across individuals by age and level of earnings, increasing with age and earnings: prime-aged males with recent earnings of $100,000 (in 2005 dollars) face earnings shocks with a kurtosis above 30, whereas young workers with recent earnings of $10,000 face a kurtosis of only 4.

A second important deviation from log-normality is that the distribution of earnings shocks is not symmetric: it displays large negative skewness. Specifically, large downward movements in earnings (disaster shocks) are more likely than large upward swings. Furthermore, shocks become more negatively skewed with higher earnings and with age. This worsening is due entirely to the fact that large upside earnings moves become less likely from age 25 to 45 and to the increasing disaster risk after age 45.

What do these deviations from lognormality mean for analyses of risk? A back-of-the-envelope calculation gives some idea. Consider the well-known thought experiment (Arrow (1965), Pratt (1964)) in which an individual is indifferent between (i) a gamble that changes his consumption level by a random proportion (1+δ), and (ii) a fixed payment π, the risk premium, to avoid the gamble. Let us compare two scenarios for the standard constant relative risk aversion utility function with a curvature of 10. In the first one, δ is drawn from a Gaussian distribution with zero mean and a standard deviation of 0.10. In the second, δ has the same mean and standard deviation but has a skewness coefficient of -2 and a kurtosis of 30 (consistent with our empirical findings for a 45 year old male earnings 100,000 in the previous year). An individual would be willing to pay 22.1 percent of his average consumption to avoid the non-normal bet compared to about 4.9 percent for the normal, an amplification of risk aversion of 450 percent.

While this example is only intended to be suggestive, recent papers have found important effects of these deviations from lognormality in more realistic settings. For example, Constantinides and Ghosh (2014) show that an incomplete markets asset-pricing model with countercyclical (negative) skewness shocks generates plausible asset pricing implications. Schmidt (2015) goes one step further and considers both negative skewness and thick tails (targeting the moments documented in Guvenen-Ozkan-Song (2014)) and finds that the resulting model provides a plausible set of predictions for asset prices. Finally, turning to fiscal policy, Golosov, Troshkin and Tsyvinski (2014) show that using an earnings process with negative skewness and excess kurtosis implies a marginal tax rate on labor earnings for top earners that is substantially higher than under a traditional calibration with Gaussian shocks with the same variance.Higher-order moments are gaining a more prominent place in recent work in monetary economics (e.g., Midrigan (2011) and Berger and Vavra (2011); see Nakamura and Steinsson (2013) for a survey) as well as in the firm dynamics literature (e.g., Bloom et al (2011) and Bachmann and Bayer(2014)).

To summarize, a broader message of this paper is a call for researchers to reconsider the standard approach in the literature to studying earnings dynamics. The covariance matrix approach that dominates current work (whereby the variance-covariance matrix of earnings changes are the only set of moments considered in pinning down parameters) is too opaque and a bit mysterious: it is difficult to judge the economic implications of matching or missing certain covariances. Furthermore, the standard model in the literature assumes lognormal shocks, whereas this analysis find large deviations from log-normality, in the form of very high kurtosis and negative skewness. With the increasing availability of very large panel data sets, I believe that researchers’ priority in choosing methods needs to shift from efficiency concerns to transparency. The approach adopted here is an example of the latter, and we believe it allows economists to be better judges of what each moment implies for the economic questions they have at hand.


Arrow, Kenneth, 1965. Aspects of the Theory of Risk Bearing, Yrjö Jahnsson lectures, Yrjo Jahnssonin Saatio, Helsinki.

Bachmann, Rüdiger, and Christian Bayer, 2014. “Investment Dispersion and the Business Cycle,” American Economic Review, vol. 104(4), pages 1392-1416, April.

Barth, Erling, Alex Bryson, James C. Davis, and Richard Freeman, 2014. “It’s Where You Work: Increases in Earnings Dispersion across Establishments and Individuals in the U.S.,” NBER Working Paper 20447, September.

Berger, David and Joseph Vavra, 2011. “Dynamics of the U.S. Price Distribution,” Working Paper, Yale University 2011.

Bloom, Nicholas, 2009. “The Impact of Uncertainty Shocks,” Econometrica, vol. 77 (3), pages 623-685.

Bloom, Nicholas, Fatih Guvenen, and Sergio Salgado, 2015. “Firms over the Business Cycle: Fluctuations in Higher-Order Uncertainty,” Working Paper, University of Minnesota.

Busch, Christopher, David Domeij, Fatih Guvenen, and Rocio Madera, 2015. “Higher-Order Income Risk and Social Insurance Policy Over the Business Cycle,” Working Paper, University of Minnesota.

Card, David, Jörg Heining, and Patrick Kline, 2013. “Workplace Heterogeneity and the Rise of West German Wage Inequality,” The Quarterly Journal of Economics, vol. 128 (3), pages 967-1015.

Constantinides, George M. and Anisha Ghosh, 2014. “Asset Pricing with Counter-cyclical Household Consumption Risk,” Working Paper, University of Chicago.

Dunne, Timothy, Lucia Foster, John Haltiwanger, and Kenneth R. Troske, 2004. “Wage and Productivity Dispersion in United States Manufacturing: The Role of Computer Investment,” Journal of Labor Economics, vol. 22 (2), pages 397-430, April.

Golosov, Michael, Maxim Troshkin, and Aleh Tsyvinski, 2014. “Redistribution and Social Insurance,” Working Paper, Princeton University.

Guvenen, Fatih, Fatih Karahan, Serdar Ozkan, and Jae Song, 2014. “What Do Data on Millions of U.S. Workers Say About Labor Income Risk?” Working Paper, University of Minnesota.

Guvenen, Fatih, Greg Kaplan, and Jae Song, 2014. “The Glass Ceiling and The Paper Floor: Gender Differences Among Top Earners, 1981-2012,” Working Paper 716, Federal Reserve Bank of Minneapolis.

Guvenen, Fatih, Serdar Ozkan, and Jae Song, 2014. “The Nature of Countercyclical Income Risk,” Journal of Political Economy, vol. 122 (3), pages 621-660.

Midrigan, Virgiliu, 2011. “Menu Costs, Multiproduct Firms, and Aggregate Fluctuations,” Econometrica, vol. 79(4), pages 1139-1180, July.

Mishel, Lawrence, and Natalie Sabadish, 2014. “CEO Pay and the top 1%: How executive compensation and financial-sector pay have fueled income inequality,” EPI Issue Brief 331, Economic Policy Institute, May.

Nakamura, Emi, and Jón Steinsson, 2013. “Price Rigidity: Microeconomic Evidence and Macroeconomic Implications,” Annual Review of Economics, vol. 5(1), pages 133-163, May.

Piketty, Thomas, 2013. Capital in the Twenty-First Century, Harvard University Press.

Pratt, John W., 1964. “Risk Aversion in the Small and in the Large,” Econometrica, vol. 32 (1/2), pages 122-136.

Schmidt, Lawrence, 2015. “Climbing and Falling Off the Ladder: Asset Pricing Implications of Labor Market Event Risk,” Working Paper, University of California at San Diego.

Schwert, G. William, 1989. “Why Does Stock Market Volatility Change over Time?,” Journal of Finance, vol. 44 (5), pages 1115-53.

Song, Jae, David Price, Fatih Guvenen, and Nicholas Bloom, 2015. “Firming Up Inequality,” Research Mimeo, University of Minnesota.

November 2014, Volume 15, Issue 2

The Evolution of Factor Shares, by Loukas Karabarbounis and Brent Neiman

Loukas Karabarbounis is an Associate Professor of Economics at the University of Chicago Booth School of Business. His research interests are at the intersection of macroeconomics, labor economics, and international macro. Brent Neiman is an Associate Professor of Economics at the University of Chicago Booth School of Business. His research interests are at the intersection of international finance, macroeconomics, and trade. Karabarbounis’s RePEc/IDEAS profile and Neiman’s RePEc/IDEAS profile

Ricardo (1817) argued that the principal problem of Political Economy is to understand the laws governing the distribution of income between labor and capital. Kaldor (1961) characterized the apparent stability of the share of income accruing to labor as a key stylized fact. Despite some scepticism (see, for example, Solow, 1958), the constancy of the labor share has disciplined myriad models over the past half-century. The requirement that the labor share be constant in theoretical models has shaped many economists’ intuitions regarding the aggregate production function, economic growth, and inequality.

At odds with this background, the labor share of income has exhibited a pervasive global decline since the early 1980s. In this research overview, we summarize our work on the decline in the labor share. We first describe global trends in the labor share and discuss some measurement issues. Then, we summarize evidence that ties the labor share decline to the decline in the price of investment goods and contrast this with alternative explanations. Next, we present our recent work that studies the implications of joint trends in depreciation and labor shares for the structure of production, inequality, and macro dynamics. The conclusion outlines some future avenues of research.

1. Labor Share Decline: The Facts

The labor share is the fraction of gross domestic product (GDP) paid as compensation to labor for its services in the form wages, salaries in cash or in kind, and various supplements such as employer contributions for sickness, pensions, and insurance. “The Global Decline of the Labor Share” (Karabarbounis and Neiman, 2014a) provides a broad and systematic account of medium to long-term trends in the labor share of income. Few studies have documented how labor shares have evolved after the 1980s, with some notable exceptions being Blanchard (1997), Blanchard and Giavazzi (2003), and Jones (2003). Our paper is a first attempt to quantify trends in the labor share in a comprehensive sample of countries and industries in the past 35 years, offering new stylized facts for macroeconomists.

We build a new dataset from national income and product accounts for many countries and use it to document that the labor share has declined by more than 5 percentage points globally since the early 1980s. The decline in the labor share has been pervasive. It can be found in the United States and in 7 out of the 8 largest economies of the world (the exception is the United Kingdom for which our data starts in the late 1980s). The labor share has declined in all Scandinavian countries, where labor unions have been strong traditionally. The labor share decline is also observed in many emerging markets that recently opened up to trade including China, India, and Mexico.

The majority of industries also experienced declines in their labor shares. In most countries, changes in the aggregate labor share predominantly reflect changes in industry-level labor shares rather than changes in the size of industries with different labor share levels. This finding argues against otherwise plausible explanations for the decline of the labor share that operate through sectoral shifts in economic activity.

Our new cross-country dataset (which we have made publicly available) allows us to circumvent important measurement difficulties confronted by most of the labor share literature. We measure labor shares within the corporate sector, which largely excludes unincorporated enterprises and sole proprietors whose income combines payments to both labor and capital. As highlighted by Gollin (2002), this “mixed income” poses problems for the consistent measurement of the labor share across countries and over time. By contrast, international comparisons of corporate labor share measures are cleaner.

Focusing on labor share measures within the corporate sector is desirable for three additional reasons. First, the production function and optimization problem in the government sector may be quite different from that in the rest of the economy and likely varies across countries. Second, labor share measures within the corporate sector are insensitive to the measurement and economic interpretation of residential housing, a controversial topic in studies of the economy-wide labor share. Most structures in the corporate sector are offices, stores, and factories and therefore should unambiguously be treated as assets that enter the production function. Finally, the depreciation rate applied to the aggregate capital stock is sensitive to the large fluctuations in residential housing prices. As we discuss below, the dynamics of depreciation are crucial for the interpretation of trends in factor shares and capital accumulation.

2. Labor Share Decline: Explanations

The decline in the price of investment relative to the price of consumption goods accelerated globally starting around 1980. This happened roughly at the same time when the labor share started to decline. The hypothesis we put forward in Karabarbounis and Neiman (2014a) is that the decline in the labor share can be explained by the decline in the relative price of investment goods. Decreases in the relative price of investment goods, often attributed to advances in information technology and the computer age, induced firms to shift away from labor and toward capital as the cost of capital declined. If the elasticity of substitution between capital and labor in the aggregate production function exceeds one, then the shift of production toward capital is sufficiently strong to induce a decline in the labor share.

Most prior estimates used time series variation within a country in factor shares and factor prices to identify the elasticity of substitution in the aggregate production function. By contrast, our estimates of this elasticity are identified from cross-country and cross-industry variation in trends in labor shares and rental rates of capital. Therefore, these estimates are not influenced by the global component of the labor share decline, the object we intend to explain. The rental rate of capital can be influenced at high frequency by various factors such as short-run changes in interest rates, adjustment costs, or financial frictions. These factors, however, are unlikely to have a significant influence on long-run trends in the rental rate, particularly compared to the relative price of investment goods, which moves proportionately with the rental rate in the long run.

Countries and industries in which the relative price of investment goods declined the most experienced larger declines in their labor shares. This finding implies that the elasticity of substitution between capital and labor exceeds one. Given an estimated elasticity of substitution of 1.25, we conclude that roughly half of the global decline in the labor share can be attributed to the observed (more than 25 percent) global decline in the relative price of investment goods.

This explanation fits well with other major macroeconomic developments over the past decades. As Greenwood, Hercowitz, and Krusell (1997) argue, technology-driven changes in the relative price of investment goods constitute a major factor in economic growth. Krusell, Ohanian, Rios-Rull, and Violante (2000) show that the increase in capital equipment is a key force for understanding the increase in the skill premium. Shocks to the relative efficiency of investment goods (as in Greenwood, Hercowitz, and Huffman, 1988) are now considered a standard input into dynamic stochastic general equilibrium models that generate cyclical fluctuations in economic activity.

What about other factors potentially influencing the labor share? The hypothesis that trade and globalization have affected the labor share is theoretically appealing. The simplest story is that, following reductions in global trade frictions, capital-abundant countries have shifted production toward sectors that use capital more intensively in production. These countries import from labor-abundant countries that have shifted production toward sectors that use labor more intensively.

This Heckscher-Ohlin based explanation cannot be easily reconciled with the available evidence. First, labor-abundant countries such as China, India, and Mexico actually also experienced rapid declines in their labor shares, not the increases that this theory would predict. Second, this story attributes an important role for the between-industry component of the labor share decline. However, our evidence shows that the within-industry component is most important in developed economies. While there are other mechanisms through which international trade could affect the labor share (e.g. trade-induced declines in the relative price of investment goods), more evidence is needed before concluding that international trade plays an important role for the labor share decline.

What is the role of price markups and profit shares for the labor share decline? In a world with monopoly power, income is split between compensation to labor, rental payments to capital, and economic profits. Since in many countries capital shares did not display significant increases (reflecting the relative stability of investment rates), increasing profits shares are important in understanding the labor share decline. However, given that the estimated elasticity of substitution remains relatively stable when taking into account changes in markups, the decline in the relative price of investment still explains roughly half of the labor share decline.

Countries in our sample have experienced diverse wage growth and heterogeneous paths of economic development over the past decades. The estimates of the elasticity of substitution we described above are based on the first-order condition for capital, a condition that relates the labor share to markups, capital-augmenting technology, and rental rates. Therefore, the effect of the declining relative price of investment on the labor share is compatible with any given cross-country variation in levels or in growth of both wages and labor-augmenting technology, once we take into account variations in markups, capital-augmenting technology, and rental rates.

A plausible hypothesis is that countries experiencing larger declines in the relative price of investment goods also experienced larger increases in capital-augmenting technological change. An important result is that such a case would never lead one to conclude that the elasticity of substitution is below one when the true elasticity of substitution is above one. The results in Karabarbounis and Neiman (2014a) do not exclude the possibility that capital-augmenting technological progress is important for the labor share decline. On empirical grounds we find declines in the relative price of investment goods a more appealing explanation than increases in capital-augmenting technology because the former are observed whereas the latter are typically estimated as residuals from first-order conditions. Nevertheless, with an elasticity of substitution greater than one, a combination of observed declines in the relative price of investment and (unobserved) increases in capital-augmenting technology can explain the decline in the labor share.

In many developed economies both the fraction of the workforce with college education and the college wage premium have increased during the past decades. This resulted in an increase in the share of income accruing to skilled labor relative to the share of income accruing to unskilled labor. A reasonable view of the world is that changes in the skill composition of the labor force interact both with the decline in the labor share and with the decline in the relative price of investment goods. However, our estimates of the role of the decline in the relative price of investment for the decline in the labor share do not change once we incorporate heterogeneity across countries and industries in changes in the skill composition of the labor force.

3.Depreciation, Technology, and Inequality

The first paper we discussed documented a pervasive decline in the labor share since the early 1980s and argued that the decreasing relative price of investment goods played an important role for this decline. In related work, Piketty (2014) and Piketty and Zucman (2014) discussed long-term movements in capital shares and highlighted the comovement between increasing capital shares and increasing capital-output ratios. An emerging literature motivated by these facts stresses that the interpretation of these trends depends on whether one considers concepts that are inclusive or exclusive of depreciation. For example, Krusell and Smith (2014) argue that the exclusion of depreciation significantly changes Piketty’s predictions of how a growth slowdown would impact the capital-output ratio.

The analysis in Karabarbounis and Neiman (2014a) is done in terms of gross variables, whereas the analysis in Piketty (2014) is done in terms of variables measured net of depreciation. The labor share is typically measured as compensation to labor relative to gross value added (“gross labor share”). One argument in favor of using gross concepts is based on empirical grounds. Depreciation is an imputed item in the national income and product accounts, and so the principle of using more direct measurements would argue for the use of gross instead of net concepts. Since the measurement of depreciation differs across countries, the use of net concepts is even more problematic in an international context. On the other hand, depreciation represents a payment implicitly consumed by the use of fixed capital. As a result, this flow cannot be consumed by households. At least since Weitzman (1976), therefore, economists have recognized that net concepts such as the net domestic product and the net labor share may be more closely associated with welfare and inequality than their gross counterparts.

Depreciation, typically treated in macroeconomics as an uninteresting accounting concept, is a crucial input in understanding the joint dynamics of factor shares and inequality. In an important new paper, Rognlie (2014) highlights a mismatch between the behavior of labor’s share of income net of depreciation (“net labor share”) — a focus of Piketty’s theory — and estimates of the elasticity of substitution between capital and labor that typically come from studies of the gross labor share (including the estimates in Karabarbounis and Neiman, 2014a). In fact, in his review of Piketty (2014), Summers (2014) also highlights the key role of depreciation:

“Piketty argues that the economic literature supports his assumption that returns diminish slowly (in technical parlance, that the elasticity of substitution is greater than 1), and so capital’s share rises with capital accumulation. But I think he misreads the literature by conflating gross and net returns to capital. It is plausible that as the capital stock grows, the increment of output produced declines slowly, but there can be no question that depreciation increases proportionally. And it is the return net of depreciation that is relevant for capital accumulation. I know of no study suggesting that measuring output in net terms, the elasticity of substitution is greater than 1, and I know of quite a few suggesting the contrary.”

Capital Depreciation and Labor Shares Around the World: Measurement and Implications (Karabarbounis and Neiman, 2014b) documents the global patterns of depreciation and labor shares and explains the implications of these patterns for inferring the shocks that hit the economy, the structure of production, and inequality. Our main empirical finding is that both gross and net labor shares have in general declined around the world over the past four decades. Some countries, including the United States, experienced increases in the value of depreciation as a share of gross domestic product. As a result, these countries experienced smaller declines in their net labor share relative to their gross labor share. However, the average economy in the world experienced a decline of similar magnitude in both measures. Further, the cross-country pattern of declines in the net labor share closely resembles the cross-country pattern of declines in the gross labor share.

To understand the implications of these trends, we develop a simple variant of the neoclassical growth model in which the production function uses labor and two types of capital. Labor and aggregate capital combine with an elasticity of substitution greater than one. One type of capital depreciates at a low rate (for example, structures and transportation equipment) and the other type depreciates at a high rate (for example, capital related to information and communication technologies). Depreciation as a share of GDP introduces a wedge between the net and the gross labor share. For a given decline in the gross labor share, the decline in the net labor share is smaller when the increase in depreciation’s share of GDP is larger. Consistent with measurement practices in national income and product accounts, depreciation as a share of GDP fluctuates in response to shifts in the composition of capital and to changes in the aggregate nominal capital-output ratio.

In this environment, we confirm the hypothesis of Summers (2014) and reproduce the finding of Rognlie (2014) that gross and net labor shares may move in different directions in response to changes in the real interest rate. A decline in the interest rate affects the net rental rate proportionately more than the gross rental rate. The large increase in the nominal capital-output ratio increases depreciation as a share of GDP, which in turn mutes the decline of the net labor share relative to the decline of the gross labor share. For reasonable parameterizations, reductions in the real interest rate cause the net labor share to increase despite a decrease in the gross labor share.

Very few countries, however, experienced opposite movements in net and gross labor shares over the past 40 years. We demonstrate theoretically that, unlike shocks to the real interest rate, technology-driven changes in the relative price of investment goods cause gross and net labor shares to always move in the same direction. Declines in the price of capital tend to offset increases in the real capital-output ratio, which dampens the increase in depreciation’s share of GDP and allows net and gross labor shares to fall together. This dynamic results in behavior at odds with the description in Summers (2014) because declines in the relative price of investment affect both the net and the gross return to capital proportionally. Equivalently, in response to changes in the relative price of investment, the elasticities of substitution in the gross and the net production functions are on the same side of (or equal to) one. Collectively, these theoretical and empirical results can reconcile the global decline in the relative price of investment, as analyzed in Karabarbounis and Neiman (2014a), with the narrative of Piketty (2014) that rests on a high net elasticity of substitution.

A contribution of this work is to clarify that both gross and net concepts can be useful and complementary. The argument for using net domestic product and net labor shares instead of their gross counterparts is that the former are more relevant for welfare and inequality. It is useful to note that this logic most naturally applies in an economy’s steady state. It is not obvious whether gross or net concepts are most informative for thinking about welfare and inequality during the economy’s transition.

In the simple variant of the neoclassical growth model that we described above, there are two types of agents, workers and capitalists. Workers cannot save and simply consume their labor earnings in every period. The dynamics of consumption inequality between these two groups are governed by the assumption that capitalists, in contrast to workers, are forward looking and have a positive saving rate. Using simple examples, we illustrate that both the gross and the net labor shares can be jointly informative about the evolution of consumption inequality. The net labor share perfectly summarizes inequality between workers and capitalists in the steady state of the model as workers consume their wages each period and capitalists consume their capital income net of depreciation expenses. This simple relationship, however, ceases to hold along the transition. Intuitively, the net labor share only captures the net income position of workers relative to capitalists in a specific time period. Net income inequality need not translate into consumption inequality when capitalists are forward looking and can save to achieve an optimal allocation of resources across time.

4. Work in Progress and Future Plans

The decline in the labor share has generated attention in part due to its association with increasing inequality. Our view is that the labor share is a useful starting point for thinking about distributional issues, but more work is necessary in order to link factor shares to income and wealth inequality. For example, even in a very stylized model with a striking division between hand-to-mouth workers and forward-looking capitalists, Karabarbounis and Neiman (2014b) demonstrate the inadequacy of either gross or net labor share measures to fully capture inequality in a satisfactory way outside of the steady state.

A fruitful direction for future research is to develop more realistic models that help us understand the joint dynamics of inequality and factor shares. Overall income inequality depends on a host of additional factors, such as the correlation of capital income with labor income and each of the within components of labor and capital income inequality, that also change when some shock causes the labor share to fluctuate. In research in progress together with Jon Adams (a graduate student at Chicago Econ), we examine theoretically the link between factor shares and overall income inequality in a rich model with incomplete markets, worker heterogeneity along various dimensions, bequests, redistributive taxation, and production that combines skilled and unskilled labor with different capital goods.

In other research in progress together with Sara Moreira (a graduate student at Chicago Econ), we have started creating a dataset of labor shares in the United States at the industry-state level between the late 1960s and 2012. As a first step in this empirical analysis, we have focused on the measurement of the labor component of sole proprietors’ income at the industry-state level, using both aggregate and micro data. This dataset will allow researchers to better understand the patterns of labor share changes at a less aggregated level and how these patterns are related to industry and regional economic outcomes.

Finally, the decline in the labor share has been associated with significant changes in the flow of funds between households and corporations. “Declining Labor Shares and the Global Rise of Corporate Savings” (Karabarbounis and Neiman, 2012) documents a substantial change in the distribution of saving between households and corporations. Using sectoral data from more than 50 countries, we show that by 2010, corporations, as opposed to households and governments, supplied saving that financed over 60% of global investment. The corresponding number in the early 1980s was roughly 40%.

Declines in the relative price of investment are consistent both with the decline in the labor share and the global rise of corporate saving. Corporate saving increases as it is the cheapest means to finance increased desired investment. Investment here should be broadly interpreted as encompassing both tangibles and intangibles. The latter types of investment have increased dramatically over the past 30 years (Corrado, Hulten, and Sichel, 2009).


Blanchard, O. (1997): “The Medium Run,” Brookings Papers on Economic Activity, 2, 89-158.

Blanchard, O., and F. Giavazzi (2003): “Macroeconomic Effects of Regulation And Deregulation In Goods and Labor Markets,” Quarterly Journal of Economics, 118(3), 879-907.

Corrado, C., C. Hulten, and D. Sichel (2009): “Intangible Capital and U.S. Economic Growth,” Review of Income and Wealth, 55(3), 661-85.

Gollin, D. (2002): “Getting Income Shares Right,” Journal of Political Economy, 110(2), 458-74.

Greenwood, J., Z. Hercowitz, and G. Huffman (1988): “Investment, Capacity Utilization, and the Real Business Cycle,” American Economic Review, 78(3), 402-17.

Greenwood, J., Z. Hercowitz, and P. Krusell (1997): “Long-Run Implications of Investment-Specific Technological Change,” American Economic Review, 87(3), 342-62.

Jones, C. (2003): “Growth, Capital Shares, and a New Perspective on Production Functions,” Proceedings, Federal Reserve Bank of San Francisco.

Kaldor, N. (1961): “Capital Accumulation and Economic Growth,” in F.A. Lutz and D.C. Hague, eds., The Theory of Capital, St. Martins Press, 177-222.

Karabarbounis, L., and B. Neiman (2012): “Declining Labor Shares and the Global Rise of Corporate Savings,” NBER Working Paper No. 18154.

Karabarbounis, L., and B. Neiman (2014a): “The Global Decline of the Labor Share,” Quarterly Journal of Economics, 129(1), 61-103.

Karabarbounis, L., and B. Neiman (2014b): “Capital Depreciation and Labor Shares Around the World: Measurement and Implications,” NBER Working Paper No. 20606.

Krusell, P., L. E. Ohanian, J.-V. Rios-Rull, and G. L. Violante (2000): “Capital-Skill Complementarity and Inequality: A Macroeconomic Analysis,” Econometrica, 68(5), 1029-53.

Krusell, P., and T. Smith (2014): “Is Piketty’s “Second Law of Capitalism” Fundamental?,” Working Paper, Yale University.

Piketty, T. (2014): Capital in the Twenty-First Century. Harvard University Press.

Piketty, T., and G. Zucman (2014): “Capital is Back: Wealth-Income Ratios in Rich Countries 1700-2010,” Quarterly Journal of Economics, 129(3).

Ricardo, D. (1817): Principles of Political Economy and Taxation. London: John Murray.

Rognlie, M. (2014): “A Note on Piketty and Diminishing Returns to Capital,” Working Paper, Massachusetts Institute of Technology.

Solow, R. (1958): “A Skeptical Note on the Constancy of Relative Shares,” American Economic Review, 48(4), 618-631.

Summers, L. (2014): “The Inequality Puzzle: Piketty Book Review,” DEMOCRACY: A Journal of Ideas, Issue 32.

Weitzman, M. (1976): “On the Welfare Significance of National Product in a Dynamic Economy,” Quarterly Journal of Economics, 90, 156-62.

Volume 15, Issue 1, April 2014

Marcus Hagedorn and Iourii Manovskii on Theory Ahead of Identification

Marcus Hagedorn is Professor of Economics at the University of Oslo. Iourii Manovski is Associate Professor of Economics at the University of Pennsylvania. Their research interests are at the intersection of macroeconomics and labor economics. Hagedorn’s RePEc/IDEAS profile and Manovski’s RePEc/IDEAS profile

The empirical research methodology in economics is based, with a few exceptions, on one of two approaches. In one, economic theory underlining the analysis is left unspecified or is used to loosely “inspire” the measurement strategy. In the other, the full model structure is imposed on the data. Our research strategy is based on the view that answers to many substantive questions can be obtained using a methodology that is less extreme. In particular, we use theory to prove identification, i.e., to establish a precise mapping between the available data and the answer to the substantive question of interest. As this mapping is often independent of the formulation of many elements of the model, it can be measured without having to specify and estimate the full model structure, preserving some of the flexibility of the non-structural approaches. Of course, the theoretical challenge is to identify the minimal set of model elements needed to achieve identification, which depends both on the research question and on the nature of the available data. This strategy is less simple than the two extreme ones as it requires both a theoretical identification proof and a careful data analysis. Yet, the answers it delivers are more general enabling a faster scientific progress.

Below we describe four substantive research agendas that we are currently working on and where we expect substantial scientific advances to be made in the near future.

1. Labor Market Sorting

Suppose one day all workers in the U.S. were randomly reallocated across all existing jobs. Would there be any effect on output? It seems likely that the answer is “yes”. As worker and firm attributes observable in the data account for only some 30% of the variation in wages, the answer will likely remain “yes” even if we condition the experiment on all such characteristics. This is indicative of complementarities between workers and jobs and of sorting of workers across jobs based on unobserved (to the economist) characteristics.

In Hagedorn, Law, and Manovskii (2012) we show that, using only routinely available matched employer-employee data sets, it is possible to fully non-parametrically recover the unobserved worker and firm productivities and the production function, i.e., the consequences for output and productivity of moving any worker to any firm in the economy.

Of course, this can be done only in the context of an explicit sorting theory. A typical starting point for thinking about assignment problems in heterogeneous agent economies is the model of Becker (1973). It was extended by Shimer and Smith (2000) to allow for time consuming search between heterogeneous workers and firms. We further extend the model to allow for search on the job, which is a key feature of the data, and stochastic match quality of individual matches. Importantly, we do not place any assumptions on the production function, except for being smoothly increasing in worker and firm types.

The identification is achieved in three steps. First, we rank workers. We show that workers can be ranked based on their wages within firms (potentially observed with an error). Workers who change firms provide links between the partial rankings inside the firms they work at. This enables us to solve a rank aggregation problem which effectively maximizes the likelihood of the correct global ranking. Second, we rank firms. To do so we show that the value of a vacant job is increasing in firm type. We assume that wage bargaining is such that when the match surplus increases, both parties benefit. This implies that more productive firms deliver more to the workers they hire relative to the reservation wage of those workers. These are statistics based on wages that can be easily computed to obtain the ranking of firms. Third, we recover the production function. The observed wages of a match between a particular worker and firm are a function of the match output and the outside options of the worker and the firm. The outside option of the worker is the value of receiving the measured reservation wage. The outside option of the firm is the value of the vacancy computed using wage data in the previous step. Thus, the wage equation can simply be inverted for output. Finally, although each worker is typically observed working at only a few firms, we estimate his output in other firms by considering how much similarly ranked workers who work at those firms produce.

Implementing this simple algorithm in the data, we are able to provide coherent answers to classic questions in economics. We list some of the applications that we are working on. It is well known that the college premium increased substantially in the US and many other countries starting in the 1980s. One potential explanation is that there was a skill-biased technical change. Alternatively, the sorting of workers to the right jobs might have improved, e.g., due to the spread of the new information technologies. Our method allows to tell these potential explanations apart in that we can explicitly measure the change in technology and in sorting patterns. Similar issues also arise in the trade literature. We can not only disentangle why firms engaged in trade have higher output per hour and pay higher wages — because they have better workers or are inherently more productive, but also understand the effects of trade liberalizations on technology adoption and worker reallocation. We can also address the perennial questions of whether the differences in unobserved worker quality can explain why firms of a particular size or belonging to different industries pay persistently different wages. Having identified the production function in the data, we can also readily solve for the optimal (e.g., output-maximizing) assignment of individual workers to individual firms. This not only yields an aggregate estimate of the cost of mismatch, but also allows to assess the impact of various policies on productivity and matching patterns at a very detailed level. It also allows to study the dynamics of misallocation at the micro level, which is relevant for the macro literature as it typically reduces total factor productivity with a potentially important impact on, e.g., income differences across time and across countries.

What sets our method apart is that it does not impose restrictions on the production function, such as the typical global restrictions on the sign of the cross-partial in the theoretical literature. Because of not imposing such an assumption, we are able to show that it is not verified in the data sets we have worked with. Moreover, we show that even the assumption of monotonicity in worker and firm types that we made above can be relaxed. In addition, our method has excellent properties in samples featuring size limitations of the available data sets and is robust to the presence of large measurement error in wages. It is somewhat more computationally intensive than estimating the regressions with worker and firm fixed effects as typical in the empirical literature. But it is by now well understood that the estimates from such regressions have no economic interpretation in the context of the standard theory of assortative matching.

Thus, we view this research agenda as being extremely promising. It represents a very active area of research with important recent contributions by Pieter Gautier, Philipp Kircher, Rasmus Lentz, Jeremy Lise, Rafael Lopes de Melo, Jean-Marc Robin and Coen Teulings. There are clear limitations to what we can currently do that are mainly due to the underdeveloped theory of assortative matching in more complex but realistic environments. We are hopeful that many such limitations can be overcome, however.

2. Unemployment Insurance and Unemployment

While there is an enormous literature devoted to understanding the elasticity of labor supply, the research on the responsiveness of labor demand to macroeconomic policies is almost non-existent. Yet, in the modern theory of frictional labor markets, it is the labor demand response of firms that drives the response to shocks and policy changes.

In Hagedorn, Karahan, Manovskii, and Mitman (2013) we provide indirect evidence on this elasticity. Specifically, we evaluate the impact of the unprecedented unemployment benefit extensions on unemployment during the Great Recession. To put the labor supply and demand responses into perspective, note that the probability of finding a job for an unemployed worker depends on how hard this individual searches and how many jobs are available:

Chance of Finding Job = Search Effort x Job Availability

Both the search effort of the unemployed and job creation decisions by employers are potentially affected by unemployment benefit extensions.

The recent empirical literature focused exclusively on evaluating the effect of benefit extensions on search effort. The ideal experiment this literature is trying to implement given the available data is as follows. Compare two observationally identical unemployed individuals (same age, gender, occupation, location, etc) who have different duration of benefits available. Then ask whether the individual with more weeks of benefits remaining is less likely to find a job in a given week. The existing empirical literature finds that the difference is very small. This result suggests that search effort is little affected by benefit duration. On the basis of this finding, the literature concluded that extending benefits has no negative effect on employment and unemployment. This conclusion is unwarranted: Suppose both individuals are willing to accept the same jobs, but employers cut job creation in response to benefit extensions. Then both individuals are equally less likely to find a job. The experiment, by its very design, is incapable of capturing the effect of a decrease in job creation.

We instead measure the effect of benefit extensions on unemployment and find it to be quite large. In fact, our estimates imply that the unprecedented benefit extensions can account for much of the persistently high unemployment following the Great Recession. Modern theory of the labor market due to Mortensen and Pissarides, provides one possible explanation. Unemployment benefit extensions improve workers’ well-being when unemployed. This puts an upward pressure on wages they demand. If wages go up, holding worker productivity constant, the amount left to cover the cost of job creation by firms declines, leading to a decline in job creation. As a consequence, unemployment rises and employment falls.

Our empirical approach is based on the pioneering work by Holmes (1998) and involves comparing pairs of counties that border each other but belong to different states. As unemployment insurance extensions are implemented at the state level, there is a large amount of variation in benefit durations across counties within each pair. By comparing how unemployment, job vacancies, employment, and wages respond to changes in the differences in benefit durations, we uncover the effects of benefit durations on these economic variables. The key assumption underlying this measurement approach is that while policies are discontinuous at state borders, economics shocks evolve continuously and do not stop when reaching a state border. We explicitly verify the validity of this assumption. Of course, different states have different policies, industrial composition, housing markets etc. and as a consequence respond differently to the same aggregate shocks. Our measurement approach accounts for this. Finally, the estimator we developed in the paper takes into account that workers and firms are forward looking so that expectations about the future may affect job creation and search effort decisions today.

Thus, methodologically our paper is entirely structural in the sense that all results are clearly interpreted in the context of standard equilibrium models. Yet, it is as general as a reduced-form paper in that we do not impose any unnecessary structure on the data. We used cutting-edge econometric techniques that are appropriate for our environment. We prove identification of the policy effects and verify the validity of the identifying assumptions. We do this not only in the data, but by simulating explicit equilibrium models to verify the good properties of our methods.

Our findings surprised many economists, whose views are well summarized by Chetty (2013): “Consider the politically charged question of whether extending unemployment benefits increases unemployment rates by reducing workers’ incentives to return to work. Nearly a dozen economic studies have analyzed this question by comparing unemployment rates in states that have extended unemployment benefits with those in states that do not. These studies approximate medical experiments in which some groups receive a treatment — in this case, extended unemployment benefits — while “control” groups don’t. These studies have uniformly found that a 10-week extension in unemployment benefits raises the average amount of time people spend out of work by at most one week. This simple, unassailable finding implies that policy makers can extend unemployment benefits to provide assistance to those out of work without substantially increasing unemployment rates.” Indeed, classic research based on large benefit extensions during the recessions of the 1980s, reached consensus estimates that a one week increase in benefit duration increases the average duration of unemployment spells by 0.1 to 0.2 weeks (although there are plenty of highly respected studies that find even larger effects). But consider the implications of these estimates. During the Great Recession unemployment benefits were extended 73 weeks from 26 to 99 weeks. Thus, these estimates imply an increase in unemployment duration between 7.3 and 14.6 weeks, i.e. the duration at least doubles. But a doubling of duration implies that the exit rate from unemployment fell by a factor of two. This would then imply roughly a doubling of the unemployment rate, as can be seen from, e.g., the basic steady state relationship that balances flows in and out of unemployment. This is a substantially larger effect than the one we find.

One could worry that these findings were based on the records of UI recipients and that non-recipients might react differently. But this was shown to be not the case by Rothstein (2011). Indeed, his contribution was to show that the job finding rate of ineligible workers responds as much as that of the eligible ones to benefit extensions.

Some may also hypothesize that the recessions of the 1980s were somehow fundamentally different. Consider the experience of New Jersey that awarded 13 extra weeks of benefits to those whose regular 26 weeks of benefits expired between June and November of 2006. Card and Levine (2000) estimate that this temporary unemployment benefit extension led to a 17% decline in the exit rate from unemployment. This suggests a much larger effect on unemployment than what our estimates imply for such a small and transitory extension. Further, we find that the effects of benefit extensions during the Great Recession are similar to the effects of the extensions following the 2001 recession.

Thus, the available evidence suggests a large effect of unemployment benefit extensions on unemployment. How can one reconcile the robust evidence of very large effects of benefit extensions on unemployment with a small or non-existent response of worker search effort? Standard economic theory on which much of macroeconomics is based provides a clear answer: it is driven by the equilibrium response of job creation by firms.

Of course, given the central role the distinction between labor supply and demand effects plays in guiding the design of macro models and in shaping the understanding of business cycle fluctuations and the effects of policies, additional evidence is sorely needed. Twenty years ago Daniel Hamermesh passionately appealed to his colleagues: “One bit of evidence for the neglect of labor demand by mainstream labor economists is a recent monograph on empirical labor economics that is divided into “halves” dealing with supply and demand (Devine and Kiefer, 1991). The second “half” takes up 14 pages of the 300-page book!” The profession needs the answer!

3. Demand Stimulus and Inflation

An important motivation for unemployment benefit extensions in recessions is that they represent a demand stimulus. Indeed, since the beginning of the Great Recession, the Council of Economic Advisors and the Congressional Budget Office have issued a number of statements predicting hundreds of thousands of jobs created if benefits are extended due to this effect.

More generally, the effectiveness of fiscal policy as a macroeconomic stabilization policy depends on the size of the fiscal multiplier. In standard New Keynesian models with sticky prices the multiplier is large whenever nominal interest rates are not responsive to inflation. The model mechanism underlying this result is particularly clear in Farhi and Werning (2013). Government spending increases marginal costs which leads firms to increase prices, resulting in higher inflation. With fixed nominal interest rates — e.g., in a liquidity trap with a nominal interest rate of zero — the increase in inflation translates one-for-one into a reduction in the real interest rate, boosting current private spending. This increase in demand leads to further increases in inflation, and so on, explaining the quantitatively important feedback loop.

Thus, the link between fiscal stimulus and inflation is at the heart of the theory. Surprisingly, it has not been assessed in the literature. In Hagedorn, Handbury, and Manovskii (2014) we fill this gap by once again exploiting policy discontinuities at the state borders. We use the New Keynesian theory to derive a relationship between unemployment benefit generosity and inflation. The specification is quite general in that it applies to e.g., models with time- and state-dependent pricing as well as to models with complete and incomplete markets.

We use the Kilts Nielsen Retail Scanner Data to construct county-level inflation measures and control for demand spillovers using the Consumer Panel data. We find that exogenous increases in unemployment benefit generosity do not have a statistically significant effect on inflation, with the point estimate being negative but very small. In contrast, the effect on price levels is significantly positive, as implied by the theory in which prices are flexible and the observed stickiness is not allocative. The apparent conclusion is that either the stimulative effects of such policies are indeed tiny or they arise due to a different mechanism from the one at the foundation of the standard New Keynesian theory.

We think that additional research using alternative sources of exogenous variation in firms’ marginal costs, presumably in the micro data, would be very helpful for building consensus on the usefulness of this class of models.

4. Identifying Neutral Technology Shocks

The objective of this research is to develop a method to identify neutral labor-augmenting technology shocks in the data. Classic results, starting with Uzawa (1961), establish that these shocks drive the long-run economic behavior along the balanced growth path. They are also the key driving force inducing fluctuations in real business cycle (RBC) models pioneered by Kydland and Prescott (1982), Long and Plosser (1983), and play a quantitatively important role in New Keynesian models, e.g., Smets and Wouters (2007). Moreover, the relationships between various economic variables and neutral technology shocks identified in the data are routinely used to assess the model performance and to distinguish between competing models.

However, the methods used in the literature to identify technology shocks are not designed to measure neutral technology shocks. Clearly, the Solow residual combines neutral and non-neutral technology changes such as shocks to the relative productivity or substitutability of various inputs. These shocks are often considered important in e.g., accounting for the evolution of the skill premium over time. These shocks, if persistent, will also affect, e.g. labor productivity (output per hour) in the long run and will thus be captured by structural vector autoregressions identified with long-run restrictions. Yet, while the models typically have clear predictions on the response of variables to neutral shocks, the response of variables such as hours worked or credit spreads to non-neutral shocks are ambiguous. Thus, while we are sympathetic to the idea of measuring technology shocks in the data using a set of assumptions satisfied by wide classes of models and assessing the models by their ability to match conditional impulse responses of endogenous variables to identified shocks, the shocks identified using the existing methods are of limited use for this purpose.

In Bocola, Hagedorn, and Manovskii (2014) we propose a method for estimating neutral technology shocks. To do so, we assume a constant returns to scale aggregate production function and exploit the rich implications of Uzawa’s characterization of neutral technology on a balanced growth path. We do not assume the economy to be on a balanced growth path but instead use a weak conditional form of this assumption. We only require that the impulse responses to a permanent neutral technology shocks have the standard balanced growth properties in the long run. This is sufficient to identify the neutral technology shock because we are able to prove that no other shock (to non-neutral technology, preferences, etc.) satisfies these restrictions.

To implement this identification strategy we use a state-space model collecting various macroeconomic time-series and estimate it with filtering/smoothing techniques. Since we do not treat the technology shock as a residual, our method does not require to specify an explicit function that aggregates heterogeneous labor and capital inputs. Instead, all this information is summarized in the unobserved states which we identify without the need to specify the structure behind the dynamics of these states. Moreover, our method does not require the parameters of the production function to be invariant over time. The identification is achieved conditional on a testable assumption on a time series process for neutral technology and other unobserved states. This process is only required to provide a good statistical approximation and does not have to be consistent with a structural model since we do not need to assign a structural interpretation to the other shocks affecting the economy.

We assess the small sample properties of the proposed method in a Monte Carlo study using samples drawn from estimated benchmark business cycle models. We consider the RBC and the New-Keynesian models with worker heterogeneity. We find that the proposed method is successful in identifying neutral technology shocks in the model generated data and does not confound neutral technology with other disturbances such as non-neutral technology innovations, preference shifts, wage markup shocks, etc. We are currently working on applying this method in the data in a hope of finally providing conclusive answers to some of the classic questions in macroeconomics.


Gary Becker, 1973. “A Theory of Marriage: Part I,” Journal of Political Economy, vol. 81(4), pages 813-46.

David Card and Phillip B. Levine, 2000. “Extended Benefits and the Duration of UI Spells: Evidence from the New Jersey Extended Benefit Program,” Journal of Public Economics, vol. 78, pages 107-138.

Raj Chetty, 2013. “Yes, Economics is a Science,” New York Times, Oct. 21 issue, page A21.

Luigi Bocola, Marcus Hagedorn, and Iourii Manovskii, 2014. “Identifying Neutral Technology Shocks,” Manuscript, University of Pennsylvania.

Emmanuel Farhi and Ivan Werning, 2013. “Fiscal Multipliers: Liquidity Traps and Currency Unions,” Manuscript, Harvard University and MIT.

Marcus Hagedorn, Jessie Handbury, and Iourii Manovskii, 2014. “Demand Stimulus and Inflation: Empirical Evidence,” Manuscript, University of Pennsylvania.

Marcus Hagedorn, Fatih Karahan, Iourii Manovskii, and Kurt Mitman, 2013. “Unemployment Benefits and Unemployment in the Great Recession: The Role of Macro Effects,” NBER Working Paper 19499.

Marcus Hagedorn, Tzuo Law, and Iourii Manovskii, 2012. “Identifying Equilibrium Models of Labor Market Sorting,” NBER Working Paper 18661.

Daniel S. Hamermesh, 1991. “Labor Demand: What Do We Know? What Don’t We Know?” NBER Working Paper 3890.

Thomas J. Holmes, 1998. “The Effect of State Policies on the Location of Manufacturing: Evidence from State Borders,” Journal of Political Economy, vol. 106(4), pages 667-705.

Finn E. Kydland and Edward C. Prescott, 1982. “Time to Build and Aggregate Fluctuations,” Econometrica, vol. 50(6), pages 1345-70.

John B. Long, Jr., and Charles Plosser, 1983. “Real Business Cycles,” Journal of Political Economy, vol. 91(1), pages 39-69.

Robert Shimer and Lones Smith, 2000. “Assortative Matching and Search,” Econometrica, vol. 68(2), pages 343-70.

Frank Smets and Rafael Wouters, 2007. “Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach,” American Economic Review, vol. 97(3), pages 586-606.

Hirofumi Uzawa, 1961. “Neutral Inventions and the Stability of Growth Equilibrium,” Review of Economic Studies, vol. 28(2), pages 117-24.

Volume 14, Issue 2, November 2013

Greg Kaplan and Guido Menzio on the Macroeconomics of Bargain Hunting

Greg Kaplan is a Assistant Professor of Economics at Princeton University. His research interests are in applied macroeconomics. Guido Menzio is Associate Professor of Economics at the University of Pennsylvania. His focus is on macroeconomic applications of search theory. Kaplan’s RePEc/IDEAS profile and Menzio’s RePEc/IDEAS profile

Bargain hunting refers to the activities in which buyers can engage in order to acquire goods and services at lower prices. For example, buyers may acquire goods and services at lower prices by spending more time searching for cheap sellers or by waiting for temporary sales. The goal of our current research is to understand the macroeconomic implications of aggregate changes in the extent of bargain hunting. In particular, we want to understand how aggregate changes in the extent of bargain hunting affect the pricing strategy of sellers, the incentives of sellers to enter or expand their presence in the product market and, in turn, their demand for the inputs used in production and retailing. Given the availability of pricing data for consumption goods, our research focuses on the effect of bargain hunting in the retail market. Yet, the mechanisms highlighted in our research are likely to operate at any other stage of the production chain.

1. Different people, different prices

The first step in our analysis is to identify the types of buyers who pay low prices in the consumption goods market. Aguiar and Hurst (2007) documented that older people pay lower prices than younger people. For example, they showed that people aged 60 to 64 pay roughly 3% less for the same consumption goods than people aged 25 to 29. In Kaplan and Menzio (2013a), we use the Kielts Nielsen Consumer Panel (KNCP) to document that–among the working age population–the non-employed pay lower prices than the employed. Indeed, we found that the non-employed pay between 1 and 5% less than the employed for the same consumption goods. The smaller difference obtains when we define goods at the level of the barcode. The larger difference obtains when we define goods by their characteristics, rather than by their barcode.

2. Price dispersion: evidence and theory

The second step in our analysis is to understand why sellers charge different prices for identical goods, as this determines the cause of price differentials between different types of buyers, as well as the effect on sellers of changes in the distribution of buyers’ types. In Kaplan and Menzio (2013a), we use KNCP to measure the extent of price dispersion for identical goods within the same city and during the same quarter, and to decompose price dispersion into three different sources, each related to alternative theories of price dispersion. To illustrate the spirit of our decomposition, consider two bottles of ketchup that sold at different prices in the same market and during the same period of time. First, the two bottles may have sold at different prices because one was sold at an expensive store (i.e. a store where goods are on average expensive) and the other was sold at a cheap store. We refer to this source of price dispersion as the store component. Second, the two bottles of ketchup may have sold at different prices because, although they were sold at equally expensive stores, one was sold at a store where ketchup is expensive (relative to the average price of that store) and the other was sold at a store where ketchup is cheap (relative to the average price of that store). We refer to this source of price dispersion as the store-specific good component. Third, the two bottles of ketchup may have sold at different prices because, although they were sold at the very same store, one was sold at a high price and the other was sold at a low price perhaps because of a temporary sale. We refer to this source of price dispersion as the transaction component.

The decomposition of price dispersion allows us to assess the relative importance of four popular theories of price dispersion: (i) amenities, (ii) heterogeneous monopolists, (iii) intertemporal price discrimination and (iv) search frictions. According to the amenity theory of price dispersion, the product market is perfectly competitive and, yet, identical goods trade at different prices only because they are bundled with different amenities (e.g., location of the store, customer care provided at the store, etc…). For example, a bottle of ketchup will be expensive at a store with a parking lot reserved to its customers and will be cheap at a store without a reserved parking lot. Since amenities are generally specific to a store, rather than to a particular good or transaction, the amenity theory implies that, that for any good, most of the dispersion in prices should be accounted for by variation in the expensiveness of the stores at which the good is sold. That is, the store component should account for most of price dispersion.

According to the monopoly theory of price dispersion, identical goods are sold at different prices because they are traded by local monopolists who face different marginal costs or different demand elasticities (see, e.g., Golosov and Lucas 2007). For example, a monopolist who faces a relatively inelastic demand for ketchup will charge a higher price for the same bottle of ketchup than a monopolist who faces a relatively elastic demand. As long as the differences in marginal costs and demand elasticities between stores are correlated across goods, then the monopoly theory implies that most of the dispersion in prices for any particular good should be accounted for by variation in the expensiveness of the stores at which the good is sold. That is, the store component should again account for most of price dispersion.

According to the theory of price discrimination, identical goods are sold at different prices because local monopolists vary their price over time in order to discriminate between different types of buyers (see, e.g., Conlisk et al. 1984, Sobel 1984 or Albrecht et al. 2012). For example, consider a monopolist facing a constant inflow of low valuation buyers who have a high intertemporal elasticity of substitution for consumption and a flow of high valuation buyers who cannot substitute consumption intertemporally. The monopolist will find it optimal to follow a pricing cycle. In particular, the monopolist will keep the price relatively high for several periods. At this relatively high price, high valuation buyers will purchase the good, while low valuation buyers will wait. Eventually, the number of low valuation buyers will be sufficiently large to induce the monopolist to lower the price for one period and sell to all of them. According to the theory of intertemporal price discrimination, the variation in prices for the same good should be accounted for by variation in the price at which the good is sold at the same store on different days during the same quarter. That is, the transaction component should account for most of price dispersion.

The presence of search frictions in the product market can simultaneously explain why buyers do not arbitrage away price differences and why sellers choose to charge different prices (see, e.g., Burdett and Judd 1983). Consider a market populated by a large number of sellers and buyers. Due to search frictions, an individual buyer cannot purchase from any seller in the market, but only from a subset of sellers. In particular, some buyers are able to purchase from only one seller (uncontested buyers), while other buyers are able to purchase from multiple sellers (contested buyers). In this environment, if all sellers charged the same price, an individual seller could increase its profits by posting a slightly lower price and sell not only to the uncontested buyers it meets, but also to the contested ones. Hence, in equilibrium, identical sellers must randomize over the price of the good and price dispersion obtains. Depending on the pattern of randomization across goods and days, the search theory of price dispersion may generate variation that is accounted for by the store component (if sellers randomize in a way that is strongly correlated across goods), by the store-good component (if sellers randomize independently across goods) and by the transaction component (if sellers randomize independently across goods and days). What distinguishes the search theory of price dispersion from other theories is the fact that it can generate dispersion in the price of a good that is sold at stores that are on average equally expensive.

Empirically, we find that the store component accounts for only 10% of the variance of transaction prices for the same good in a given city and quarter. This finding suggests that the amenity and monopoly theories of price dispersion are unlikely to be quantitatively very important. In contrast, the store-good component accounts for 35 to 45% of the variance of prices, while the transaction component accounts for the remaining variance. These findings suggest that search frictions and intertemporal price discrimination are the most likely causes of price dispersion. Importantly, both the search and intertemporal price discrimination theories imply that the types of buyers who pay lower prices (e.g., the old and the unemployed) achieve such lower prices because they are more likely to be bargain hunters, that is, by devoting time and effort to visiting multiple stores, seeking out temporary sales or finding close substitutes for goods. Both theories imply that an increase in the fraction of bargain hunters will induce sellers to lower their prices without any concurrent change in the costs of producing and retailing goods.

3. Bargain hunting and shopping externalities

In Kaplan and Menzio (2013b), we combine a search-theoretic model of the product market with a search theoretic model of the labor market to understand the general equilibrium implications of aggregate changes in bargain hunting brought about by changes in the fractions of employed and unemployed buyers. In particular, we model the product market as in Burdett and Judd (1983). The equilibrium of this market determines the extent of price dispersion and, given the difference in search intensity between employed and unemployed buyers, the extent to which unemployed buyers pay lower prices. We model the labor market as in Mortensen and Pissarides (1994). The equilibrium of this market determines the fraction of workers who are unemployed and the difference in income between employed and unemployed workers.

Our main theoretical finding is that changes in the composition of buyers can have such a strong effect on sellers as to generate multiple equilibria. The finding is intuitive. When a firm expands its workforce, it creates external effects on other firms. On the one hand, the expanding firm increases the tightness of the labor market and hence makes it more costly for other firms to hire additional workers. We refer to this effect as the congestion externality of employment. On the other hand, the expanding firm tilts the composition of buyers towards types who have more income to spend and less time to search for low prices (i.e. employed buyers). This increases other firms’ demand and market power, and hence, increases their value from expanding their presence in the product market, which entails hiring additional workers. We refer to these effects as the shopping externalities of employment. If the differences in income and/or shopping time between employed and unemployed buyers are sufficiently large, the shopping externalities dominate the congestion externality, employment decisions of different firms become strategic complements and multiple rational expectations equilibria obtain. Different equilibria are associated with different expectations about future unemployment. Yet, in all equilibria, expectations are rational, in the sense that the realized path of unemployment coincides with the expected one.

Our main quantitative finding is that–when calibrated to the observed differences in shopping behavior between the employed and the unemployed–the economy features multiple rational expectations equilibria. In particular, we calibrate the model economy to match the empirical differences in shopping time (25%), prices paid (-2%) and expenditures (-15%) between unemployed and employed workers, as well as the rates at which workers transit between unemployment and employment. Given these calibration targets, the economy has three steady states: one with an unemployment rate of approximately 5%, one with an unemployment rate of approximately 9% and one with no economic activity. Moreover, for any initial unemployment rate, there are rational expectations equilibria leading to each one of the three steady states. Multiplicity obtains because the firms’ value from entering or scaling up their presence in the product market turns out to be fairly sensitive to the unemployment rate. Interestingly, this happens not so much because unemployed buyers spend less than employed buyers, but mainly because unemployed buyers search more than employed buyers. That is, the firms’ value from participating in the product market is quite sensitive to the unemployment rate because the unemployment rate has a rather strong effect on competitiveness of the product market.

The existence of multiple rational expectations equilibria suggests that economic fluctuations may be due not only by changes in fundamentals (i.e. technology, preferences or policy), but also to changes in the agents’ expectations about future unemployment. We formalize this idea by developing a version of the calibrated model in which the agents’ expectations about long-run unemployment follow a 2-state Markov switching process. In the optimistic state, agents expect to reach the steady state with the lowest unemployment rate (5%). In the pessimistic state, agents expect to reach the steady state with the intermediate unemployment rate (9%). Shocks to the agents’ expectations generate fluctuations in unemployment, vacancies and job-finding rates that are large compared to those generated by productivity shocks. Moreover, unlike productivity shocks, shocks to the agents’ expectations generate large, procyclical fluctuations in the value of firms and rather small, countercyclical fluctuations in real labor productivity. Interestingly, the response of the economy to a negative expectation shock looks a lot like the behavior of the US economy during the Great Recession and its aftermath. This finding suggests the possibility that the financial crisis may have acted as a coordination device in focusing the agents’ expectations about future unemployment towards the pessimistic steady state.

Our theory of multiple equilibria is theoretically novel. Unlike Benhabib and Farmer (1994), our theory does not require increasing returns to scale in production. Unlike Diamond (1982), our theory does not require increasing returns in matching. Unlike Heller (1986), our theory does not hinge on demand externalities. Instead, our theory of multiple equilibria builds on two simple mechanisms. The first mechanism links unemployment, search and competition: when unemployment is lower, buyers spend less time searching for low prices and, in doing so, they make the product market less competitive and drive prices up. The second mechanism links revenues, entry and labor demand: when revenues are higher because of either higher demand or higher prices, new firms want to enter the product market, established firms want to scale-up their presence in the product market and, since both activities require some labor, labor demand increases.

4. Direction for future research

The fact that buyers can affect the price they pay for goods and services by engaging in bargain hunting activities has profound implications for the behavior of the macroeconomy. Our current work shows that, because of the differences in the amount of time spent shopping by employed and unemployed buyers, the unemployment rate has a strong effect on the competitiveness of the product market, on the number and size of sellers and, in turn, on labor demand. Indeed, the effect of the unemployment rate is so strong as to create multiple equilibria and, hence, open the door for non-fundamental shocks. Our current work provides just one example of the effect of bargain hunting on the macroeconomy. For instance, it would be interesting to study the macroeconomic effects of changes in bargain hunting brought about by changes in the age distribution rather than by changes in unemployment. Similarly, it would be interesting to study the macroeconomic effect of aggregate changes in bargain hunting in the intermediate market rather than in the consumption goods market.


Mark Aguiar and Erik Hurst, 2007. “Life-Cycle Prices and Production,” American Economic Review, vol. 97(5), pages 1533-1559, December.

James Albrecht, Fabien Postel-Vinay and Susan Vroman, 2013. “An Equilibrium Search Model Of Synchronized Sales,” International Economic Review, vol. 54(2), pages 473-493.

Jess Benhabib and Roger E. A. Farmer, 1994. “Indeterminacy and Increasing Returns,” Journal of Economic Theory, vol. 63(1), pages 19-41, June.

Kenneth Burdett and Kenneth Judd, 1983. “Equilibrium Price Dispersion,” Econometrica, vol. 51(4), pages 955-69, July.

John Conlisk, Eitan Gerstner, and Joel Sobel, 1984. “Cyclic Pricing by a Durable Goods Monopolist,” The Quarterly Journal of Economics, vol. 99(3), pages 489-505, August.

Peter A. Diamond, 1982. “Aggregate Demand Management in Search Equilibrium,” Journal of Political Economy, vol. 90(5), pages 881-94, October.

Mikhail Golosov and Robert E. Lucas Jr., 2007. “Menu Costs and Phillips Curves,” Journal of Political Economy, vol. 115, pages 171-199.

Walter Heller, 1986. “Coordination Failure Under Complete Markets with Applications to Effective Demand.” Equilibrium analysis: Essays in Honor of Kenneth J. Arrow, vol. 2, pages 155-75.

Greg Kaplan and Guido Menzio, 2013a. Deconstructing Price Dispersion. Manuscript, Princeton University and University of Pennsylvania.

Greg Kaplan and Guido Menzio, 2013b. “Shopping Externalities and Self-Fulfilling Unemployment Fluctuations,” NBER Working Paper 18777.

Dale T. Mortensen and Christopher A. Pissarides, 1994. “Job Creation and Job Destruction in the Theory of Unemployment,” Review of Economic Studies, vol. 61(3), pages 397-415, July.

Joel Sobel, 1984. “The Timing of Sales,” Review of Economic Studies, vol. 51(3), pages 353-68, July.

Volume 14, Issue 1 November 2012

Michèle Tertilt on Gender in Macroeconomics

Michèle Tertilt is a Professor of Economics at the University of Mannheim. Tertilt’s research has been concerned with the family and especially the interaction between the family and the macroeconomy. Tertilt’s RePEc/IDEAS profile.

1. Introduction

A large empirical and experimental literature exists that documents important gender differences in preferences and behavior (e.g. Croson and Gneezy 2009, Niederle and Vesterlund 2007). Relative to men, women are more risk averse, have a higher labor market elasticity, engage in less competitive behavior, and often face different legal constraints. Men and women also tend to specialize in different economic activities. For example, men are overrepresented in the army, in mining, and as CEOs, while women are more likely to raise children, have part-time jobs, and work in low-wage occupations. These gender differences are typically ignored in macroeconomic models where the “representative household” is often modeled after a representative man. (A notable exception is Galor and Weil (1996) who were the first to theoretically investigate the implications of a gender wage gap for economic growth.) In my research, I explore to what extent gender differences and interactions between genders have economic consequences. In particular, my work tries to understand whether the interaction between men and women is important for economic development. My research ranges from analyzing polygyny, to the evolution of women’s rights, to sexual behavior in the face of HIV. One outcome of spousal interaction are obviously children, thus, part of my research is dedicated to the positive and normative analysis of fertility.

2. Polygyny and Development

One way in which men and women interact is by marrying each other. Societies differ in their marriage regimes. For example, sub-Saharan Africa has a high incidence of polygyny – men marrying multiple women – a practice that is illegal in most other parts of the world today. Sub-Saharan Africa is also the poorest region of the world.

In “Polygyny, Fertility, and Savings” I argue that polygyny could be a contributing factor to underdevelopment in parts of Africa. In the paper I build a theoretical model of polygyny, where men buy brides, and make fertility and savings decisions. Women obey their fathers and are sold to their future husbands. The theory shows that polygyny leads to high bride-prices to ‘ration’ women, which makes buying wives and selling daughters a good investment, thus crowding out investment in physical assets. The model shows that enforcing monogamy lowers fertility, shrinks the spousal age gap, and reverses the direction of marriage payments. I quantify this effect using data from sub-Saharan African countries. In the calibrated model, I find that banning polygyny decreases fertility by 40 percent and increases savings by 70 percent. The resulting increase in physical capital and drop in labor supply increases GDP per capita by 170 percent.

Given these large benefits, it may seem puzzling why polygyny has not been banned in many countries. To understand the incentives to pass a reform, one may ask who the winners and losers from a marriage reform would be. In “Marriage Laws and Growth in sub-Saharan Africa,” Todd Schoellman and I show that the initial generation of men are clear losers from banning polygyny. In particular, those men who had planned to use the revenues from selling daughters as a retirement fund, would suddenly be deprived of the expected payments. The reason is that a ban on polygyny would lower the demand for brides (and hence daughters) and thereby decrease the price (or even make it negative). But even currently young men would suffer from a reform. They lose the ability to use women as assets and accordingly save more. The increase in savings leads to a large drop in the interest rate, which depresses their lifetime income. Future generations of men, on the other hand, would benefit because the larger capital stock means higher wages, but this effect is not present for currently young men. Therefore, as long as the political power is firmly in the hands of men, a reform would not pass majority voting. If women also voted, a tie would result.

Since enforcing monogamy appears to be difficult both in theory and in reality, in “Polygyny, Women’s Rights, and Development” I investigate an alternative policy: transferring the right of choosing a husband from fathers to daughters. I find that giving daughters more choices has similar economic effects as a ban on polygyny. Both policies decrease the return on wives for men and thereby raise the incentive to invest in alternative assets. This increases the capital stock and hence GDP per capita. Quantitatively, however, enforcing monogamy has much larger effects.

3. Women’s Rights and Development

As my work on polygynous societies shows, more rights for women may be good for development. But why do women have more rights in some countries than in others? Analyzing the evolution of women’s rights in today’s rich countries may help shed some light on this question. The nineteenth century witnessed dramatic improvements in the legal rights of married women in England, the U.S. and several other countries. Given that these improvements took place long before women gained the right to vote, these changes amounted to a voluntary renouncement of power by men. In “Women’s Liberation: What’s in it for Men?” Matthias Doepke and I investigate men’s incentives for sharing power with women. The paper sets up a political economy model of women’s rights. In the model women’s legal rights determine the bargaining power of husbands and wives. We show that men face a tradeoff between the rights they want for their own wives (namely none) and the rights of other women in the economy. Men prefer other men’s wives to have rights because they care about their own daughters and because an expansion of women’s rights increases educational investments in children. A general increase in education benefits men because it means higher quality spouses for their children. Assuming women care more about children than men, when women have more power, human capital investments in children go up. But then, why would men change their attitude on women’s rights over time? We show that the key factor is the importance of education in the economy. If technology is such that human capital plays no role, then patriarchy is optimal (for men). However, if returns to human capital are high, then the inefficiently low educational investments (and high fertility rates) caused by patriarchy dominate and men prefer to share power. Assuming that technological change increases the importance of human capital over the course of the 19th century, it is not surprising then that men changed their voting and voluntarily extended some power to women. Once women have more say, human capital investment goes up, which directly translates into a higher growth rate. Thus, our theory generates a two-way interaction between women’s rights and development.

Our argument has several empirical implications. The timing of legal changes should coincide with the onset of mass education. Moreover, it should also go hand in hand with the fertility decline. We document this timing in the data using historical evidence on the expansion of women’s rights in England and the United States.

A key assumption in “Women’s Liberation: What’s in it for Men?” is that mothers care more about children than fathers do and hence invest more in them. There is also a large empirical literature documenting that women spend more money on children than men do. Does it imply that mothers necessarily care more about children than fathers? And does it further imply that targeting transfers to women is good economic policy? In fact, much development policy (such as cash-transfer programs like PROGRESA or micro-credit programs that are targeted exclusively at women) is already based on this premise. In ongoing work with Matthias Doepke we try to address these questions (‘Does Female Empowerment Promote Economic Development?’). We develop a series of non-cooperative family bargaining models to understand what kind of frictions can give rise to the observed empirical relationships and then use the framework to study policy implications.

One interesting finding from our work is that it is possible to construct mechanisms where women spend more on children without assuming that mothers intrinsically care more about children than fathers. For example, when women have lower wages than men, it may be optimal for them to specialize in child care, while men focus on market work. If spending is complementary to the time allocation, then when given a transfer women will spend more on children, while men may spend more on fixing the car, for example. A second possible mechanism is related to product market discrimination. If women are precluded from some markets (e.g. they are not allowed to drive cars in some countries), then they may spend more on children simply because of the lack of other spending opportunities.

We then assess the policy implications of these models. We find that targeting transfers to women can have unintended consequences and may fail to make children better off. In particular, if women spend more on human capital and men more on physical capital, then the growth rate may actually go down when money is taken from men and given to women. In the case of product market discrimination, female empowerment (i.e. eliminating product market discrimination) will lower child spending, since women will use the resources for themselves. Thus, a main conclusion arising from our work is that more measurement and theory is needed to arrive at a robust analysis of gender-based development policies.

4. Normative and Positive Analysis of Fertility

Much of my work on women has implications for fertility. For example, the evolution of women’s rights went hand in hand with a fertility decline. I also argued that banning polygyny would lead to a large drop in fertility. Does it mean that fertility is sometimes inefficiently high? If so, what are the frictions? And does it mean that a policy like banning polygyny would be welfare improving? It is not obvious which welfare concept should be used to answer these questions. In “Efficiency with Endogenous Population Growth,” Mike Golosov, Larry Jones and I generalize the notion of Pareto efficiency to make it applicable to environments with endogenous populations. We propose two different efficiency concepts: P-efficiency and A-efficiency. The two concepts differ in how they treat potential agents that are not born. We show that these concepts are closely related to the notion of Pareto efficiency when fertility is exogenous.

We prove a version of the first welfare theorem for Barro-Becker (1988) type fertility choice models and discuss how this result can be generalized. That is, using our concepts, we show that one can think about inefficiencies in fertility decision-making in much the same way as about other market failures. To show what can go wrong, we study examples of equilibrium settings in which fertility decisions are not efficient, and we classify them into settings where inefficiencies arise inside the family and settings where they arise across families. For example, a global externality, such as pollution, may lead to inefficiently many people being born. The reason is that parents, when making private fertility decisions, do not take into account that they are also producing future polluters. We show that in this context, a standard Pigouvian tax would not be sufficient to address the inefficiency. Rather, both consumption and fertility need to be taxed to assure both the efficient level of pollution and the efficient number of polluters.

Of course other frictions may point in the opposite direction. Concern over extremely low fertility rates is on the agenda of many policy-makers in Europe today. Some countries have introduced generous child benefits to stimulate fertility. Is there an economic rationale for such pro-natalist policies? In “Property Rights and Efficiency in OLG Models with Endogenous Fertility” Alice Schoonbroodt and I analyze this question. Specifically, we propose and analyze a particular market failure that may lead to inefficiently low fertility in equilibrium. The friction is caused by the lack of ownership of children: if parents have no claim to their children’s income, the private benefit from producing a child can be smaller than the social benefit.

We show this point formally in an overlapping-generations model with fertility choice and parental altruism. Ownership is modeled as a minimum constraint on transfers from parents to children. Using the efficiency concepts proposed in “Efficiency with Endogenous Population Growth,” we find that whenever the transfer floor is binding, fertility is lower than socially optimal. We also use our framework to revisit standard results on dynamic inefficiency. We find that when fertility is endogenous, the usual conditions for efficiency are not sufficient. An interest rate higher than population growth no longer guarantees efficiency because now not only over-saving has to be considered, but also ‘under-childbearing.’ Finally, we also find that, in contrast to settings with exogenous fertility, a pay-as-you-go social security system cannot be used to implement efficient allocations. To achieve an efficient outcome, government transfers need to be tied to fertility choice. For example, one could make pension payments depend on fertility choices.

On the positive aspects of fertility, it has often been argued that who has how many children may matter for growth, as shown e.g. in de la Croix and Doepke (2003). It is therefore of interest to analyze the empirical relationship between fertility and income historically. In “An Economic History of Fertility in the U.S.: 1826-1960” Larry Jones and I use data from the US census to document the history of the relationship between fertility choice and key economic indicators at the individual level for women born between 1826 and 1960. Using survey data allows us to construct a measure of cohort fertility, by using self-reported children ever born of a given birth cohort of women. We document several new facts. First, we find a strong negative relationship between income and fertility for all cohorts and estimate an overall income elasticity of about -0.38 for the period. We also find systematic deviations from a time invariant, isoelastic, relationship between income and fertility. The most interesting of these is an increase in the income elasticity of demand for children for the 1876-1880 to 1906-1910 birth cohorts. This implies an increased spread in fertility by income which was followed by a dramatic compression. Second, using our reported fertility measure, we find some interesting deviations from previous work using total fertility rates. The reduction in fertility known as the Demographic Transition (or the Fertility Transition) seems to be much sharper based on cohort fertility measures compared to usual measures like the Total Fertility Rate. Further, the baby boom was not quite as large as suggested by some previous work. These facts should be useful for researchers trying to model fertility.

5. Sexual Behavior and HIV

Another area in which the interaction of men and women is key, is the spread of sexually transmitted diseases such as HIV. About 2.7 million new HIV infections occur each year and roughly 2 million people die of AIDS annually. The most affected continent is Africa, and interestingly about 60% of HIV infected individuals in Africa are women — compared to only about 30% in North America and Western Europe. The reason is that most transmissions within Africa occur through heterosexual sex and, for physiological reasons women face a higher transmission risk. Given the severity of the situation, an obvious question to ask is what are effective prevention policies? Randomized field experiments can only give a partial answer because they necessarily ignore general equilibrium effects. Epidemiological studies, on the other hand, ignore that people may adjust their sexual behavior in response to the policies.

In “An Equilibrium Model of the African HIV/AIDS Epidemic,” Jeremy Greenwood, Philipp Kircher, Cezar Santos and I take a different approach. We build an equilibrium model of sexual behavior to analyze the African HIV/AIDS epidemic. Individuals engage in different types of sexual activity, which vary in their riskiness. When choosing a sexual activity, such as sex without a condom, a person rationally considers its risk. We use data from the epidemic in Malawi to calibrate the model. We study several topical policies, e.g., male circumcision, treatment of other sexually transmitted diseases, and promoting marriage. Several interesting findings emerge. Some of the policies have the potential to backfire: Moderate interventions may actually increase the prevalence of HIV/AIDS, due to shifts in human behavior and equilibrium effects. We also use the model to quantify how much epidemiological studies and field experiments may get it wrong. We simulate field experiments (i.e. treating only a small proportion of the population) and epidemiological studies (i.e. keeping behavior fixed) in our quantitative model. We find that neglecting both equilibrium effects and behavioral adjustments may lead to sizeable over-estimation of the effectiveness of policies.

6. Outlook

Many open questions remain in this research agenda. In addition to legal rights (or lack thereof), note that there are also many traditions and customs that effectively impose constraints on women, such as footbinding and female circumcision. Investigating the origins of such customs and their connection to development is an important avenue for further research. Also, one may look beyond growth and development and analyze the interaction of men and women in the short term. For example, in ongoing work with Gerard van den Berg, we investigate the incidence of domestic violence over the business cycle. Preliminary findings suggest that recessions significantly increase domestic violence. A related, and largely unexplored, question is to what extent family interaction dampens or amplifies the business cycles.

7. References

Becker, G. S., and R. J. Barro, 1988. “A Reformulation of the Economic Theory of Fertility,” The Quarterly Journal of Economics, vol. 103(1), pages 1-25.
Croson, R., and U. Gneezy, 2009. “Gender Differences in Preferences,” Journal of Economic Literature, vol. 47(2), pages 448-74.
de la Croix, D., and M. Doepke, 2003. “Inequality and Growth: Why Differential Fertility Matters,” American Economic Review, vol. 93(4), pages 1091-1113.
Doepke, M., and M. Tertilt, 2009. “Women’s Liberation: What’s in It for Men?,” The Quarterly Journal of Economics, vol. 124(4), pages 1541-1591.
Doepke, M., and M. Tertilt, 2011. “Does Female Empowerment Promote Economic Development?,” Discussion Paper 5637, Institute for the Study of Labor (IZA).
Doepke, M., M. Tertilt, and A. Voena, 2012. “The Economics and Politics of Women’s Rights,” Annual Review of Economics, vol. 4(6), pages 339-372.
Galor, O., and D. Weil, 1996. “The Gender Gap, Fertility, and Growth,” American Economic Review, vol. 86(3), pages 374-87.
Greenwood, J., P. Kircher, C. Santos, and M. Tertilt, 2012. “An Equilibrium Model of the African HIV/AIDS Epidemic,” unpublished manuscript, University of Mannheim.
Golosov, M., L. Jones, and M. Tertilt, 2007. “Efficiency with Endogenous Population Growth,” Econometrica, vol. 75(4), pages 1039-1071.
Jones, L., A. Schoonbroodt, and M. Tertilt, 2010. “Fertility Theories: Can they explain the Negative Fertility-Income Relationship?,” in “Demography and the Economy, edited by J. Shoven, University of Chicago Press.
Jones, L., and M. Tertilt, 2008. “An Economic History of Fertility in the U.S.: 1826-1960,” in: “Frontiers of Family Economics,” edited by P. Rupert, Emerald Press.
Niederle, M., and L. Vesterlund, 2007. “Do Women Shy Away from Competition? Do Men Compete Too Much?,” The Quarterly Journal of Economics, vol. 122(3), pages 1067-1101.
Schoellman, T., and M. Tertilt, 2006. “Marriage Laws and Growth in Sub-Saharan Africa,” American Economic Review, vol. 96(2), pages 295-298.
Schoonbroodt, A., and M. Tertilt, 2012. “Property Rights and Efficiency in OLG Models with Endogenous Fertility,” unpublished manuscript, University of Mannheim.
Tertilt, M., 2005. “Polygyny, Fertility, and Savings,” Journal of Political Economy, vol. 113(6), pages 1341-1370.
Tertilt, M., 2006. “Polygyny, Women’s Rights, and Development,” Journal of the European Economic Association, vol. 4(2-3), pages 523-530.
Tertilt, M., and G. van den Berg, 2012. “Domestic Violence over the Business Cycle.” ongoing work.

Volume 13, Issue 2, April 2012

Stijn Van Nieuwerburgh on Housing and the Macroeconomy

Stijn Van Nieuwerburgh is Professor of Finance at New York University’s Stern School of Business. His research interests lie in housing, macroeconomics, and finance. Van Nieuwerburgh’s RePEc/IDEAS entry.

1. Introduction

An important part of my research focuses on the intersection of real estate, the largest financial asset for most households, asset markets, and the real economy. In the US, aggregate household residential real estate wealth is currently about $18 trillion and residential mortgage debt about $13 trillion. A common theme in my work is that housing plays a key role as collateral against which households can borrow. In several papers, I model the extent to which households use their house to insure against income shocks and study how changes in the value of housing affects interest rates and rates of return on risky assets. The main message from this research agenda is that, through its effect on risk sharing, fluctuations in housing collateral wealth can help explain puzzling features of stock returns, house prices, interest rates, and the cross-sectional dispersion in households’ consumption. The research speaks to the dramatic swings in real estate markets we observed in the last fifteen years. In this overview I take the opportunity to report on some of my ongoing work in this area and to review some of the main findings of earlier research.

2. The Housing Boom and Bust: Time-Varying Risk Premia

An important challenge in the housing literature is to explain why house prices are so volatile relative to fundamentals such as rent (rental cost) and why price-to-rent ratios exhibit slow-moving boom-bust cycles all over the world. The unprecedented amplitude of the boom-bust cycle between the years 2000 and 2010 in particular begs for a coherent explanation.

In Favilukis, Ludvigson and Van Nieuwerburgh (2010), we generate booms and busts in house price-to-rent ratios that quantitatively match those observed in U.S. data in a model that accounts for the observed equity risk premium and risk-free rate behavior. A large preceding literature makes clear that this is a difficult task, especially in a model with production and realistic business cycle properties like ours (e.g., Davis and Heathcote 2005, Jermann 1998).

Specifically, we study a two-sector general equilibrium model of housing and non-housing production where heterogeneous households face limited risk-sharing opportunities as a result of incomplete financial markets. A house in the model is a residential durable asset that provides utility to the household, is illiquid (expensive to trade), and can be used as collateral in debt obligations. The model economy is populated by a large number of overlapping generations of households who receive utility from both housing and non-housing consumption and who face a stochastic life-cycle earnings profile. We introduce market incompleteness by modeling heterogeneous agents who face idiosyncratic and aggregate risks against which they cannot perfectly insure, and by imposing collateralized borrowing constraints on households (standard down-payment constraints). Within this context, we focus on the macroeconomic consequences of three systemic changes in housing finance, with an emphasis on how these factors affect risk premia in housing markets, and how risk premia in turn affect home prices. First, we investigate the impact of changes in housing collateral requirements. Second, we investigate the impact of changes in housing transactions costs. Third, we investigate the impact of an influx of foreign capital into the domestic bond market.

These changes are meant to capture important changes to the U.S. economy over the last fifteen years. Taken together, the first two factors represent the theoretical counterpart to the relaxation of credit standards in mortgage lending that took place in the real world between the late 1990s and the peak of the housing market in 2006, and the subsequent tightening of credit standards after 2006. We refer to these two changes as financial market liberalization (FML) and its reversal. During the boom years, the U.S. mortgage market saw a massive increase in the use of subprime mortgages, negative amortization and teaser rate loans, and low or no-documentation loans. It also saw a massive increase in the incidence and dollar volume of second mortgages and home equity lines of credit, and with it a large rise in the fraction of borrowers with combined loan-to-value ratios above 95 or even above 100%. Finally, the transaction costs associated with mortgage borrowing, home equity extraction, and mortgage refinancing fell rapidly while borrowers’ awareness of the opportunities to tap into one’s home equity rose. During the housing crisis and to this day, mortgage credit constraints tightened substantially, costs of tapping into one’s home equity rose and both reverted to their pre-boom levels. Favilukis, Kohn, Ludvigson, and Van Nieuwerburgh (2011) provide detailed evidence as well as references to this literature.

The last 15 years were also marked by a sustained depression of long-term interest rates that coincided with a vast inflow of capital into U.S. safe bond markets. While in 1997 foreigners only held $1.6 trillion in U.S. Treasury and Agency bonds, that number had grown to $5.2 trillion by June 2010, representing nearly half of the amounts outstanding. Interestingly, foreign purchases of safe U.S. securities not only rose sharply during the housing boom, but the inflows continued unabated during the housing bust. The vast bulk of these foreign purchases over this period (80%) were made by foreign official institutions, mostly Asian central banks. The increase in foreign purchases of U.S. safe assets accounts for the entire rise in the U.S. net foreign liability position in all securities, because the net position in risky securities hovers around zero.

The main impetus for rising price-rent ratios in the model in the boom period is the simultaneous occurrence of positive economic (TFP) shocks and a relaxation of credit standards, phenomena that generate an endogenous decline in risk premia on housing and equity assets. As risk premia fall, the aggregate house price index relative to aggregate rent rises. A FML reduces risk premia for two reasons, both of which are related to the ability of heterogeneous households to insure against aggregate and idiosyncratic risks. First, lower collateral requirements directly increase access to credit, which acts as a buffer against unexpected income declines. Second, lower transactions costs reduce the expense of obtaining the collateral required to increase borrowing capacity and provide insurance. These factors lead to an increase in risk-sharing, or a decrease in the cross-sectional variance of marginal utility. The housing bust is caused by a reversal of the FML, negative economic shocks, and an endogenous decrease in borrowing capacity as collateral values fall. These factors lead to an accompanying rise in housing risk premia, driving the house price-rent ratio down. Thus, in contrast with the literature, housing risk premia play a crucial role in house price fluctuations.

It is important to note that the rise in price-rent ratios caused by a FML in our study must be attributed to a decline in risk premia and not to a fall in interest rates. Indeed, the very changes in housing finance that accompany a FML drive the endogenous interest rate up, rather than down. It follows that, if price-rent ratios rise after a FML, it must be because the decline in risk premia more than offsets the rise in equilibrium interest rates that is attributable to the FML. This aspect of a FML underscores the importance of accounting properly for the role of foreign capital over the housing cycle. Without an infusion of foreign capital, any period of looser collateral requirements and lower housing transactions costs (such as that which characterized the housing boom) would be accompanied by an increase in equilibrium interest rates, as households endogenously respond to the improved risk-sharing opportunities afforded by a FML by reducing precautionary saving.

To model capital inflows, the third structural change in the model, we introduce foreign demand for the domestic riskless bond into the market clearing condition. We model foreign capital inflows as driven by foreign governments who inelastically place all of their funds in U.S. riskless bonds. Krishnamurty and Vissing-Jorgensen (2012) estimate that such foreign governmental holders, such as central banks, have a zero price elasticity for U.S. Treasuries, because they are motivated by reserve currency or regulatory motives (Kohn, 2002).

Our model implies that a rise in foreign purchases of domestic bonds, equal in magnitude to those observed in the data from 2000-2010, leads to a quantitatively large decline in the equilibrium real interest rate. Were this decline not accompanied by other, general equilibrium, effects, it would lead to a significant housing boom in the model. But the general equilibrium effects imply that a capital inflow is unlikely to have a large effect on house prices even if it has a large effect on interest rates. One reason for this involves the central role of time-varying housing risk premia. In models with constant risk premia, a decline in the interest rate of this magnitude would be sufficient by itself to explain the rise in price-rent ratios observed from 2000-2006 under reasonable calibrations. But with time-varying housing risk premia, the result can be quite different. Foreign purchases of U.S. bonds crowd domestic savers out of the safe bond market, exposing them to greater systematic risk in equity and housing markets. In response, risk premia on housing and equity assets rise, substantially offsetting the effect of lower interest rates and limiting the impact of foreign capital inflows on home prices. There is a second offsetting general equilibrium effect. Foreign capital inflows also stimulate residential investment, raising the expected stock of future housing and lowering the expected future rental growth rate. Like risk premia, these expectations are reflected immediately in house prices (pushing down the national house price-rent ratio), further limiting the impact of foreign capital inflows on home prices. The net effect of all of these factors is that a large capital inflow into safe securities has only a small positive effect on house prices.

In summary, there are two opposing forces simultaneously acting on housing risk. During the housing boom, there is both a FML and a capital inflow. The FML lowers risk premia, while foreign purchases of domestic safe assets raise risk premia. Under the calibration of the model, the decline in risk premia resulting from the FML is far greater than the rise in risk premia resulting from the capital inflow. The decline in risk premia on housing assets is the most important contributing factor to the increase in price-rent ratios during the boom. During the bust, modeled as a reversal of the FML but not the capital inflows, risk premia unambiguously rise while risk-free interest rates remain low. The rise in risk premia drives the decline in house-price rent ratios. Time variation in risk premia is the distinguishing feature that permits our model to explain not just the housing boom, but also the housing bust. Moreover, the model underscores the importance of distinguishing between interest rate changes (which are endogenous) and exogenous changes to credit supply. In the absence of a capital inflow, an expansion of credit supply in the form of lower collateral requirements and lower transactions costs should lead, in equilibrium, to higher interest rates, rather than lower, as households respond to the improved risk-sharing/insurance opportunities by reducing precautionary savings. Instead we observed low real interest rates, generated in our model by foreign capital inflows, but the inflows themselves are not the key factor behind the housing boom-bust.

Our model is silent on the origins of the relaxation of credit constraints and its subsequent tightening, but it is worthwhile to briefly digress and consider some possibilities. A first possibility is that mortgage lenders were confronted with exogenous changes in technology that affected mortgage finance. The boom period witnessed the birth of private-label securitization, collateralized debt obligations, credit default swaps, as well as automated underwriting and new credit scoring techniques employed in that underwriting (Poon, 2009). These innovations have been linked to the boom in mortgage credit and house price growth by Mian and Sufi (2009) and Keys, Seru, Piskorski and Vig (2012). Second, there was substantial legislative action that gave banks much more leeway to relax lending standards: Mian, Sufi and Trebbi (2010) mention 700 housing-related legislative initiatives that Congress voted on between 1993 and 2008 while Boz and Mendoza (2010) highlight the 1999 Gramm-Leach-Bliley and the 2000 Commodity Futures Modernization Acts. Third, in this period, regulatory oversight over investment banks and mortgage lenders weakened substantially (Acharya and Richardson, 2009). For example, the regulatory treatment of AA or better rated private label residential mortgage-backed securities (MBS) was lowered in 2002 to the same low regulatory capital level as that applied to MBS issued by the Agencies since 1988. Also, since 2004 investment banks were allowed to use their internal models to assess the risk of the MBS and capital requirements fell even further. Regulatory capital rules were relaxed on guarantees that banks extended to the special purpose vehicles they set up and that housed a good fraction of mortgage credit (Acharya, Schnabel, and Suarez, 2012). These changes took place in an environment where private sector mortgage lenders where engaged in a race to the bottom with the government-sponsored enterprises, who themselves were substantially affected by regulatory changes and implicit government guarantees (Acharya, Richardson, Van Nieuwerburgh and White, 2011). Faced with such changes in their economic environment, mortgage lenders formed expectations of higher future house price growth, justifying more and riskier mortgages as in the optimal contracting framework of Piskorski and Tchystyi (2010). The bust saw a tightening of regulatory oversight and the Dodd-Frank Act (Acharya, Cooley, Richardson and Walter, 2011), to which lenders responded by cutting back on credit.

3. International Evidence and the Role of Capital Flows in the Housing Boom and Bust

In follow-up empirical work, Favilukis, Kohn, Ludvigson and Van Nieuwerburgh (2011) study the empirical relationship between house prices, foreign capital flows, and a direct measure of credit standards for a cross-section of countries. Across countries, we find a positive correlation between house price growth and foreign capital inflows (current account deficits) during the boom period, but a negative correlation during the bust. For a smaller subset of countries we have a direct measure of the tightness of credit constraints from senior loan officers’ surveys on banks’ standards of supplying mortgage credit to households. In a panel regression for 11 countries for a sample that spans the boom and bust, we find a strong positive association between the fraction of banks that eases credit standards and house price growth. Over the same sample, such a relationship is absent between current account deficits and house price growth. These results are robust to alternative measures of capital flows. Longer time series evidence for the U.S. suggests that more than 50% of variability in house price growth is accounted for by changes in credit standards, and very little by the dynamics of the current account. Our measure of credit standards is positively related to the ratio of non-conforming to conforming mortgage originations. In sum, the time series and cross-country data seem supportive of the notion that changes in international capital flows played, at most, a small role in driving house prices during this time, both in the U.S. and around the world.

4. Foreign Holdings of U.S. Safe Assets: Welfare Effects for U.S. Households

In Falukis, Ludvigson and Van Nieuwerburgh (2012), we use a similarly rich framework to evaluate the implications of the dramatic rise on foreign holdings of U.S. safe assets for the welfare of U.S. households. Despite a vigorous academic debate on the question of whether global imbalances are a fundamentally benign or detrimental phenomenon (see Gourinchas (2006) Mendoza, Quadrini and Rios-Rull (2007), Caballero, Fahri, and Gourinchas (2008a), Caballero, Fahri and Gourinchas (2008b), Obstfeld and Rogoff (2009), and Caballero (2009)), little is known about the potential welfare consequences of these changes in international capital flows, or of foreign ownership of U.S. safe assets in particular. We argue in this paper that a complete understanding of the welfare implications requires a model with realistic heterogeneity, life-cycle dynamics, and plausible financial markets. The model has a special role for housing as a collateral asset.

The model economy implies that foreign purchases (or sales) of the safe asset have quantitatively large distributional consequences, reflecting sizable tradeoffs between generations, and between economic groups distinguished by wealth and income. Indeed, the results suggest that a sell-off of foreign government holdings of U.S. safe assets could be tremendously costly for some individuals, while the possible benefits to others are many times smaller in magnitude.

Welfare outcomes are influenced by the endogenous response of asset markets to fluctuations in foreign holdings of the safe asset. Foreign purchases of the safe asset act like a positive economic shock and have an economically important downward impact on the risk-free interest rate, consistent with empirical evidence. Although lower interest rates boost output, equity and home prices relative to measures of fundamental value, foreign purchases of the domestic riskless bond also reduce the effective supply of the safe asset, thereby exposing domestic savers to greater systematic risk in equity and housing markets. In response, risk premia on housing and equity assets rise, substantially (but not fully) offsetting the stimulatory impact of lower interest rates on home and equity prices. These factors imply that the young and the old generations experience welfare gains from a capital inflow, while middle-aged savers suffer. The young benefit from higher wages and from lower interest rates, which reduce the costs of home ownership and of borrowing in anticipation of higher expected future income. On the other hand, middle-aged savers are hurt because they are crowded out of the safe bond market and exposed to greater systematic risk in equity and housing markets. Although they are partially compensated for this in equilibrium by higher risk premia, they still suffer from lower expected rates of return on their savings. By contrast, retired individuals suffer less from lower expected rates of return, since they are drawing down assets at the end of life. They also receive social security income that is less sensitive to the current aggregate state than is labor income, making them more insulated from systematic risk. Taken together, these factors imply that the oldest retirees experience a significant net gain even from modest increases in asset values that may accompany a capital inflow.

The magnitude of these effects for some individuals is potentially quite large. For example, in the highest quintile of the external leverage distribution, the youngest working-age households would be willing to give up over 2% of life time consumption in order to avoid just one year of a typical annual decline in foreign holdings of the safe asset (which amounts to about 2% of U.S. trend GDP). This effect could be several times larger for a greater-than-typical decline, and many times larger for a series of annual declines in succession or spaced over the remainder of the household’s lifetime. By contrast, the absolute value of the equivalent variation welfare measure we study is often one-tenth of the size (and in general of the opposite sign) for sixty year-olds than it is for the youngest or oldest households. Thus, middle-aged households often stand to gain from an outflow, but their gain is much smaller in magnitude than are the losses for the youngest and oldest.

We also compute welfare consequences for groups that vary according to total wealth, housing wealth, and income, as well as an ex-ante measure for agents just being born. The latter provides one way of summarizing the expected welfare effects over the life cycle, as experienced by a newborn whose stochastic path of future earnings and foreign capital inflows is unknown. Under the veil of ignorance, newborns benefit from foreign purchases of the safe asset and would be willing to forgo up to 18% of lifetime consumption in order to avoid a large capital outflow.

Our study focuses on the effect of a reserve-driven upward trend in the U.S. net foreign debtor position over time on the macroeconomy and welfare. Our model is silent on the economic implications of gross flows, and we do not study cyclical fluctuations in the value of net foreign holdings of other securities which, unlike net foreign holdings of U.S. safe assets, show no upward trend (Favilukis, Kohn, Ludvigson and Van Nieuwerburgh, 2011). By contrast, Gourinchas and Rey (2007) and Maggiori (2011) investigate how the net foreign asset position of the U.S. invested in risky securities varies cyclically across normal and crisis times, as well as how gross flows are affected. On the other hand, these papers are silent on the reasons for the large and growing net foreign debtor position of the U.S. in good times, and on its upward trend over time. We view these studies as complementary to our study. Integrating both aspects of foreign flows in one model seems like a priority for future research.

5. Housing Collateral, Financial Market Puzzles, and Measures of Risk Sharing

My earlier work explores the role of housing as a collateral asset in models of limited commitment, along the lines of Krueger (1999), Alvarez and Jermann (2000), and Chien and Lustig (2010). Lustig and Van Nieuwerburgh (2005) predicts that households are less keen to take on financial risks, and therefore demand a higher return for bearing these risks, when housing collateral is scarce. In U.S. aggregate data, we show that a decrease in housing collateral is followed by higher future stock returns, in excess of the risk-free rate and that this relationship is statistically significant. The cross-sectional prediction of the model is that assets whose returns covary more positively with the value of housing must offer their investors higher returns relative to other assets. In contrast, assets whose value increases when housing collateral is scarce are a valuable hedge against the risk of being borrowing-constrained. This additional benefit induces the holders of these assets to accept lower returns. In the data, this mechanism explains more than 80% of the cross-sectional difference between average returns on value (high book-to-market ratio) and growth stocks (low book-to-market ratio). Its pricing errors compare favorably to those of competing asset pricing models. The model upon which these empirical results are based, spelled out in Lustig and Van Nieuwerburgh (2007), also provides an explanation for why short-duration assets, whose risky cash flows accrue in the near future, have higher risk premia than long-duration assets, an empirical fact highlighted by Binsbergen, Brandt and Koijen (2011). The second piece of evidence on the housing collateral and risk sharing mechanism comes from quantity data for U.S. metropolitan areas. Lustig and Van Nieuwerburgh (2010) measures the degree of risk sharing as the cross-sectional variance of consumption relative to the cross-sectional variance of income. The model aggregates heterogeneous, borrowing-constrained households into regions characterized by a common housing market and solves for the equilibrium consumption dynamics. It generates a lower degree of risk sharing when housing collateral is scarce to an extent similar to what we find in the data.

6. Regional Variation in Housing Prices

My interest in regional variations across housing markets led to a project that explores why house prices differ across regions and over time. The spatial location model in Van Nieuwerburgh and Weill (2010) is one of the first dynamic versions of the seminal Rosen (1979) and Roback (1982) model in urban economics. Regions differ in their productivity levels and therefore the wages paid to their resident workers. Since workers are free to move across regions, house prices must adjust to make them indifferent between living in any region. Regions which experience fast wage growth attract new households who bid up house prices. Housing supply regulation constrains the number of new units that can be built per period in each area; muting the response of quantities amplifies price changes. By feeding realized regional wages into a calibrated version of the model, we can explain the magnitude of the increase in average house prices and the increase in the dispersion of house prices across regions over the 1975-2005 period. Interestingly, a tightening in housing supply regulation by itself -an alternative candidate explanation for the observed changes in the house price distribution- does not generate much of an increase in the price level or its dispersion in the model because households can relocate.

While the paper produces rich patterns for house prices across time and space and matches important features of the data over the sample period of study, it would fall short in accounting for house prices over the recent boom and bust period described above. This is because the model does not generate time variation in risk premia associated with relaxing and tightening credit constraints. An important research challenge going forward is to enrich the spatial housing models so that they imply richer asset pricing dynamics. This would allow us to understand better the heterogeneous house price experience of U.S. metropolitan areas over the last decade.

7. Conclusion

In light of the recent events, there has never been a more relevant time to work on housing and its implications for macroeconomics and asset markets at large. There is a flurry of exciting research in progress by established and young researchers alike, studying a range of interesting questions. How can we account for the magnitude and dynamics of mortgage foreclosures and how do they affect the macro-economy? How successful are the government’s mortgage modification programs in getting the U.S. economy back on track? What are the macro-economic implications of the credit crunch that is currently taking place in mortgage markets in the U.S.? What should the future architecture of the U.S. housing finance system look like and what can we learn from other countries? Finally, commercial real estate remains a largely unexplored asset class in the macro-finance literature despite its size and importance to the macroeconomy. These are some of the questions I hope the profession will continue to make progress on going forward.

8. References

Restoring Financial Stability: How to Repair a Failed System. Wiley finance series. (NYU Stern’s response to the financial crisis, part 1)
Acharya, V. V., T. Cooley, M. Richardson, and I. Walter, 2011. Regulating Wall Street: The Dodd-Frank Act and the New Architecture of Global Finance. Wiley finance series. (NYU Stern’s response to the financial crisis, part 2)
Acharya, V. V., P. Schnabl, and G. Suarez, 2012. “Securitization without Risk Transfer,” Journal of Financial Economics, forthcoming.
Acharya, V. V., M. Richardson, S. Van Nieuwerburgh, and L. J. White, 2011. Guaranteed To Fail: Freddie, Fannie, and the Debacle of U.S. Mortgage Finance. Princeton University Press. (NYU Stern’s response to the financial crisis, part 3)
Alvarez, F., and U. J. Jermann, 2000. “Efficiency, Equilibrium, and Asset Pricing, with Risk of Default,” Econometrica, vol. 68(4), pages 775-797.
Binsbergen, J. H. V., M. W. Brandt, and R. S. J. Koijen, 2011. “On the Timing and Pricing of Dividends,” American Economic Review, forthcoming.
Boz, E., and E. Mendoza, 2010. “Financial Innovation, the Discovery of Risk, and the U.S. Credit Crisis,” NBER Working Paper No. 16020.
Caballero, R. J., 2009. “Discussion of ‘Global Imbalances and the Financial Crisis: Products of Common Causes, by M.Obstfeld and K.Rogoff’.” Unpublished paper, M.I.T.
Caballero, R. J., and A. Krishnamurthy, 2009. “Global Imbalances and Financial Fragility,” American Economic Review, vol. 99(2), pages 584-588.
Caballero, R. J., E. Fahri, and P.-O. Gourinchas, 2008. “An Equilibrium Model of Global Imbalances and Low Interest Rates,” American Economic Review, vol. 98(1), pages 358-393.
Chien, Y., and H. Lustig, 2010. “The Markets Price of Aggregate Risk and the Wealth Distribution,” Review of Financial Studies, vol. 23(4), pages 1596-1650.
Davis, M., and J. Heathcote, 2005. “Housing and the Business Cycle,” International Economic Review, vol. 46(3), pages 751-784.
Favilukis, J., D. Kohn, S. C. Ludvigson, and S. Van Nieuwerburgh, 2011. “International Capital Flows and House Prices: Theory and Evidence.” In: E. Glaeser and T. Sinai, Eds., Housing and the Financial Crisis, NBER, Cambrige, MA.
Favilukis, J., S. C. Ludvigson, and S. Van Nieuwerburgh, 2010. “The Macroeconomic Effects of Housing Wealth, Housing Finance and Limited Risk Sharing in General Equilibrium,” NBER Working paper 15988.
Favilukis, J., S. C. Ludvigson, and S. Van Nieuwerburgh, 2012. “Foreign Ownership of U.S. Safe Assets: Good or Bad?” NYU Working Paper FIN-11-057.
Gourinchas, P.-O., 2006. “The Research Agenda: Pierre-Olivier Gourinchas on Global Imbalances and Financial Factors,” Economic Dynamics Newsletter, 2006, vol. 7(2).
Gourinchas, P.-O., and H. Rey, 2007. “From World Banker to Venture Capitalists: US External Adjustment and Exhorbitant Privilege.” In: R. Clarida (ed.), G-7 Current Account Imbalances: Sustainability and Adjustment, pages 11-55, North Holland, Chicago, USA.
Jermann, U. J., 1998. “Asset pricing in production economies,” Journal of Monetary Economics, vol. 41(2), pages 257-275.
Kehoe, P., and F. Perri, 2004. “Competitive Equilibria With Limited Enforcement,” Journal of Economic Theory, vol. 119, pages 184-206.
Keys, B. J., T. Piskorski, A. Seru, and V. Vig, 2012. “Mortgage Financing in the Housing Boom and Bust.” In: E. Glaeser and T. Sinai (eds.), Housing and the Financial Crisis, NBER.
Kohn, D. L, 2002. “Panel: Implications of Declining Treasury Debt. What Should the Federal Reserve Do as Treasury Debt Is Repaid?Journal of Money, Credit and Banking, vol. 34(3), pages 941-945.
Krishnamurthy, A., and A. Vissing-Jorgensen, 2012. “The Aggregate Demand for Treasury Debt,” Journal of Political Economy, forthcoming.
Krueger, D., 1999. Risk Sharing in Economies with Incomplete Markets, PhD Thesis University of Minnesota.
Lustig, H., and S. Van Nieuwerburgh, 2005. “Housing Collateral, Consumption Insurance and Risk Premia: an Empirical Perspective,” Journal of Finance, vol. 60(3), pages 1167-1219.
Lustig, H., and S. Van Nieuwerburgh, 2007. “Can Housing Collateral Explain Long-Run Swings in Asset Returns?” Unpublished paper, New York University.
Lustig, H., and S. Van Nieuwerburgh, 2010. “How Much Does Household Collateral Constrain Regional Risk Sharing?Review of Economic Dynamics, vol. 13(2), pages 265-294.
Maggiori, M., 2011. “Financial Intermediation, International Risk Sharing, and Reserve Currencies,” Unpublished paper, UC Berkeley.
Mendoza, E. G., V. Quadrini, and J.-V. Rios-Rull, 2009. “Financial Integration, Financial Development, and Global Imbalances,” Journal of Political Economy, vol. 117, pages 371-416.
Mian, A., and A. Sufi, 2009. “The Consequences of Mortgage Credit Expansion: Evidence from the U.S. Mortgage Default Crisis,” Quarterly Journal of Economics, vol. 124(4), pages 1449-1496.
Mian, A., A. Sufi, and F. Trebbi, 2010. “The Political Economy of the U.S. Mortgage Default Crisis,” American Economic Review, vol. 100(1), pages 67-98.
Obstfeld, M., and K. Rogoff, 2009. “Global Imbalances and the Financial Crisis: Products of Common Causes,” CEPR Discussion Paper 7606.
Piskorski T., and A. Tchistyi, 2010. “Optimal Mortgage Design,” Review of Financial Studies, vol. 23, pages 3098-3140
Poon, M., 2009. “From New Deal Institutions To Capital Markets: Commercial Consumer Risk Scores and the Making of Subprime Mortgage Finance,” Accounting, Organizations, and Society, vol. 34, pages 654-674.
Roback, J., 1982. “Wages, Rents, and the Quality of Life,” Journal of Political Economy, vol. 90, pages 1257-1278.
Rosen, S., 1979. “Wages-based Indexes of Urban Quality of Life.” In: P. Mieszkowski and M. Straszheim (eds.), Current Issues in Urban Economics, Johns Hopkins University Press.
Van Nieuwerburgh, S., and P. Weill, 2010. “Why Has House Price Dispersion Gone up?Review of Economic Studies, vol. 77(4), pages 1567-1606.
Volume 13, Issue 1, November 2011

Jan Eeckhout and Philipp Kircher on Sorting in Macroeconomic Models

Jan Eeckhout is a Professor of Economics at University College London and at Barcelona GSE/UPF. Eeckhout’s research has been concerned with labor markets, matching and sorting. Eeckhout’s RePEC/IDEAS profile.Philipp Kircher is a Reader of Economics at the London School of Economics. Kircher’s research has been concerned with labor markets, matching and sorting. Kircher’s RePEC/IDEAS profile.

1. Introduction

We address the notion of skill allocation across firms and across jobs, and how we can introduce the allocation of skills in otherwise standard macro models. Heterogeneity in skills and jobs is without doubt an important component of the labor market. Individuals are born with different innate ability and non-cognitive skills, they are brought up in diverse households, they have varying educational backgrounds, and their work experience and learning tends to further exacerbate differences between workers. In addition there are also differences on the demand side as jobs differ in their productivity, the span of control of managers over their workers varies, and firms employ different technologies.

In the presence of two-sided heterogeneity, the key determinant of the observed allocation and wages is whether there are complementarities between worker skills and job characteristics. Without complementarities (for example when individuals only differ in efficiency units of labor) it does not matter for efficiency where each individual is working. Putting it stark: A CEO would add no more to the value of the economy cleaning offices than orchestrating mergers and acquisitions. In a competitive market she would earn no more in one activity than the other. Her productivity could be decomposed in an additive effect for the worker and the firm: output might be higher in some occupations such orchestrating mergers and acquisitions, but it is the same for high-trained professionals as for untrained high-school dropouts.

Instead, symptomatic of complementarities in value creation is that equilibrium wages depend on both the worker characteristics and the firm types in ways that are not easily decomposable. Sorting, i.e., the matching pattern between jobs and workers, is crucial for the efficiency of the market. Efficiency is no longer simply about whether workers are employed, but the central question is whether they are employed at the right jobs. And whether the right number of people are employed in the right kind of job. A central theme in our research is the question how such complementarities shape employment patterns and wages, how this changes our modeling and thinking about the labor market, and how one might conceptually measure the importance of complementarities in existing datasets.

The aim of this research is investigate how the issue of complementarity can be embedded into standard macro environments. The models should be sufficiently tractable to gain understanding by deriving analytical results, and sufficiently rich so they answer interesting macroeconomic questions. We illustrate this approach by considering three recent strands of research on two-sided matching environments: (1) the interplay firm size and workforce quality, (2) the implications of search frictions on the sorting between firms of different productivity and workers of different qualities, and (3) the quest for evidence of sorting in existing datasets. We will discuss applications to labor economics, trade, and management as we proceed.

2. Sorting, Span of Control, and Factor Intensity

First, we consider the role of span of control and the size of firms in labor markets with heterogeneously skilled workers. Can we explain for example why the high skilled upper management in firms like Walmart have an enormous span of control over relatively low skilled workers, while in mom-and-pop retail stores the span of control is small and skills of both managers and workers are average? Or what are the consequences of information technology that improves the ability to manage many workers, such as monitoring and GPS tracking devices?

Most theories of sorting follow the tradition on Becker’s (1973) canonical model of the labor market where each firm consists of exactly one job. There the firm’s choice is about the extensive margin, i.e., which worker to hire. For a given job type, the firm chooses the optimal worker type taking wages as given. To get an intuition for the operation of this market, one key insight is the following: if more productive firms have a higher marginal product from better workers, then in equilibrium these will be the firms that indeed hire the better workers. Such complementarity between firm productivity and worker skill shapes the matching pattern. This simple theory provides interesting links between firm heterogeneity and worker’s wages. For example, if the heterogeneity of firms increases, worker’s wages become more spread out and increase especially at the top, which has been used for example to explain the changes of CEO compensation (e.g., Terviö, 2008, and Gabaix and Landier, 2007).

The main drawback of this theory is that it misses the intensive margin that is at the heart of most macro-economic models: How many workers does the firm employ? How much of the resources should be devoted to each worker in the work force? Models in the tradition of Lucas (1978) that are used to explain the size distribution of firms, address this issue of the intensive margin. They consist of a firm with one scarce resource, the time of its manager. Managers differ in productivity and they can leverage their ability over more or less workers, which are assumed to be homogenous. The key question is how many workers each manager hires. Here the complementarity is between the productivity of the manager and the size of her workforce, i.e. the intensive margin: if this is positive then more productive managers will lead larger teams, explaining the firm-size distribution in plausibly calibrated models. In recent applications Restuccia-Rogerson (2008) and Hsieh-Klenow (2010), amongst others, argue that such heterogeneity levied across different workforce size can help to explain differences across countries in capital, TFP, and factor prices.

While both the extensive and intensive margin in isolation have attracted interest, their combination raises interesting issues: Would more productive firms hire more workers, better workers, or both? How are workers with different skills affected? How does this affect managerial compensation? What are the effects of improved information technology that allows the supervision of a larger workforce? And does it depend on the particular industry and country we are considering? The objective is to incorporate a broad notion of heterogeneity on both sides of the market.

In Eeckhout and Kircher (2011b) we extend the idea of span-of-control to a heterogeneous workforce. Managers simultaneously decides on both margins: the extensive margin of worker skills and the intensive margin of workforce size. The latter determines how much managerial time can be devoted to each of the workers. The output of each worker depends on his own skill, on the quality of the manager, and the amount of supervision time that he receives. Our goal is to understand the equilibrium assignment, wages and managerial profits, and firm size. This general setup was also proposed in Rosen (1982), but solved only for a functional form that is a special case of our model, that of efficiency units of labor. Our setup also includes as special or limiting cases the functional forms of several existing models in this line of research such as Sattinger (1975), Garicano (2000), and Van Nieuwerburgh and Weill (2010). We can also adjust the setup to match the features of the Roy model (Heckman and Honore, 1990). Here we consider the competitive equilibrium outcome of the general model.

The interpretation of our results obviously extends to other setting beyond managers and workers: managerial time can as well be interpreted as the firm’s capital, time per worker represents the capital intensity, and differences in managerial skills constitute the technological productivity differences among firms. Our analysis reveals that the equilibrium sorting patterns in these markets by and large be understood by looking at four key margins. (1) Complementarities in types (extensive margins): Do better managers have a higher marginal product from working with better workers? This is the standard requirement in Becker (1973). (2) Complementarities in quantities (intensive margins): the marginal product of having more workers is increasing if more time is spent by the manager. This is standard for example in CES technologies. (3) Complementarities between manager skill and workforce size, or span-of-control: Do better managers have a higher marginal product of supervising more workers of a given skill? This is the span-of-control condition that features in Lucas (1978). (4) Complementarities between worker skills and managerial time: Do better workers have a higher marginal product of receiving more supervision time?

In general, these different margins are present, and the interesting question is how these complementarities trade off against each other. We find that better managers hire better workers if the product of the first two complementarities outweighs the product of the latter two complementarities, i.e., if (1) * (2)>(3) * (4). From standard assumptions on quantities, (2) is always positive. So the left hand side simply captures the standard “Becker” effect, and if we shut down the intensive margin by means of a Leontieff structure we recover exactly Becker’s condition ((1)>0). Yet in the presence of the intensive margin, better managers can be good in two dimensions: they can be good at working with better workers ((1) large) or they can be good at managing many worker ((3) large). And as a result, the span-of-control effect can override the standard Beckerian complementarity. Good managers have so much span that it is efficient to manage many low skilled workers rather than few high skilled ones. This holds despite the Beckerian skill complementarity. This then also gives a prediction for the firm size distribution: the better managers supervise larger groups if (3)-(4)>0 under positive sorting (and (3)+(4)>0 under negative sorting). Managers end up managing larger teams if the span effect (3) outweighs the complementarity between time spent and worker type (4). If the marginal benefit of spending time is larger than the effect of span-of-control, efficient teams are smaller for better managers.

How does this manifest itself in different industries? In the retail sector for example, high profit companies such as Walmart invest in information technology that reduces the need for high skills relative to smaller mom and pop stores ((1) small or even negative) because the cash registers and inventories are nearly trivial to operate. They also heavily invest in management and control tools that allow the supervision of many workers ((3) positive and large) because it allows them to get centralized information on performance on all registers and inventories. If supervision and training time generates more impact with better workers ((4) positive), then stores like Walmart employ the unskilled workers relative to their mom and pop counterparts. This implies negative sorting. Under negative sorting this (3) and (4) work in the same direction to create very large firms at the top: They do not need to spend much time with each employee because it is not worthwhile, and have the tools to supervise many. In that light it might not be surprising that Walmart is the largest employer worldwide. In industries with positive sorting it is much more difficult to form large teams, since it is worthwhile to spend time with each high-skilled employee. Consider management consulting, with strong complementarities in manager and subordinate skill ((1) large) but moderate span of control technologies (3 moderate). This implies positive sorting. Top firms are only larger than bottom firms if their span of control (3) outweighs the benefits from training and interacting with employees (4). Given that the two counteract, top consulting firms tend to be only moderately larger than other firms in the industry.

How can we view changes in technology? Skill-biased technological change is usually viewed as a change that makes the complementarity between worker skill and firm technology larger. But much of technological change is in terms of information technology that changes the complementarity between manager skill and the amount of workers he supervises. In this model, increases in (3) change the sorting pattern, but in particular it spreads out the firm size distribution. It makes the difference between the two parts of the second condition even larger. Big firms become even bigger relative to the small firms.

The exact levels of wages, managerial profits, and skill assignment are characterized by a simple system of two differential equations. Changes in skills or changes in technology can explicitly be analyzed by studying the response to this system, which will give deeper insights into the consequences of technological change. This is particularly relevant for international trade, where trade changes the availability of factors of production and sometimes introduces new technologies. So far, such changes have been analyzed mainly for settings in which the size of each firm is limited by the extent of the demand. Typically, firms operate in Dixit-Stiglitz type markets where consumers have preference for variety (e.g., Costinot (2010)). Our framework is different and adds to those models of trade: output has decreasing returns because of scarce managerial resources, which limits the size of the firms. The advantage is that it can be studied without functional form assumptions. But it can also be integrated into a Dixit-Stiglitz type framework. Finally, the framework is easily extended to unemployment as well, which allows to study both the compensation and unemployment for workers of different skills. Again, this might be important in trade settings, where this has been studied recently by Helpman, Itskohki and Redding (2011), yet in their setting workers are ex-ante identical and earn identical expected-payoffs, while in many trade settings we would like to start from a situation where workers of different types exist in the population.

Returning to the discussion of cross-country TFP differences, it will be interesting to see to which extent not only the heterogeneity in firm size as in Restuccia-Rogerson (2008) and Hsieh-Klenow (2010) matters to explain the differences. By introducing firm size into an otherwise standard model of sorting, the debate can be illuminated taking into account differences in skill distributions across countries, as well as the size distribution across firms. We should mention, though, that the tractability of this line of research relies on the assumption that workers and supervisors interact, but the interaction among workers is limited. They interact only to the extent that more resources devoted to one worker means that less resources (supervision time) is available for another. While substantial work on competitive markets and on combinatorial matching theory has been devoted to capture complementarities among workers (e.g., Kelso and Crawford (1982), Cole and Prescott (1997), Gul and Stacchetti (1999), Milgrom and Hatfield (2010)) the results are usually confined to existence theorems. The line of work that we follow is more restrictive, but allows clear characterizations of the size and skill level of firms, and of wages and firm profits. Conditions like the one characterizing the equilibrium allocation in our model can help build intuition for the economic mechanisms in these markets.

3. Market Frictions and Sorting

The allocation of heterogeneously skilled workers across different jobs plays a crucial role in markets with frictions. Frictions are non-negligible in the allocation process of many environments. For example in the labor market, unemployment is considered to be a natural feature that arises when firms and workers need time to find a suitable match. Sorting models that go beyond the competitive market conditions can describe unemployment patterns across worker skills.

Recall that Becker (1973) showed that in a market without frictions, complementarities — or equivalently supermodularity of the match output — between firm and worker types lead to positive sorting where more productive firms hire better skilled workers. The match surplus is supermodular if the marginal contribution of a better worker is higher in a better firm, i.e., if the cross-partial of match output with respect to worker and firm type is positive. For the case of frictions, the most well-known analytic result by Shimer and Smith (2000) is derived in a setting with random search frictions and pairwise matching. Parties that are matched bargain whether to stay together and produce, or to separate and wait for another meeting, where the future is discounted. They prove that complementarities between worker and firm types (supermodularity of the match surplus) are not sufficient to ensure that more productive firms hire more productive workers. That means that there are production technologies where the better firms have a larger gain from hiring the better workers, but still they tend to hire less able workers.

Intuitively the reason is the following. In competitive markets the firms know they can trade, and their only consideration is which worker they would rather hire. In the presence of frictions, they do not only care about whom to hire, but also about whether they can hire at all. For a more productive firm the opportunity cost of being without a worker is higher, and so they are more eager to ensure a match now rather than waiting. This logic extends to matching patterns in the marriage and housing markets, which makes the model generally applicable. Unfortunately, because of the mismatch inherent in random search, the mathematical conditions to ensure positive sorting do not relate directly to the matching frictions, and it is difficult to get an intuition about the forces that operate in this market. Nor are the wages or employment patterns easily characterized because the randomness of the process exposes firms and workers to many trading partners.

In Eeckhout and Kircher (2010) we build on this work and that by Shi (2001). We point out that when there is heterogeneity, the absence of information about prices in the random search model is a strong assumption. Agents are assumed to meet many trading partners that they would have rather avoided, and the transfer price has to be determined at the time of the meeting through bargaining. In contrast, we analyze a world where buyers can observe the type of their trading partner as well as the price the seller posts. Because trade is decentralized, trading frictions still exist, for example due to congestion. In this world, prices guide the trading decisions just like in the Walrasian model of Becker (1973), only now delay remains an equilibrium feature that is taken into account in the price setting.

We address the role of price competition in markets with matching frictions and how it leads to sorting of heterogeneous agents. With frictions there are two aspects of value creation: the match-value when two agents actually trade, and the probability of trading governed by the search technology. We find that positive assortative matching obtains if the complementarities in output creation are larger than the complementarities in finding a trading partner, as measured by the elasticity of substitution in the output and the matching function. The condition has a simple economic interpretation. Complementarities in matching mean that better firms would like to employ better workers, capturing the forces in Becker (1973). But in case a firm does not manage to find a worker is cannot produce, and the productive firms have most to lose from inactivity. If they can increase their matching prospects by attracting low-skilled workers, they would do this, given a tendency against positive sorting captured through the matching function.

For standard matching functions, our condition is fullfiled if and only if the output function is root-supermodular, i.e., the (square-)root of the output function is supermodular. This means that the extent of complementarity needed is less than under random search, but still stronger than in the frictionless environment. To see this, we show that in the presence of random search frictions as in Shimer and Smith (2000), log-supermodularity is neccessary for positive assortative matching, while with no frictions at all (Becker 1973) there is positive assortative matching under mere supermodularity. In the neoclassical world, there are no frictions and all agents are assumed to have full information about the prices and types when they decide which type to accept. At the other extreme, Shimer and Smith (2000) assume that there are random search frictions and agents cannot observe prices and types until after they meet. When there is price competition, prices partly mitigate frictions by directing the heterogeneous types to the most adequate market, thus avoiding inefficient meetings with undesirable types.

The economic interpretation of this result is transparent in terms of the fundamentals of the economy, and it prominently features the role of heterogeneity together with matching frictions. In the absence of any complementarities, sorting is not important for the creation of match-value. The key aspect is to get matched at all. Due to congestion, high-type buyers would like to trade where few other buyers attempt to trade. This allows them to secure trade with high probability, and they are willing to pay for this. While sellers know that they might be idle if they attract few buyers on average, some are willing to do this at a high enough price. The low-type sellers are those who find it optimal to provide this trading security, as their opportunity cost of not trading is lowest. This results in negative assortative matching: high-type buyers match with low-type sellers. It follows that sufficient complementarity is needed in order to obtain positive assortative matching.

We can also introduce frictions when firms differ in size, i.e. as above, when there is both an intensive and an extensive margin to the firm decision. Integrating labor market frictions into the model, we show how unemployment varies across worker types. It naturally follows form the setup that unemployment decreases in the skill type of the worker. Instead, the frictions of the firms in vacancy creating are ambiguous. Larger firms can in general face higher or lower frictions, depending on whether firm size is increasing in type.

4. Using Mismatch to Identify Complementarities

Despite the casual observation that better firms hire better workers, there is unfortunately little or no evidence to support this. Are more skilled workers really more productive in better firms? The amount of effort and resources organizations invest in hiring the “right” person for the job indicates that they are. This then is indirect evidence of complementarities in production and implies that the exact allocation is important for efficiency. Yet, there is little direct evidence. The most widely cited work concludes that there is no corroboration of complementarity between workers and jobs. In a seminal paper, Abowd, Kramarz and Margolis (1999) analyze the correlation between firm and worker fixed effects from wage regressions. The obtained correlation aims to provide evidence whether or not there is complementarity or substitutability, and if so how big the coefficient is. The idea is that more productive firms pay higher wages than lower wage firms irrespective of the exact worker they hire, and the firm fixed effect therefore recovers the ranking of the firms.

While this appears plausible, it turns out that in a simple model this logic is flawed. The key ingredient to identify the presence of complementarities is mismatch. Whether it be due to search frictions or information frictions, the fact that we observe agents in less than the optimal job generates an inefficient allocation relative to the frictionless outcome, and at the same time it provides sufficient information on the extent of the complementarity. Consider a worker-job pair with mismatch. In the presence of a friction, there is a tradeoff between separation followed by a new match and staying in the current match. For given frictions, the larger the mismatch, the larger the incentive to face the cost of search and rematch.

This has implications for how the wages are determined. In Eeckhout and Kircher (2011a) we show first that the wage for a given worker is non-monotonic in the type of his employer. This is due to the fact that in a sorting model, wages reflect the opportunity cost of mismatch. The key observation here is that for a given worker there can be mismatch both with too bad a firm and too good a firm. The surplus of a match is determined by the value of the match after subtracting the outside option of rematching. When matched with too low a firm type, the worker is better off with a higher firm type, and when matched with too high a firm type, the worker is better off matching with a worse firm type. Therefore match surplus for a given worker is inverted U-shaped in firm type. With transferable utility, this surplus is divided and therefore wages are also inverted U-shaped. In particular, the marginal firm type that is too low and the marginal firm type that is too high must generate a surplus that is zero in both cases: continuing the match must generate the same value as separation. This then implies that wages at the marginal firm type are the same.

The non-monotonicity of wages in firm type implies that the standard procedure to use firm fixed effects and correlate it with worker type is ill-suited. That procedure requires the identifying assumption that wages are monotonic in firm type, which is not the case when there is mismatch. Because of the non-monotonic effect of firm type on wages, the wage cannot be decomposed in an additively separable firm and worker fixed effect. We show analytically that the misspecification is not innocuous: for the most common specifications in the literature the firm fixed effect misses any direct connection to the true type of the firm.

Instead, a simple algorithm allows us to back out (the absolute value of) the degree of complementarity. The main source of identification is the search behavior by workers that differs when the degree of complementarity is high, and when as a result, sorting is important. First, we extract from the range of wages paid what the cost of search is. The highest observed wage corresponds to the wage obtained in a frictionless market and we use this to order the workers and obtain the type distribution. Likewise, we can obtain an order of the firms by the level of wages that they pay. The difference between the highest and the lowest wage corresponds to the cost of search. Second, given the search cost, the fraction of the firm population that an agent is willing to match with, i.e., the matching set, identifies the strength of the complementarity as expressed by the (absolute value of the) cross-partial of the production function. This is possible because the strength of the cross-partial directly reflects the output loss due to mismatch.

The shortcomings of the fixed effects regressions have also been pointed out in other work (Lopes de Melo, 2008, Lise, Meghir and Robin, 2008, and Bagger and Lentz, 2008). Their simulations and calibrations of search models with strong complementarities and sorting nonetheless generate small or even negative correlations of the simulated fixed effects of workers and firms. We provide a theoretical foundation for this finding, and Gautier and Teulings (2004, 2006) propose a second-order approximation method to get around the shortcomings of the fixed effect regressions.

Looking forward, for applied work it is desirable to introduce heterogeneity and allocative efficiency in otherwise standard macro models. Too often models of heterogeneity are augmented representative agent models. For good reasons of course, because modeling is complicated. That makes the quest to find simple results and a tractable setup in the context of sufficiently rich economic heterogeneity important, despite the obvious challenges.

5. References

Abowd, John M., Francis Kramarz and David N. Margolis, 1999. “High Wage Workers and High Wage Firms,” Econometrica, Econometric Society, vol. 67(2), pages 251-334.
Bagger, Jesper and Rasmus Lentz, 2008. “An Empirical Model of Wage Dispersion with Sorting,” University of Wisconsin manuscript.
Becker, Gary S, 1973. “A Theory of Marriage: Part I,” Journal of Political Economy, University of Chicago Press, vol. 81(4), pages 813-46.
Cole, Harold L. and Edward C. Prescott, 1997. “Valuation Equilibrium with Clubs,” Journal of Economic Theory, Elsevier, vol. 74(1), pages 19-39.
Costinot, Arnaud,2009. “An Elementary Theory of Comparative Advantage,” Econometrica, Econometric Society, vol. 77(4), pages 1165-1192.
Eeckhout, Jan and Philipp Kircher, 2010. “Sorting and Decentralized Price Competition,” Econometrica, Econometric Society, vol. 78(2), pages 539-574.
Eeckhout, Jan and Philipp Kircher, 2011a. “Identifying Sorting–In Theory,” Review of Economic Studies, Oxford University Press, vol. 78(3), pages 872-906.
Eeckhout, Jan and Philipp Kircher, 2011b. “Assortative Matching and the Size of the Firm”, manuscript.
Gabaix, Xavier and Augustin Landier, 2008. “Why Has CEO Pay Increased So Much?,” The Quarterly Journal of Economics, MIT Press, vol. 123(1), pages 49-100.
Garicano, Luis, 2000. “Hierarchies and the Organization of Knowledge in Production,” Journal of Political Economy, University of Chicago Press, vol. 108(5), pages 874-904.
Gautier, Pieter A. and Coen N. Teulings, 2004. “The Right Man for the Job,” Review of Economic Studies, Wiley Blackwell, vol. 71(2), pages 553-580.
Gautier, Pieter A. and Coen N. Teulings, 2006. “How Large are Search Frictions?,” Journal of the European Economic Association, MIT Press, vol. 4(6), pages 1193-1225.
Gul, Faruk and Ennio Stacchetti, 1999. “Walrasian Equilibrium with Gross Substitutes,” Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124.
Hatfield, John William and Paul R. Milgrom, 2005. “Matching with Contracts,” American Economic Review, American Economic Association, vol. 95(4), pages 913-935.
Heckman, James J. and Bo E. Honoré, 1990. “The Empirical Content of the Roy Model,” Econometrica, Econometric Society, vol. 58(5), pages 1121-49.
Helpman, Elhanan, Oleg Itskhoki and Stephen Redding, 2010. “Inequality and Unemployment in a Global Economy,” Econometrica, Econometric Society, vol. 78(4), pages 1239-1283.
Hsieh, Chang-Tai Peter J. Klenow, 2010. “Development Accounting,” American Economic Journal: Macroeconomics, American Economic Association, vol. 2(1), pages 207-23.
Kelso, Alexander S. Jr and Vincent P. Crawford, 1982. “Job Matching, Coalition Formation, and Gross Substitutes,” Econometrica, Econometric Society, vol. 50(6), pages 1483-1504.
Lise, Jeremy, Costas Meghir, and Jean-Marc Robin, 2008. “Matching, Sorting and Wages”, UCL manuscript.
Lopes de Melo, Rafael, 2008. “Sorting in the Labor Market: Theory and Measurement”, Yale manuscript.
Robert E. Lucas Jr., 1978. “On the Size Distribution of Business Firms,” Bell Journal of Economics, The RAND Corporation, vol. 9(2), pages 508-523.
Restuccia, Diego and Richard Rogerson, 2008. “Policy Distortions and Aggregate Productivity with Heterogeneous Plants,” Review of Economic Dynamics, Elsevier, vol. 11(4), pages 707-720.
Sattinger, Michael, 1975. “Comparative Advantage and the Distributions of Earnings and Abilities,” Econometrica, Econometric Society, vol. 43(3), pages 455-68.
Shi, Shouyong, 2001. “Frictional Assignment. I. Efficiency,” Journal of Economic Theory, Elsevier, vol. 98(2), pages 232-260.
Shimer, Robert and Lones Smith, 2000. “Assortative Matching and Search,” Econometrica, Econometric Society, vol. 68(2), pages 343-370.
Terviö, Marko, 2008. “The Difference That CEOs Make: An Assignment Model Approach,” American Economic Review, American Economic Association, vol. 98(3), pages 642-68.
Van Nieuwerburgh, Stijn and Pierre-Olivier Weill, 2010. “Why Has House Price Dispersion Gone Up?,” Review of Economic Studies, Wiley Blackwell, vol. 77(4), pages 1567-1606.

Volume 12, Issue 2, April 2011

Karel Mertens and Morten Ravn on Fiscal Policy, Anticipation Effects, Expectations and Crisis

Karel Mertens is an Assistant Professor at Cornell University. Karel’s research has been concerned with monetary and fiscal policy. Merten’s RePEc/IDEAS profile.Morten O. Ravn is a Professor of Economics at University College London and a Research Fellow of the Centre for Economic Policy Research, London. Ravn’s research has been concerned with fiscal policy, business cycles, and international macroeconomics. Ravn’s RePEC/IDEAS profile.

1. Introduction

Our recent research has focused upon macroeconomic aspects of fiscal policy but we have also looked into liquidity traps and theories of expectations driven crises. We have been particularly interested in the topic of expectations and fiscal policy. In a line of papers we have examined the empirical evidence regarding anticipation effects of fiscal interventions. We have also examined how modern DSGE models can account for the empirical regularities that we uncover regarding the impact of tax policies. We find that DSGE models are powerful labs for thinking about tax policies. Another line of our research is examining how to exploit narrative accounts when estimating the impact of fiscal shocks but without making extreme assumptions regarding the reliability of the narratives.

We have also looked into the question about the efficacy of fiscal policy instruments in situations where there are binding constraints on the standard monetary policy instrument (the short term interest rate). We have shown how models that form the basis for arguments in favor of large spending multipliers and small (even negative) labor income tax multipliers in liquidity traps allow for the existence of another –expectations-driven– liquidity trap. Importantly, in this alternative equilibrium, government spending loses potency while labor income tax changes gain efficacy. We have also shown how financial frictions can lead to very deep recessions following a wave of pessimistic beliefs that drive the short term nominal interest rate to its lower floor.

2. Estimating anticipation effects of tax policy interventions

Fiscal interventions are often partially known well in advance of their implementation. For that reason, fiscal policy interventions may be associated with anticipation effects, i.e. policies may affect the economy prior to their actual implementation. A partial list of reasons for the presence of such anticipation effects include: (i) Fiscal interventions usually need to pass through democratic institutions resulting in delays between the formulation of a policy and its implementation; (ii) Temporary tax or spending changes introduce anticipation effects through sunsets. Such measures are common for e.g. investment tax credits and for consumption taxes (the 2008/09 temporary VAT cut in the UK is a recent example); (iii) Major policy interventions may sometimes be phased-in; (iv) Policies may have been part of election campaigns and therefore anticipated long before their implementation.

Whatever the reason, the presence of such anticipation effects may be an important aspect to take into account when estimating fiscal shocks and their impact upon the economy. If ignored, researchers not only exclude potentially important information but may also mistime shocks. Moreover, fiscal policy shocks provide an interesting lab for examining the empirical relevance of “news driven business cycles,” see e.g. Beaudry and Portier (2007). In their seminal piece, Blanchard and Perotti (2002) found anticipation effects to be of little empirical relevance. Their estimation approach exploits the existence of reaction lags to obtain identification of fiscal shocks in a vector autoregression (VAR) framework. In the face of anticipation effects, this approach requires one to assume reaction lags that exceed the anticipation period. Thus, when using quarterly data, if fiscal shocks are anticipated, say 3 or 6 months in advance, reaction lags need to be at least 9 months, an assumption that appears implausible. For that reason, their analysis of anticipation effects was limited to a one quarter anticipation horizon and they found little evidence that fiscal shocks impact on the economy ahead of their implementation. Moreover, their estimates of the effects of implemented fiscal policies were very similar regardless of whether they allowed for a one quarter anticipation period or not.

In practice, fiscal policy interventions may sometimes be known years in advance of their implementation making the Blanchard and Perotti (2002) approach unattractive. To address this issue, Mertens and Ravn (2010a) apply a technique akin to Poterba (1988) in order to estimate anticipation effects. We study the impact of tax liability changes using the US tax narrative provided by Romer and Romer (2008). We focus upon those changes in tax liabilities that these authors deem “exogenous” (an assumption that we test formally in terms of Granger non-causality and fail to reject). For each piece of tax legislation we define an announcement date and an implementation date. When the difference between these two dates exceeds 90 days, we assume that the tax liability change is pre-announced and allow for anticipation effects. Following Poterba (1988) we define the announcement date to be the date at which the tax bill became law, a definition that is conservative but meaningful since it removes uncertainties regarding the policy’s implementation. We find that around half of the tax changes were anticipated and that the median anticipation lag is 6 quarters, a lag much longer than that considered by Blanchard and Perotti (2002).

We translate the tax liability changes into average tax rate equivalents by measuring them relative to aggregate output. We discriminate between anticipated and unanticipated tax changes by (a) allowing for differential effects after their implementation and (b) by assuming that anticipated tax changes enter the information set from their announcement.

We find that a pre-announced tax cut with an anticipation horizon of 6 quarters gives rise to pre-implementation declines in aggregate output, investment and hours worked. The largest pre-implementation drops in these variables occur around a year before the implementation and aggregate investment reacts particularly elastically with a decrease of 4% below trend following a 1% pre-announced cut in the average tax rate. The peak pre-implementation drop in output is estimated to be around 1.5%. In contrast, aggregate consumption is hardly affected by the announcement, a result that is consistent with earlier analysis of aggregate and household level consumption data, see e.g. Parker (1999), Poterba (1988), or Souleles (2002). The finding that investment, output and hours worked drop during the pre-implementation period has two important consequences. First, one cannot conclude that the lack of a consumption response to tax announcements indicates that the private sector is not forward looking. Secondly, we find that good news (a tax cut) have negative consequences before its implementation which is not consistent with the news driven business cycle hypothesis. We also show that the anticipation effects are very small at short anticipation horizons which render our results consistent with those of Blanchard and Perotti (2002).

Once a tax cut is implemented, it provides a major stimulus regardless of whether it was pre-announced or not. A 1% cut in taxes leads to an increase in aggregate output just below 2% with the maximum impact taking place around 10 quarters after the implementation of the tax cut. The results are robust to eliminating particular types of tax changes, to the choice of the sample period, and to controlling for other structural shocks such as monetary policy shocks and changes in government spending.

We then ask if tax policy shocks have been an important impulse to US business cycles. For the post World War II sample we find that tax policy shocks have accounted for 25-30% of the in-sample variance of output at the business cycle frequencies. We also find that tax policy shocks were important for particular business cycle episodes. One controversial result is that the early 1980’s recession to a large extent can be accounted for by the combination of the implementation pre-announced tax increases associated with the 1977 Social Security Tax Amendments and the announcement of future tax cuts incorporated in the Economic Recovery Tax act of 1981. This result holds after controlling for the impact of the Volcker disinflation and for changes in government spending. Thus, we argue that tax policy shocks should be high on the list of macroeconomists’ candidates for business cycle impulses.

Another implication of our results is that it might be relevant to control for fiscal shocks when estimating the impact of other structural shocks. In Mertens and Ravn (2011c) we argue that allowing tax changes to have permanent effects on labor productivity may be important for the estimation of permanent neutral technology shocks and their effects. In an application to US time-series data we show that once one controls for taxes, a positive permanent neutral technology shock implies an increase in hours worked and technology shocks matter for business cycles.

3. Anticipation and Vector Autoregressions

The results discussed in the previous section indicate that fiscal news effects are empirically relevant. This has important implications. Suppose that one was to estimate fiscal shocks and their effects using a structural VAR approach. If fiscal news is relevant but not controlled for, a VAR estimator would potentially get the timing of shocks wrong and this could lead to serious problems. In an important contribution Ramey (forthcoming, 2011) argues that such mistiming accounts for why researchers that have applied SVARs find a positive impact of government spending shocks on private consumption and on real wages. She shows that professional forecasts and narrative accounts can forecast SVAR estimates of government spending shocks. Using information from professional forecasters, she finds instead that government spending shocks lower consumption and real wages.

Building upon Hansen and Sargent (1991), a very insightful paper by Leeper, Walker and Yang (2008) develops a number of key results regarding the impact of fiscal news on VARs. A key point of their analysis is that, if news are not controlled for, fiscal VARs not only mistime the shocks but have non-fundamental moving average representations which can give rise to non-structural errors and misleading impulse response functions.

The approach in Mertens and Ravn (2010a) addresses this issue directly by including fiscal news in the relationships from which we estimate the impact of fiscal shocks but this is only possible due to the use of narrative tax data and such data may often not be available. Mertens and Ravn (2010b) demonstrate that rational expectations models introduce restrictions on the non-fundamental roots of the MA representations that allows one “ex-post” to examine the sensitivity of SVAR based estimates of the impact of fiscal shocks to news shocks. The key property that we exploit is that rational expectations models imply that fiscal news are discounted at a constant rate which we, along with Ljungqvist and Sargent (2004), denote the anticipation rate. The anticipation rate in the simplest Ramsey model corresponds to the inverse of the unstable root of the characteristic polynomial that determines the law of motion of the capital stock. This parameter turns out to be an input into Blaschke matrices that Lippi and Reichlin (1994) show can be used to flip the roots of the MA representation of the empirical VAR. To be precise, the Blaschke matrices take as inputs the anticipation rate and the anticipation horizon and we suggest that one may calibrate the former of these parameters using economic theory and then compute impulse responses for alternative anticipation horizons.

We exploit these insights to derive a new structural VAR estimator that we implement using a VECM formulation (and denote the new estimator for the VECM-BM estimator). We show that standard DSGE models imply anticipation rates that are very close to one unless agents discount future utility heavily or are close to risk neutral. For “standard” calibrations, the anticipation rate is somewhere between 92 and 96% per quarter. In this case the non-fundamentalness of SVARs is not a very serious problem. To put it simple, when the anticipation rate is high, although the econometrician’s information set when estimating a VAR is smaller than that of the agent (who has information about future fiscal innovations), current actions incorporate a lot of information about the future innovations. When the anticipation rate is low, misalignment of information is instead more serious and lead to very misleading VAR-based impulse response function estimates.

We apply the new VECM-BM estimator to quarterly US time series data for the sample period 1954-2006 and estimate the impact of permanent government spending shocks. The identifying assumptions are that government spending is unaffected contemporaneously by other structural shocks, that anticipated and unanticipated shocks are orthogonal, and that their long-run impacts are proportional. Assuming an anticipation horizon of 8 quarters we find that a permanent increase in government spending increases aggregate output and consumption when it is announced regardless of whether it is anticipated or not. This result is consistent with independent evidence in Fisher and Peters (2010). Thus, we find no evidence that mistiming accounts for the positive consumption response to government spending shocks estimated in the SVAR literature. This may imply that it is too soon to dismiss theories that deliver such positive consumption responses (see e.g. Ravn, Schmitt-Grohe and Uribe, 2006, 2007).

3. Understanding the Effects of Anticipated and Unanticipated Tax Policy Shocks

There is a long tradition in macroeconomics of thinking about the ways in which agents react to anticipated fiscal shocks. An early contribution to this literature is the seminal paper of Hall (1971) and more recent important papers include by Auerbach (1989) and Yang (2005). In Mertens and Ravn (2011a) we extend this literature by asking whether a DSGE model can account quantitatively for the impact of anticipated and unanticipated tax policy shocks that we discussed in Section II above.

Our benchmark model is a flexible price DSGE model in which a representative household maximizes utility, there are no liquidity constraints and firms are competitive. We introduce features such as variable capital utilization, investment adjustment costs, habit formation, and a distinction between durable and non-durable consumption goods. Tax liability changes derive from changes in average (and marginal) labor and capital income tax rates and from changes in capital depreciation allowances due to changes in capital income tax rates. Exogenous changes in tax rates are either anticipated or unanticipated and we assume an anticipation horizon of 6 quarters (which corresponds to the median anticipation horizon in the US data). Agents living in this economy therefore have information about current and future innovation in tax rates and their information sets evolve in a recursive manner. Interestingly, the information structure implies that agents aggregate tax news according to their remaining anticipation lag, a property that we exploited in Mertens and Ravn (2010a) discussed above. One important consideration is the financing of the changes in tax rates. In our benchmark model we assume that the government holds constant government expenditure and varies lump-sum taxes (or government debt) in response to changes in revenues deriving from factor income taxation.

We estimate a subset of the structural parameters using indirect inference by matching the empirical impulse response functions. The estimator takes into account that the empirical estimates of the impact of tax changes are based on VAR models with a finite set of lagged tax changes. The DSGE model implies a very similar VAR model but with an infinite set of lagged tax changes. The importance of the lagged tax changes depend on a dampening matrix with roots that are determined by the persistence of the tax rate processes. These roots are large in practice and for that reason we simulate data from our model and estimate the structural parameters by matching the impulse response functions subject to the VAR filter. Our benchmark estimates of the structural parameters are within the range of values estimated in other recent studies. We find, for example, a relatively high habit persistence parameter (of close to 90%) and a Frisch elasticity of labor supply in the neighborhood of one. This value is on the higher side relative to estimates from the labor literature but lower than standard estimates in the macro literature.

We find that the DSGE model can account very precisely for the estimated impulse response functions. According to our results, a typical tax liability cut is a very persistent drop in labor income tax rates and a more temporary U-shaped, drop in capital income tax rates. As in the data, the model implies that implemented tax cuts give rise to a major boom in the economy with a elastic response of investment and a muted increase in hours worked. The model is also consistent with the empirical finding that a pre-announced tax cut leads to a pre-implementation drop in aggregate output, hours worked and investment.

It would appear a priori that the biggest challenge would be to account for the lack of a positive consumption response to a pre-announced tax cut that we estimate in the US data. The model’s ability to account for this feature derives from the importance of substitution effects relative to wealth effects. Wealth effects are small because the cut in income tax rates are debt financed but substitution effects can be large (and indeed are so in our benchmark results). Another important feature of the model in accounting for the shape of the consumption response is complementarity between consumer durables and consumer non-durables. Habit formation is also an important aspect but mostly when it comes to accounting for the gradual response of consumption to implemented tax cuts estimated in the US data. We also show that the muted response of hours worked to implemented tax cuts derive from the opposing effects of a temporary increase in after-tax wages and a more persistent (and bell-shaped) increase in the after- tax real return on capital which initially holds down the labor supply response.

A skeptic’s response to these results could be that we minimize the importance of wealth effects by assumption by excluding liquidity constraints and by not allowing changes in tax revenues to affect government spending. We therefore extend our analysis along both these lines. We find that allowing for feedback of tax revenues on government spending improves the fit of the model but changes little in terms of implications. Our estimates imply an elasticity of government spending to tax revenues of just above 20%. Following Galí, Lopez-Salido, and Valles (2007), we combine the introduction of liquidity constraints with a labor market distortion. We find an estimate of the share of liquidity constrained agents of only 15% of the population. The reason for this is very low estimate is that a high share of liquidity constrained agents is inconsistent with the elastic response of investment to changes in tax rates. This estimate is much smaller than the calibration of 50% in Galí, Lopez-Salido, and Valles (2007) (see also Canova and Ravn, 2000, for a similar calibration in a model of taxes and the welfare state).

We take away from this analysis the lesson that DSGE models are powerful laboratories for thinking about the macroeconomic impact of tax liability changes. There is still much to be explored such as monetary-fiscal interactions, the importance of fiscal rules, the impact of nominal rigidities etc. but even a quite stylized model appears broadly consistent with the empirical evidence on the impact of tax changes.

As mentioned, a key aspect one needs to consider when formulating fiscal policy models are how fiscal instruments adjust endogenously to changes in output, debt, etc. It is well-known that the impact of government spending shocks depends crucially upon their financing. When distortionary tax rates adjust endogenously to finance spending induced deficits, the distortions may partially undo the stimulating impact of higher government spending that occurs through wealth effects in standard models. The difficulty is that it is challenging to estimate such feedback mechanisms in practice. In Cloyne, Mertens and Ravn (2011) we address these issues by estimating the endogenous responses from narrative data and then feeding them into a DSGE model. The use of narrative data allows us to explore interesting non-linear features such as the fact that it is to some extent random under which circumstances policy makers adjust instruments in response to e.g. changes in government debt. We believe that this analysis is very important especially in the current environment where fiscal retrenchments are taking place and where there are rising concerns about rising levels of government debt.

5. Estimating the Impact of Fiscal Shocks Using Narrative Data

The empirical fiscal policy literature has lived a rather schizophrenic life in which one part of the literature has applied VAR based estimators while another part of the literature has relied upon narrative accounts. The former of these strands assumes fiscal policy shocks unobservable but estimable subject to identifying assumptions typically relating to timing assumptions, calibration of contemporaneous elasticities, or the use of sign restrictions (see Mountford and Uhlig, 2009, for an example of the latter). Another literature instead adopts the narrative approach and relies on the exogeneity of particular tax or spending episodes for identification. This divide would be of little interest were it not the case that key objects of interest such as the implied tax multipliers differ wildly across estimators and appear to be related to methodology. Thus, while Blanchard and Perotti (2002) find tax multipliers typically below one, Romer and Romer (2010) find a multiplier of 3 (but with a long lag). Clearly, such levels of discrepancy in the results are worrying.

Mertens and Ravn (2011d) analyzes how these two strands of the literature can be combined and we find results that allow one to understand why previous estimates have differed so markedly. We assume that narratively identified fiscal policy shocks are noisy signals of the “true” latent policy shocks. This assumption reflects both that narrative accounts carry information but also that measurement error may be a concern. We also assume that the narratively identified fiscal shocks are Granger non-caused by the observables and orthogonal to other structural shocks. We then derive a new narrative fiscal VAR estimator that relies on the use of narratively identified policy innovations as proxies of the structural fiscal shocks. We apply the estimator to US data using the Romer and Romer (2008) narrative tax account as a proxy for the tax shock. Our identification scheme allow for estimation of both the spending response to tax shocks and of the tax revenue response to contemporaneous changes in aggregate output. The former of these two parameters is customarily assumed to be zero in the SVAR literature while the latter is calibrated to values that derive from estimates of the elasticity of tax base to (cyclical) output combines with institutional information regarding the elasticity of tax revenues to the tax base.

We find estimates of the impact of tax shocks that are much larger than those of Blanchard and Perotti (2002). A one dollar cut in taxes according to our results give rise to an impact increase in output of more than 2 dollars and the peak response of output is above 3 dollars which occurs around 1.5 years after the tax cut. What accounts these much larger tax multipliers? Our estimates imply a much higher elasticity of tax revenues to GDP (3.14) than the calibration of Blanchard and Perotti (2002) who assume a value of 2. Since an increase in taxes lowers output, this higher estimate of this elasticity implies (due to a standard endogeneity bias) a higher tax multiplier. We believe that this is important because the SVAR literature’s calibration of this parameter relies upon estimates from studies that may suffer from the exact same endogeneity problem that led the SVAR literature to calibrate certain parameters. Caldara (2010) contains an insightful discussion of these issues in a VAR setting. We provide further evidence on the plausibility of this higher contemporaneous elasticity of tax revenues to output by showing that it implies a much better out-of-sample forecast of tax revenues than standard VAR estimates.

Relative to Romer and Romer (2010), our analysis allows for measurement error in the mapping between the narrative identification of the tax shock and the “true” tax shocks while Romer and Romer (2010) along with the rest of the literature assumes that the narrative identification delivers the actual tax shocks. Thus, we argue that there may be an attenuation bias at short forecast horizons and find higher impact responses of output to tax shocks than Romer and Romer (2010). Finally, we evaluate the precision of the Romer and Romer (2008) narrative tax shock identification by means of estimate of its statistical reliability measure which we find to be close to 70%.

We believe that the estimator has a lot of interesting future applications since it allows one to exploit narrative identifications without making extreme assumptions regarding their quality.

6. Fiscal Policy in a Liquidity Trap

The recent downturn in aggregate activity in much of the world economy has triggered a lively discussion about fiscal policy effectiveness. In a line of very influential papers, Christiano, Eichenbaum and Rebelo (2010), Eggertsson (2009) and Woodford (2011) examine the impact of fiscal shocks in sticky price models where monetary policy is described by a rule for the short term nominal interest rate and where a shock takes the economy to the zero lower bound. In these analyses, a sufficiently large and temporary decline in the “efficient rate of interest” (due to a large increase in desired savings, an increase in the interest rate differential between lending and deposit rates, productivity shocks etc.) is the source of the liquidity trap (see Eggertsson, 2010). When the shock is so large that the central bank’s attempts to cut the real interest rate takes the nominal rate to its lower bound, a potentially large drop in output is needed to clear the goods market. These papers argue that the government spending multiplier (and the consumption tax multiplier) can be very large in a liquidity trap when the lower bound on the nominal interest rate is binding (or the interest rate is constant). Moreover, the marginal spending multiplier is very large when the drop in output in liquidity trap is very large. Labor income taxes instead lose potency in a liquidity trap and it may even be the case that higher taxes stimulate output in a liquidity trap. These results all refer cases in which the fiscal stimuli are removed once the liquidity trap terminates. Woodford’s analysis shows that expansionary fiscal policies may be optimal in such circumstances.

In Mertens and Ravn (2010c) we build on an insight from the seminal contribution of Benhabib, Schmitt-Grohe and Uribe (2002) that interest rate rules can lead to multiple steady-states where one of these is is a permanent liquidity trap. We examine stochastic temporary sunspot equilibria – temporary episodes of expectations driven liquidity traps. We show that such equilibria exist in the sticky price model when pessimistic beliefs are sufficiently persistent. Intuitively, if agents become pessimistic for a sufficiently long period, their pessimism drives them to increase savings and producers to cut prices making this liquidity trap equilibrium self-fulfilling. The per-period drop in output is more dramatic the less persistent is the pessimistic state (but the equilibrium ceases to exist if the pessimistic state is too transitory) and also depends on preferences and on the extent of nominal rigidities. One could wonder whether higher inflation targets would eliminate these types of equilibria? We find that higher inflation targets increase the critical level for the persistence of pessimistic beliefs for which the self-fulfilling expectational equilibria can exist but only marginally so and come with cost of more dramatic output costs in a liquidity traps when they occur.

We examine the potency of fiscal policy in a liquidity trap when it arises due to expectations. We find that a (marginal) government spending stimulus implemented during an expectations driven liquidity trap is less potent than during normal times. The same is the case for a marginal cut in consumption taxes. A marginal cut in labor income taxes instead is associated with a larger multiplier than in normal times. These results are exactly the opposite of those of the literature referred to above. How come? Consider first the fundamentals driven liquidity trap case. Suppose agents’ valuation of current consumption drops drastically which leads to an increase in desired savings and a drop in inflation. If the economy ends up with nominal short-term interest rates at their lower bound, output needs to drop significantly to clear the goods market. In such a situation, an increase in government spending stimulates output through demand directly and indirectly through the real interest rate drop implied by the inflationary pressures that occur after an increase in spending. A cut in labor income taxes in contrast stimulates even further savings (for intertemporal reasons) and lowers current output even more because of a further fall inflation. Now consider an expectations driven liquidity trap. Agents start expecting lower income and inflation and if these pessimistic beliefs are sufficiently persistent, the economy sets on a path of self-fulfilling pessimistic expectations. In this scenario, when government spending rises, agents need to be even more pessimistic for the equilibrium to survive and this gives rise to a considerable amount of crowding out. A cut in labor income taxes instead is very effective because it implies that the self-fulfilling equilibrium can occur with milder drops in output.

One direct implication of these results is that statements about the potency of fiscal policy in a liquidity trap need to be made contingent upon its source. Without such information, caution may be the better option. Another implication is that it is important to reconsider ways in which policies can help avoiding expectations driven liquidity traps.

One reaction to our analysis would be that the implications do not seem consistent with empirical evidence regarding the effectiveness of fiscal policy during the Great Depression. On the other hand, it is hard to find any hard evidence that government spending was particularly effective during Japan’s long-lived liquidity trap. Added to this is the recent experience of a country like the UK where there seems to be little evidence that the spending hike during the early parts of the crisis did much to hinder a significant drop in output. Yet we do not know the counterfactuals so future research will hopefully help in settling the score between the competing theories.

7. Liquidity Traps and Credit Channels

One result coming out of the research discussed above is that the output drop in a stochastic sunspot can be quite large. This result is important because the (per period) output losses that occur in a permanent (expectations driven) liquidity trap tend to be minor. This result has led us to further explore the properties of stochastic sunspot equilibria in models with more elaborate financial markets.

Mertens and Ravn (2011b, 2011e) consider stochastic sunspot equilibria in a model with patient consumers and impatient entrepreneurs, housing, and collateral constraints as formulated by Iacoviello (2005). Housing provides utility for households and is an input to production for entrepreneurs. We assume a collateral constraint for entrepreneurs which allows for leverage and relates entrepreneurial real estate debt to the expected resale value of their property portfolios. In a self-fulfilling expectations driven liquidity trap, the collateral constraint leads to a process of debt deflation and entrepreneurial fire sales of property and the financial accelerator may be very large. These aspects give rise to potentially large drops in output and in property prices.

In Mertens and Ravn (2011e) we decompose the channels through which this amplification process takes place. We show that the financial accelerator is large when (a) housing debt is written in nominal contracts, (b) the borrowing constraint is formulated as a collateral constraint, and (c) the amount of leverage is high. Each three of these requirements appear to have been present before the crisis. Mertens and Ravn (2011b) examine in some detail how financial innovation in terms of the size of the output loss in a liquidity trap and the critical persistence of the pessimistic state such that the self-fulfilling equilibria can exist. Higher leverage implies higher house prices and rules out short-lived liquidity traps but at the same time implies much more dramatic output losses when such equilibria do occur. Therefore, the process of financial innovation that took place during the 1990’s and the 2000’s may not only have spurred house price inflation but may also have laid the seeds of a severe crisis.


Auerbach, Alan J., 1989. “Tax Reform and Adjustment Costs: The Impact on Investment and Market Value“, International Economic Review, 30(4), 939-962.
Beaudry, Paul, and Franck Portier, 2007. “When Can Changes in Expectations Cause Business Cycle Fluctuations in Neo-Classical Settings?“, Journal of Economic Theory, 135(1), 458-77.
Benhabib, Jess, Stephanie Schmitt-Grohe, and Martin Uribe, 2002. “Avoiding Liquidity Traps,” Journal of Political Economy, 110, 535-563.
Blanchard, Olivier J., and Roberto Perotti, 2002. “An Empirical Investigation of the Dynamic Effects of Changes in Government Spending and Taxes on Output“, Quarterly Journal of Economics, 117(4), 1329-1368.
Caldara, Dario, 2010. “The Analytics of SVARs: AQ Unified Framework to Measure Fiscal Multipliers”, manuscript, IIES, Stockholm University.
Canova, Fabio and Morten O. Ravn, 2000. “The Macroeconomic Effects of German Unification: Real Adjustments and the Welfare State“, Review of Economic Dynamics, 3, 423-60.
Christiano, Lawrence J., Martin Eichenbaum, and Sergio T. Rebelo, 2010. “When is the Government Spending Multiplier Large?“, manuscript, Northwestern University.
Cloyne, James, Karel Mertens and Morten O. Ravn, 2011. “The Determinants and Impact of Endogenous Tax Policy Changes”, manuscript in progress, University College London.
Eggertsson, Gauti, 2009. “What Fiscal Policy is Effective at Zero Interest Rates?“, Staff Report no. 402, Federal Reserve Bank of Minneapolis.
Fisher, Jonas D.M. and Ryan Peters, 2010. “Using Stock Returns to Identify Government Spending Shocks,” Economic Journal, 120(544), 414-436.
Galí, Jordi, David López-Salido and Javier Vallés, 2007. “Understanding the Effects of Government Spending on Consumption“, Journal of the European Economic Association, 5(1), 227-270.
Hall, Robert E., 1971. “The Dynamic Effects of Fiscal Policy in an Economy with Foresight“, Review of Economic Studies, 38, 229-244.
Hansen, Lars Peter, and Thomas J. Sargent, 1991. “Two Difficulties in Interpreting Vector Autoregressions”, in L.P. Hansen and T.J. Sargent (eds.), Rational Expectations Econometrics, Boulder, Colorado: Westwood Press.
Iacoviello, Matteo, 2005. “House Prices, Borrowing Constraints, and Monetary Policy in the Business Cycle,” American Economic Review, 95(3), 739-764.
Leeper, Eric M., Todd B. Walker and Shu-Chun Susan Yang, 2008. “Fiscal Foresight: Analytics and Econometric“, CAEPR working paper 2008-13, Indiana University.
Lippi, Marco and Lucrezia Reichlin, 1994. “VAR Analysis, Nonfundamental Representations, Blaschke Matrices“, Journal of Econometrics, 73(1), 307-325.
Ljungqvist, Lars, and Thomas J. Sargent, 2004. Recursive Macroeconomic Theory, Cambridge Mass.: MIT Press.
Mertens, Karel and Morten O. Ravn, 2010a. “Empirical Evidence on the Aggregate Effects of Anticipated and Unanticipated U.S. Tax Policy Shocks“, NBER working paper no. 16289.
Mertens, Karel and Morten O. Ravn, 2010b. “Measuring the Impact of Fiscal Policy Shocks in the Face of Anticipation“, Economic Journal 120, 393-413.
Mertens, Karel and Morten O. Ravn, 2010c. “Fiscal Policy in An Expectations Driven Liquidity Trap“, CEPR Discussion paper no.7931, July.
Mertens, Karel and Morten O. Ravn, 2011a. “Understanding the Effects of Anticipated and Unanticipated Tax Policy Shocks“, Review of Economic Dynamics, 14(1), 27-54.
Mertens, Karel and Morten O. Ravn, 2011b. “Leverage and the Financial Accelerator in a Liquidity Trap”, forthcoming, American Economic Review, May (P&P).
Mertens, Karel and Morten O. Ravn, 2011c. “Technology-Hours Redux: Tax Changes and the Measurement and Impact of Technology Shocks“, forthcoming, NBER International Seminar on Macroeconomics 2010: Chicago University Press.
Mertens, Karel and Morten O. Ravn, 2011d. “Measuring Fiscal Shocks in Structural VARs Using Narrative Data”, manuscript, Cornell University and University College London.
Mertens, Karel and Morten O. Ravn, 2011e. “Credit Channels in a Liquidity Trap“, CEPR discussion paper 8322.
Mountford, Andrew, and Harald Uhlig, 2009. “What are the Effects of Fiscal Policy Shocks?“, Journal of Applied Econometrics, 24(6), 960-992.
Parker, Jonathan A., 1999. “The Reaction of Household Consumption to Predictable Changes in Social Security Taxes“, American Economic Review, 89(4), 959-973.
Poterba, James M., 1988. “Are Consumers Forward Looking? Evidence from Fiscal Experiments“, American Economic Review 78(2), 413-418.
Ramey, Valerie A., 2011. “Identifying Government Spending Shocks: It’s All in the Timing“, forthcoming, Quarterly Journal of Economics.
Ravn, Morten O., Stephanie Schmitt-Grohe and Martin Uribe, 2006. “Deep Habits“, Review of Economic Studies, 73(1), 195-218.
Ravn, Morten O., Stephanie Schmitt-Grohe and Martin Uribe, 2007. “Explaining the Effects of Government Spending Shocks on Consumption and the Real Exchange Rate“, NBER working paper no. 13328.
Romer, Christina D., and David H. Romer, 2008. “A Narrative Analysis of Postwar Tax Changes”, manuscript, University of California, Berkeley.
Romer, Christina D., and David H. Romer, 2010. “The Macroeconomic Effects of Tax Changes: Estimates Based on a New Measure of Fiscal Shocks“, American Economic Review, 100(3), 763-801.
Souleles, Nicholas S., 2002. “Consumer Response to the Reagan Tax Cut“, Journal of Public Economics, 85, 99-120.
Michael Woodford, 2011. “Simple Analytics of the Government Expenditure Multiplier,” American Economic Journal: Macroeconomics, 3(1), 1-35.
Yang, Shu-Chun Susan, 2005, “Quantifying Tax Effects Under Policy Foresight“, Journal of Monetary Economics, 52(8), 1557-1568.
Volume 12, Issue 1, November 2010

Ariel Burstein on International Trade and Macroeconomics

Ariel Burstein is Associate Professor of Economics at UCLA. His research interests lie in exchange rates, trade and business cycles. Burstein’s RePEc/IDEAS entry.

1. Introduction

My research examines a variety of central questions in international macroeconomics and trade, such as: Does international trade improve welfare by stimulating innovation? To what extent can the increase in globalization account for the observed rise in wage inequality in developed and developing countries? What are the aggregate consequences of reallocating firm-embedded know-how across countries in the form of FDI? Why are relative prices across countries so volatile over time? A unifying theme of my research is to develop quantitative models and bring in new data to shed light on these classic questions. In this article I take the opportunity to report on the progress of some of my recent and ongoing work in addressing some of these questions.

2. General Equilibrium Perspectives on Innovation by Firms

In this work, Andrew Atkeson and I explore a commonly held view that international trade has extra benefits because it stimulates innovation by firms. According to this idea, reductions in trade costs make large firms that export face a bigger global market, which increases their incentives to innovate to reduce costs. Hence, the larger exposure to trade leads to an increase in productivity by some firms, which contributes to raising aggregate productivity and welfare.

To assess this view, Andy and I (Atkeson and Burstein 2010a) develop a general equilibrium model that captures the dynamic decisions of heterogeneous firms to exit, export, and invest in innovation to both improve existing products (process innovation) and create new products (product innovation). This model can then be used to aggregate-up from firm-level decisions to obtain a deeper understanding of how aggregate productivity should be expected to respond in general equilibrium to changes in the economic environment such as international trade costs. Our model extends Hopenhayn’s (1992) and Luttmer’s (2007) model of firm dynamics with exit and entry of new firms to include a R&D decision by incumbent firms following Griliches’ (1979) model of knowledge capital. We consider an open economy version of these models with fixed and marginal international trade costs, as in Melitz (2003).

We propose a simple algorithm to assess the impact of a change in the cost of international trade on aggregate productivity and welfare in the long run. A striking feature of our results is that, across a range of model specifications that we can solve analytically, consideration of the endogeneity of firms’ decisions to exit, export, and invest in process innovation have no impact, to a first-order approximation, on our models’ implications for the long-run impact in general equilibrium of a change in international trade costs on aggregate productivity. In fact, to a first-order approximation, one would obtain the same results for the long run change in aggregate productivity in a simple model in which firms’ exit, export, and process innovation decisions were held fixed (completely inelastic) and only firms’ entry decisions responded to changes in the economic environment.

This is not to say that there are no important changes in firm dynamics that result from a change in international trade costs. In fact, for certain assumptions about the elasticity of incumbent firms’ investments in process innovation with regard to changes in the costs or benefits of such innovation, our model predicts dramatic changes in these firms’ innovative efforts and productivity growth rates. Cutting trade costs stimulates process innovation for exporting firms, as these firms seek to grow their profits by selling to a larger market at lower costs. Hence, a reduction in trade costs leads to a reallocation of production, export status, and investments in process innovation from smaller, less-productive, non-exporting firms to larger, more-productive, exporting firms and this reallocation leads to an increase in the productivity of the average firm and in the share of exports in output (some of these implications are further described in Burstein and Melitz 2010).

Yet, in general equilibrium, this reallocation does not have a first-order effect for the model’s implications for long run aggregate productivity. The rise in the productivity of the average firm stemming from the improvements in process innovation and entry into export markets is offset by a reduction in product innovation. Why is that? If other firms in the economy become more productive as they innovate more, this drives down the profitability of entering firms that tend to be small non-exporters competing with globalized firms. This is the self-limiting nature of innovation: the stimulating effect of process innovation and entry into exporting is largely offset by a reduction in product innovation.

We evaluate the strength of this offset in a version of the model that relaxes some of the assumptions that give rise to our stark analytic result described above. In particular, we consider a parameterized version of our model that accounts for some salient features on the share of exporters in output and employment and the firm size distribution in the U.S. economy. In one of our experiments, we consider a reduction in trade costs that more than doubles the share of exports in output. This greatly stimulates the innovative activity of exporters, causing a surge in average productivity: long run average productivity rises by 7.5 times the percentage change in trade costs. But this increase in average productivity is almost entirely offset by a reduction in product innovation, which falls by a factor of 7.4 times the percentage change in trade costs. Moreover, this long run rise in aggregate productivity stemming from the increase in innovation intensity turns out not to make a big difference for welfare of the representative consumer. This is due to the fact that after firms increase their process innovation, it takes a long time to materialize and impact aggregate productivity.

Andy and I (Atkeson and Burstein 2010b) are currently using our framework to more generally assess the aggregate implications of changes in economic policies that affect the costs and benefits to firms of innovative activity. In order to allow a role for welfare-enhancing policies in our model, we include spillovers from R&D. Our model nests widely-used models of semi-endogenous and endogenous growth (see e.g. Acemoglu 2009) based on the value of a key parameter determining to what extent the productivity increase in some firms crowds-out profits of other firms. In the knife-edge case in which a firm’s profits are independent of other firms’ productivities, business R&D is the engine of endogenous growth. In contrast, if productivity increase in incumbent firms crowds-out profits of other firms, business R&D is not the engine of growth, as in semi-endogenous growth models.

When business R&D is not the engine of growth, we show that the calculation of the impact of a wide array of policies directed at inducing innovation by firms on aggregate productivity in the long run can be boiled down to a relatively simple accounting procedure that is straightforward to implement. Namely, to a first-order approximation, the aggregate effects of a subsidy on innovation are the same as the effects of a subsidy on variable profits, keeping innovation decisions of incumbent firms unchanged. This procedure can be understood as follows. First, subsidies on innovation are equivalent to subsidies on firms’ variable profits because subsidizing the return to innovation is equivalent to subsidizing the cost of innovation. Second, an increase in innovation by incumbents lowers profits of entrants, keeping aggregate productivity unchanged. Once again, macroeconomic forces limit the aggregate impact of a change in incumbents’ innovation decisions.

We identify the key parameters in our model that shape the effects of innovation policies, and revisit previous empirical approaches to estimating these effects through the lens of our model. As suggested above, data on the response of R&D of incumbent firms to changes in innovation subsidies is not informative on the aggregate effects of innovation policies. Moreover, because the crowding out effects we identify arise in general equilibrium, data on the response of output of individual industries to changes in innovation policies is informative only as long as the comprehensiveness of these policy changes across industries is known. This is because, in our model, the effects on output in an industry from an innovation subsidy that affects only this industry are very different from those of a subsidy to a large number of industries.

Finally we ask, as does Griliches (1998), whether R&D policies and R&D spillovers can account for a significant proportion of differences in per capita income and measured TFP. As discussed in Prescott (1997) and Klenow and Rodriguez-Clare (2005), in constructing a theory of R&D or other unmeasured capital that can account for large differences in income per capita across countries, two important challenges for such a theory are that (1) it does not require implausibly large differences in R&D or unmeasured capital investment rates across time or countries, and (2) it does not require implausibly long transition dynamics from one steady-state to another.

3. Globalization and the skill premium

To what extent can the growth of trade and multinational production (MP) account for the rise in the skill premium in developed and developing countries? What are the different implications for the skill premium in developed countries of globalization with developing countries versus globalization with developed countries?

The classic model to study the link between international trade and inequality is the Heckscher-Ohlin (H-O) model. According to this theory, trade liberalizations shift factors of production between sectors towards a country’s comparative advantage sector and raise the relative return to the factor that is used intensively in this sector — the between effect. International trade increases the skill premium in countries that have a comparative advantage in skill-intensive sectors, and lowers the skill premium in countries that have a comparative advantage in unskill-intensive sectors. Previous empirical work (see e.g. Goldberg and Pavnick 2007), however, has cast doubt on the importance of trade in accounting for the skill premium because (i) inequality has increased both in countries abundant in unskilled labor and in countries abundant in skilled labor, and (ii) most factor reallocation occurs within rather than across sectors. An alternative interpretation of this evidence, however, is that the standard H-O model abstracts from other potentially important channels beyond the between effect through which globalization affects the skill premium.

To allow for such additional channels, Jonathan Vogel and I (Burstein and Vogel 2010a) extend the H-O model in three dimensions. First, motivated by the large heterogeneity in size and export status within sectors, we introduce productivity heterogeneity across producers within sectors. Second, motivated by the observation that, within sectors, exporters tend to be more skill-intensive than non-exporters, we allow for skill-biased technology at the producer level. Third, we allow for producers to use their technologies to produce in foreign countries, engaging in multinational production (MP). MP is an important form by which producers supply foreign countries beyond international trade (for example, sales of U.S. foreign affiliates are more than twice as large as the value of U.S. exports).

Following a reduction in trade and MP costs, our extended model predicts within sector factor reallocation from less productive non-exporters to more productive exporters, as in recent international trade models with producer heterogeneity. If a producer’s productivity is positively correlated with its skill intensity, then this reallocation of labor across producers within sectors raises the demand for skilled labor and the skill premium — the within effect. In contrast to the standard Hecksher-Ohlin model, the within effect implies that the skill premium may rise in all countries. Hence, our extended model gives globalization (both trade and MP) a better chance to account for the rise in the skill premium in developed and developing countries. Which force dominates and by how much is a quantitative question that we address in our quantitative analysis.

We consider a parameterized four-country version of our model (matching U.S. trade and MP volumes in 2006 with skill-abundant and scarce countries) to conduct a series of counterfactuals. To isolate the role of international trade in shaping the skill premium, we first consider a reduction in trade costs moving from autarky to the level of trade in 2006, holding all other exogenous variables fixed (including factor endowments) and abstracting from MP. This is a “but for” analysis: What would the skill premium be, but for the availability of international trade opportunities? The rise in the skill premium caused by trade is 1.8% in the U.S. and 2.9% in skill-scarce countries.

The two central messages from these results are as follows. First, in contrast to the standard H-O model, our parameterized model is consistent with a rising skill premium in all countries. The skill premium rises in all countries because the within effect is relatively strong compared to the between effect. The between effect is weak because, in our parameterization as in the data, the factor content of trade in the U.S. is not very high (in fact, under some assumptions of our model, the between effect is fully determined by the factor content of trade — see also Burstein and Vogel 2010b). Given that the between effect is weaker than the within effect, how much the U.S. trades matters more for its skill premium than with whom the U.S. trades (i.e. whether it trades with Europe or China). Second, the magnitudes of the changes in the skill premium of moving from autarky to 2006 levels of trade are quite small relative to, for example, the 24% rise in the (composition-adjusted) U.S. college-high school wage gap between 1966 and 2006 (see, e.g., Acemoglu and Autor 2010).

The relatively small trade share in the U.S. plays a critical role in explaining the relatively small impact of trade on the U.S. skill premium in our model. The share of MP in output, however, is at least twice as high. When we simulate a reduction in both trade and MP costs moving from autarky to the levels of trade and MP in 2006, the rise in the skill premium is much larger: 4.8% in the U.S. and 6.5% in the skill-scarce countries. MP is at least as important as international trade for determining the impact of globalization on the skill premium.

In order to assess the extent to which the growth of trade and MP can account for the rise in the skill premium between 1966 and 2006 in the U.S., we consider a second counterfactual in which we choose parameters to match the growth of trade and MP between these years. In this counterfactual we do not hold endowments or technologies fixed, but instead we target the increase in the supply of skilled labor and the greater growth of the skill-scarce countries between 1966 and 2006 and we allow for exogenous skill-biased technology growth to match the 24% increase in the U.S. skill premium. In our preferred, baseline parameterization, we show that in the absence of globalization, the rise in the skill premium in the U.S. would have been 1/9th smaller than the observed rise in the skill premium over this time period (in a less conservative parameterization in which we choose parameter values so that, given trade and MP shares, the between and within effects are strengthened, we find that in the absence of globalization the rise in the skill premium in the US would have been 1/5th smaller than the observed rise over this time period).

Whereas we use a structural, parameterized model to quantify the impact of international trade and MP on the skill premium, the empirical literature has mostly focused on three alternative approaches that emphasize: the factor content of trade, the extent of between-sector factor reallocation, and the mandated wage equation. We show that while each of these alternative approaches may provide estimates of the impact of international trade on the skill premium via the between effect, they do not capture the impact of the within effect of trade and MP. Using data generated by our model, in which the within effect is relatively strong, we show that these approaches underestimate the rise in the skill premium stemming from the increase in globalization.

Whereas in our current work we capture two important forces in the debate on globalization and the skill premium—the between and within effects—and incorporate both trade and MP, we abstract from other interesting and potentially important considerations discussed in the literature, such as endogenous skill-biased innovation or capital accumulation with capital-skill complementarity. We think that providing a framework that allows for such additional considerations is a fruitful area for future research to more fully assess the quantitative effects of globalization on inequality.

4. Understanding fluctuations in international relative prices

Why are relative prices across countries, as measured by real exchange rates (RERs), so volatile over time, and why do they so closely track movements in nominal exchange rates? These questions are at the heart of the discussions on optimal exchange rate policy (i.e.: by depreciating the exchange rate, countries may be able to reduce the relative price and raise the output of the goods they produce) and on the role of the border in creating frictions to the international trade of goods (i.e.: if trade costs were small, international trade should arbitrage large differences in relative prices across locations). The high correlation between RER and nominal exchange rate movements has been widely suggestive of nominal macroeconomic non-neutralities (see e.g. Mussa 1986).

As a starting point to understand these movements in international relative prices, consider simple models of price setting with perfect competition or imperfect competition and constant markups, in which prices change one-to-one with movements in marginal production costs. According to these models, the relative price of a traded good produced in a common location and sold in two countries (subject to a linear transportation technology) should remain constant over time. This is the hypothesis of relative purchasing power parity (relative PPP). However, a large body of empirical work suggests that relative PPP does not provide an accurate representation for movements in relative prices of many goods (see e.g. the survey in Goldberg and Knetter 1995). Another implication of models with constant markups is that, if all goods can be traded at no cost across countries, consumer-price-based RERs should be constant over time. However, RERs are very volatile, even for tradeable goods (see e.g. Engel 1999).

In order to account for the observed deviations of relative PPP and the large movements of RERs for tradeable goods, researchers have considered two key sources of departure from the constant markup costless-trade benchmark. First, many goods are not traded (see e.g. Burstein, Eichenbaum, and Rebelo 2005), and even traded goods include a substantial non-traded distribution component (see e.g. Burstein, Neves, and Rebelo 2003). Changes in relative prices across countries for these goods may simply reflect movements in relative production or distribution costs across locations. Second, movements in international relative prices may be explained by the decision of individual firms to engage in pricing-to-market — that is, to systematically vary over time the markup at which they sell their output in different locations (see e.g. Dornbusch 1987 and Krugman 1987). These movements in relative markups can stem from nominal rigidities that leave prices in the buyer’s currency unchanged to exchange rate movements, or from some feature of demand or competition that gives rise to movements in demand elasticities (and hence markups) across destinations.

Identifying whether movements in relative prices across countries reflect movements in relative markups or in relative costs is a key ingredient for the design of optimal exchange rate policy. Movements in relative prices of individual goods across countries that reflect changes in relative costs across locations are typically efficient, while movements in relative prices that reflect changes in relative markups across locations are typically inefficient (see e.g. Engel 2010). Hence, changes in exchange rates have very different normative implications in both models.

Nir Jaimovich and I (Burstein and Jaimovich 2009) take the challenge of documenting the role of pricing-to-market in accounting for the observed movements in international relative prices. We do so using detailed information on prices in Canada and the U.S. at the level of individual products. In particular, we use scanner data for the period 2004-2006 from a major retailer that sells primarily nondurable goods in multiple locations in Canada and the U.S. For each product, we observe the retailer’s purchase cost from the vendor, i.e. the wholesale price, in each location and over time. We also identify the country of production of individual products that are sold in Canada and the U.S. Under the assumption that goods produced in a common location and sold in multiple locations are subject to common percentage changes in the marginal cost, movements in relative prices across locations for these goods must arise from changes in relative markups. With this information, we can thus assess the extent to which movements in relative prices of individual products across locations reflect the practice of pricing-to-market by producers and wholesalers.

Our findings demonstrate that pricing-to-market plays an important role in accounting for movements in international relative prices. We show that movements in aggregate RERs, constructed by averaging changes in relative prices across countries (expressed in a common currency) over a large set of products sold in both Canada and the U.S., closely track the large rise in Canada-U.S. relative unit labor costs over our sample period (which are mainly accounted for by the appreciation of the Canadian dollar against the U.S. dollar). For nontraded goods that are produced in each country and sold in both countries, these movements in aggregate RERs can simply reflect changes in relative costs across countries. However, the fact that this pattern holds as well for traded goods produced in a common location and sold in both countries implies that in response to the appreciation of Canada-U.S. labor costs, markups in Canada increase systematically relative to markups in the U.S.

Pricing-to-market does not stem, in a pure accounting sense, from large movements in nominal exchange rates and small movements in nominal prices in each country. Instead, nominal prices of individual products change frequently and by large magnitudes. Moreover, changes in international relative prices at the level of individual products, product-level RERs, are very large, roughly four times as volatile (at quarterly frequencies, excluding temporary price changes in each location) as the Canada-U.S. nominal exchange rate, even for traded goods. Hence, while cross-country differences in markups on average track movements in nominal exchange rates and relative labor costs, the idiosyncratic product-specific component of pricing-to-market is significant. We also show that the idiosyncratic and aggregate components of pricing-to-market are much more prevalent across countries than across regions within countries.

Our empirical findings relate to a recent and rapidly growing literature documenting the behavior of international relative prices for tradeable (but not necessarily traded) goods using detailed product-level information (see e.g. Crucini and Shintani 2008, Broda and Weinstein 2008, and Gopinath, Gourinchas, Hsieh, and Li 2010). Our empirical contribution is to measure the extent to which movements in relative prices of matched individual products across locations reflect pricing-to-market by producers and wholesalers, which can do because of two unique features of our data. First, by observing wholesale prices, we can more accurately measure movements in relative markups at the producer level than if we used retail prices, which contain a significant non-traded distribution component. Second, by using information on the country of production of individual products, we can identify goods that are actually traded, and infer changes in relative markups for these goods from observed movements in relative prices across locations. Fitzgerald and Haller (2008), like us, also find evidence of pricing-to-market by exporters in response to exchange rate movements using detailed firm-level data.

Our empirical findings raise some important questions: Why do relative markups systematically track movements in relative costs across countries, even if nominal prices of individual products change frequently and by large amounts? Why is pricing-to-market more prevalent across countries than within countries? Nir and I address these questions using a simple model of pricing-to-market and international trade with flexible prices (that extends my previous work, Atkeson and Burstein 2007, 2008). The international border plays an important role in our model by segmenting competitors across countries (more so than within countries), leading to the practice of pricing-to-market by exporters that optimally change their markup across locations (more so across countries than within countries) in response to idiosyncratic shocks and changes in aggregate relative labor costs.

Our model is highly stylized in order to gain analytical tractability and to help us identify key forces that can account for the observed movements in product-level and aggregate RERs. In doing so, we abstract from important industrial organization considerations (for models of incomplete pass-through that incorporate some of these considerations, see e.g. Goldberg and Hellerstein 2007 and Nakamura and Zerom 2010). An important question for future research is whether richer models of demand and market structure can give rise to idiosyncratic and aggregate movements in relative markups across locations (i.e. differences in pass-through across locations) like the ones observed in the data.


Acemoglu, Daron. 2009. Introduction to Modern Economic Growth. Princeton University Press, Princeton, NJ.
Acemoglu, Daron, and David Autor. 2010. “Skills, Tasks and Technologies: Implications for Employment and Earnings.” in: Handbook of Labor Economics, Volume 4, forthcoming.
Atkeson, Andrew and Ariel Burstein. 2007. “Pricing-to-Market in a Ricardian Model of International Trade.” American Economic Review, 97(2): 362-367.
Atkeson, Andrew and Ariel Burstein. 2008. “Pricing-to-Market, Trade Costs, and International Relative Prices.” American Economic Review, 98(5): 1998-2031.
Atkeson, Andrew, and Ariel Burstein. 2010a. “Innovation, Firm Dynamics, and International Trade.” Journal of Political Economy, 118(3): 433:484
Atkeson, Andrew, and Ariel Burstein. 2010b. “What is the impact of innovation policy on aggregate output and welfare?” Working paper. UCLA
Broda, Christian, and David Weinstein. 2008. “Understanding International Price Differences using Barcode Data.” NBER working paper 14017. National Bureau of Economic Research.
Burstein, Ariel, Joao Neves, and Sergio Rebelo. 2003. “Distribution Costs and Real Exchange Rate Dynamics During Exchange-Rate-Based Stabilizations.” Journal of Monetary Economics, 50(6): 1189-1214.
Burstein, Ariel, Martin Eichenbaum, and Sergio Rebelo. 2005. “Large Devaluations and the Real Exchange Rate.” Journal of Political Economy, 113(4): 742-784.
Burstein, Ariel and Nir Jaimovich. 2009. “Understanding Movements in Aggregate and Product-Level Real Exchange Rates.” Mimeo. UCLA.
Burstein, Ariel and Marc Melitz. 2010. “Trade Liberalizations and Firm Dynamics.” Working Paper. UCLA.
Burstein, Ariel and Jonathan Vogel. 2010a. “Globalization, Technology, and the Skill Premium: A Quantitative Analysis.” NBER Working Paper 16459. National Bureau of Economic Research.
Burstein, Ariel and Jonathan Vogel. 2010b. “International Trade Patterns, the Skill Premium, and Heterogeneous Firms.” Mimeo. Columbia University.
Crucini, Mario and Mototsugu Shintani. 2008. “Persistence in law of one price deviations: Evidence from micro-data.” Journal of Monetary Economics, 55(3): 629-644.
Dornbusch, Rüdiger. 1987. “Exchange Rates and Prices.” American Economic Review, 77(1): 93-106.
Engel, Charles. 1999. “Accounting for U.S. Real Exchange Rate Changes.” Journal of Political Economy, 107(3): 507-538.
Engel, Charles. 2011. “Currency Misalignments and Optimal Monetary Policy: A Reexamination.” American Economic Review, forthcoming.
Fitzgerald, Doireann and Stefanie Heller. 2008. “Exchange Rates and Producer Prices: Evidence from Micro-Data.” Mimeo. Stanford University.
Goldberg, Pinelopi K., and Rebecca Hellerstein. 2007. “A Structural Approach for Identifying the Sources of Local Currency Price Stability with an Empirical Application.” NBER Working paper 13183.
Goldberg, Pinelopi K., and Michael Knetter. 1997. “Goods Prices and Exchange Rates: What Have We Learned?Journal of Economic Literature, 35(3): 1243-1272.
Goldberg, Pinelopi Koujianou and Nina Pavcnik. 2007. “Distributional Effects of Globalization in Developing countries.” Journal of Economic Literature, 45(1): 39-82.
Gopinath, Gita, Pierre-Olivier Gourinchas, Chang-Tai Hsieh, and Nicholas Li. 2010. “International Prices, Costs and Markup Differences.” American Economic Review, forthcoming.
Griliches, Zvi. 1979. “Issues in Assessing the Contribution of Research and Development to Productivity Growth.” Bell Journal of Economics, 10(1): 92-116.
Griliches, Zvi. 1998. “The Search for R&D Spillovers.” in: R&D and Productivity: The Econometric Evidence. National Bureau of Economic Research.
Hopenhayn, Hugo. 1992. “Entry, Exit, and Firm Dynamics in Long Run Equilibrium.” Econometrica 60(5): 1127-1150.
Klenow, Peter J. and Andres Rodriguez-Clare. 2005. “Externalities and Growth.” in: Philippe Aghion and Steven Durlauf (eds.), Handbook of Economic Growth, volume 1, chapter 11, pages 817-861.
Krugman, Paul. 1987. “Pricing to Market When the Exchange Rate Changes.” in: S. W. Arndt and J. Richardson (eds.), Real Financial Linkages Among Open Economies, London: MIT Press.
Luttmer, Erzo G.J. 2007. “Selection, Growth, and the Size Distribution of Firms.” Quarterly Journal of Economics, 122(3): 1103–1144.
Melitz, Marc. 2003. “The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity.” Econometrica. 71(6): 1695-1725.
Mussa, Michael. 1986. “Nominal Exchange Rate Regimes and the Behavior of Real Exchange Rates.” Carnegie-Rochester Series on Public Policy, 25: 117-214.
Nakamura, Emi and Dawit Zerom. 2010. “Accounting for Incomplete Pass-through.” Review of Economic Studies. 77(3): 1192-1230.
Prescott, Edward. 1997. “Needed: a theory of total factor productivity.” Staff Report 242, Federal Reserve Bank of Minneapolis.
Volume 11, Issue 2, April 2010

Martin Schneider on Multiple Priors Preferences and Financial Markets

Martin Schneider is Professor of Economics at Stanford University. His research interests lie in Financial and Monetary Economics. Schneider’s RePEc/IDEAS entry.

1. Introduction

The Ellsberg paradox suggests that people behave differently in risky situations — when they are given objective probabilities — than in ambiguous situations when they are not told the odds (as is typical in financial markets). Such behavior is inconsistent with subjective expected utility theory (SEU), the standard model of choice under uncertainty in financial economics. The multiple priors model of Gilboa and Schmeidler (1989) can accommodate ambiguity averse behavior in atemporal choice situations. This article reviews recent work that has extended the multiple priors model to accommodate intertemporal choice and learning, as well as work that has applied the model to portfolio choice and asset pricing. A more formal discussion, including a comparison of alternative models of ambiguity aversion, is available in Epstein and Schneider (2010).

The multiple priors model is attractive for finance applications because it allows uncertainty to have first order effects on portfolio choice and asset pricing. As a result, its qualitative predictions are different from those of subjective expected utility theory in a way that helps understand observed asset positions. In particular, in contrast to SEU, the multiple priors model robustly generates selective participation in asset markets, optimal underdiversification, and portfolio inertia. In heterogeneous agent models, portfolio inertia can give rise to endogenous incompleteness of markets and the “freezing up” of markets in response to an increase in uncertainty.

The multiple priors model can also help to quantitatively account for position and price behavior that is puzzling at low levels of risk aversion. This is because multiple priors agents tend to choose more conservative positions, and, in equilibrium, command additional “ambiguity premia” on uncertain assets. When agents learn under ambiguity, the arrival of new data affects their confidence, with first order implications for asset demand. In equilibrium, changes in confidence — for example due to changes in information quality — will change uncertainty premia observed in markets.

The foundations for dynamic applications of the multiple priors model are by now relatively well understood. We also have tools for tractable modeling of intertemporal choice and learning. So far, however, quantitative dynamic applications of the theory have been largely confined to representative agent asset pricing. This is somewhat unfortunate: first order effects of uncertainty are particularly interesting in models that have nontrivial extensive margins, as discussed below. Building quantitative models of portfolio choice and market participation, as well as equilibrium trading and pricing, can thus be a fruitful area of research in the future.

2. The Ellsberg Paradox and Multiple Priors

Ellsberg’s (1961) classic experiments motivate the study of ambiguity. In a variant of one of his experiments, you are told that there are 100 balls in an urn, and that each ball is either red or blue. You are not given further information about the urn’s composition. Presumably you would be indifferent between bets on drawing either color (take the stakes to be 100 and 0). However, compare these bets with the risky prospect that offers you, regardless of the color drawn, a bet on a fair coin, with the same stakes as above. When you bet on the fair coin, or equivalently on drawing blue from a second risky urn where you are told that there are 50 balls of each color, then you can be completely confident that you have a 50-50 chance of winning. In contrast, in the original “ambiguous” urn, there is no basis for such confidence. This difference motivates a strict preference for betting on the risky urn as opposed to the ambiguous one.

Such preference is incompatible with expected utility. Indeed, suppose you had in mind a subjective probability about the probability of a blue draw from the ambiguous urn. A strict preference for betting on the fair coin over a bet on a blue draw would then reveal that your probability of blue is strictly less than one half. At the same time, a preference for betting on the fair coin over a bet on a red draw reveals a probability of blue that is strictly greater than one half, a contradiction. It follows that Ellsberg’s choices cannot be rationalized by SEU.

When information is scarce and a single probability measure cannot be relied on to guide choice, it is intuitive that the decision maker thinks in terms of a set of probability laws. The multiple-priors model assumes that agents act as if they evaluate plans using a worst case probability belief drawn from a given set. For example, a decision maker might assign the interval [(1/3),(2/3)] to the probability of drawing a red ball from the ambiguous urn in the Ellsberg experiment. Being cautious, he might then evaluate a bet on red by using the minimum probability in the interval, here (1/3), which would lead to the strict preference to bet on the risky urn. Similarly for blue. In this way, the intuitive choices pointed to by Ellsberg can be rationalized.

Ellsberg type behavior violates the independence axiom of SEU. To see this, consider a lottery that promises either a bet on a red draw from the ambiguous urn or a bet on a blue draw from the ambiguous urn, each with probability one half. Such a bet is equivalent to a bet on the risky urn (or a fair coin). Ellsberg’s choices thus require strict preference for randomization between indifferent acts, whereas the independence axiom implies indifference between bets on the risky and ambiguous urns. In the Ellsberg choice situation, randomization can be valuable because it can smooth out, or hedge, ambiguity that is present in the bets on red or blue from the ambiguous urn.

The axiomatic foundations of the multiple priors model replace the independence axiom of SEU with two alternative axioms. First, uncertainty aversion refers to weak preference for randomization over indifferent plans. Second, it is assumed that randomization can be valuable only if it helps hedge ambiguity. In particular, the certainty independence axiom assumes that randomization with a constant — which provides no hedging — can never be valuable. GS show that those two axioms, together with other axioms typically imposed to derive SEU in an Anscombe-Aumann framework, imply a multiple priors representation of preferences. There are a number of other models of ambiguity aversion that also satisfy the uncertainty aversion axiom, but relax certainty independence. Those models do not share the feature that uncertainty is a first order concern of decision makers (see Epstein and Schneider (2010) for a detailed comparison of alternative models and their implications.)

3. Intertemporal Choice and Learning

Most applications to financial markets involve sequential choice. This motivated extending the GS model to intertemporal choice over contingent consumption plans. Epstein and Schneider (2003a) provide axiomatic foundations for a general updating rule for the multiple-priors model, an analog to Bayes’ rule. The key axioms are that (i) conditional preferences at every node in the decision tree satisfy (suitably adapted versions of) the Gilboa-Schmeidler axioms and (ii) conditional preferences at different nodes are connected by dynamic consistency. The main results are that (a) preferences satisfying the axioms can be represented by the multiple-priors model, where the belief set satisfies a restriction called rectangularity, (b) belief sets that represent preferences at later nodes in the decision tree can be updated from those at earlier nodes by applying Bayes’ rule “measure-by-measure” and (c) utility can be represented recursively so standard tools can be applied to solve optimization problems.

Epstein and Schneider (2007) consider a model of learning about a memoryless mechanism, an analog to the Bayesian model of learning from conditionally iid signals. As a concrete illustration, consider repeated sampling from a sequence of Ellsberg urns. If the decision-maker perceives the urns to be identical, then after many draws with replacement he will naturally become confident that the observed empirical frequency of blue draws is close to a “true” fraction of blue balls in the urn that is relevant for forecasting future draws. Thus she will eventually become confident enough to view the data as an i.i.d. process. In this laboratory-style situation, one would expect ambiguity to be resolved over time.

More generally, suppose the decision maker believes the draws to be independent, but that he has no reason to be sure that the urns are identical. For example, if she is told the same about each urn but very little (or nothing at all) about each, then she would plausibly admit the possibility that the urns are not identical. In particular, there is no longer a compelling reason why data in the future should be i.i.d. with frequency of blue draws equal to the empirical frequency of blue draws observed in the past. Indeed, in contrast to a Bayesian, he may not even be sure whether the empirical frequencies of the data will converge, let alone expect his learning process to settle down at a single i.i.d. process.

One can view our model as an attempt to capture learning in such complicated (or vaguely specified and poorly understood) environments. The learning process has two distinctive properties. First, confidence changes together with beliefs as new data arrives. Formally, this is captured by a set of beliefs that expands or shrinks in response to new information. As a result, behavior that reflects a lack of confidence (such as the willingness to bet on the ambiguous urn) can become weaker or stronger over time. Second, ambiguity averse agents need not expect that they will ever learn a “true” iid process in the long run. Instead, they may reach a state of iid ambiguity, where learning ceases, but the data are still perceived as ambiguous. The transition to this state may resolve some, but not all initial ambiguity. A version of the multiple-priors model that captures iid ambiguity is studied in more detail in Epstein and Schneider (2003b), where we also provide a version of the law of large numbers.

4. Ambiguous information

Epstein and Schneider (2008) consider a special case of learning under ambiguity with uncertain signal quality. The idea is that, when quality is difficult to judge, investors treat signals as ambiguous. They do not update beliefs in standard Bayesian fashion, but behave as if they have multiple likelihoods in mind when processing signals. A thought experiment shows that the standard Bayesian measure of signal quality, precision, is no longer sufficient to describe signal quality. Moreover, ambiguity-averse behavior can be induced by poor information quality alone: An a priori lack of confidence is not needed.

Ambiguous information quality has two key effects. First, after ambiguous information has arrived, agents respond asymmetrically: Bad news affect conditional actions — such as portfolio decisions — more than good news. This is because agents evaluate any action using the conditional probability that minimizes the utility of that action. If an ambiguous signal conveys good (bad) news, the worst case is that the signal is unreliable (very reliable). The second effect is that even before an ambiguous signal arrives, agents who anticipate the arrival of low quality information will dislike consumption plans for which this information may be relevant. This intuitive effect does not obtain in the Bayesian model, which precludes any effect of future information quality on current utility.

5. Portfolio choice and selective participation

In portfolio data, the extensive margin is important. Households and mutual funds do not typically hold diversified portfolios of all assets in the economy, as implied by the typical model with SEU preferences. SEU models that study the extensive margin have relied on ingredients such as per period fixed costs. However, quantitative work has shown that such frictions must be unreasonably large, especially if they are to explain selective participation by wealthy households (for an overview of evidence on participation, see Cao et al. (2007)).

The reason why it is hard to generate nonparticipation in SEU models is that uncertainty is a second order concern. Indeed, expected utility implies local risk neutrality: in a standard frictionless portfolio choice problem with one riskless and one risky asset, it is always optimal to take a (perhaps small) position in the risky asset except if the expected returns on the two assets are exactly equal. In other words, nonparticipation is no more than a knife edge phenomenon.

Dow & Werlang (1992) showed that, with multiple priors, nonparticipation is a robust phenomenon. To see why, consider choice between one certain and one ambiguous asset, where ambiguity is captured by a range of mean expected returns. When an ambiguity averse agent contemplates going long in the ambiguous asset, he will thus evaluate the portfolio using the lowest expected return. In contrast, when contemplating a short position he will use the highest expected return. It follows that, if the interval of expected returns contains the riskless return, then it is optimal to invest all wealth in the riskless asset.

In the Dow-Werlang example, ambiguity averse agents exhibit portfolio inertia at certainty. Indeed, consider the response to a small shift in the range of expected returns. As long as the riskless rate remains inside the range, the portfolio position will not change. This is again in sharp contrast to the risk case, where the derivative of the optimal position with respect to shifts in the return distribution is typically nonzero. The key point here is that an increase in ambiguity can be locally “large” relative to an increase in risk. Indeed, a portfolio that contains only the certain asset is both riskless and unambiguous. Any move away from it makes the agent bear both risk and ambiguity. However, an increase in ambiguity about means is perceived like a change in the mean, and not like an increase in the variance. Ambiguity can thus have a first order effect on portfolio choice that overwhelms the first order effect of a change in the mean, whereas the effect of risk is second order.

Nonparticipation and portfolio inertia are important features of portfolio choice under ambiguity beyond the simple Dow-Werlang example. Portfolio inertia can arise away from certainty if agents can construct portfolios that hedge a source of ambiguity. Illeditsch (2009) shows how this can naturally arise in a model with inference from past data. Garlappi et al. (2007) characterize portfolio choice with multiple ambiguous assets. In particular, they show how differences in the degree of ambiguity across assets leads to selective participation. Bossaerts et al. (2010) and Ahn et al. (2009) provide experimental evidence that supports first order effects of uncertainty in portfolio choice.

6. Learning and portfolio dynamics

Epstein & Schneider (2007) and Campanale (2010) study dynamic portfolio choice models with learning, using the recursive multiple-priors approach. Investors learn about the mean equity premium, and treat stock returns as a sequence of conditionally independent ambiguous signals. Updating proceeds as in the urn example described above.

Epstein and Schneider (2007) emphasize two new qualitative effects for portfolio choice. First, the optimal policy involves dynamic exit and entry rules. Indeed, updating shifts the interval of equity premia, and such shifts can make agents move in and out of the market. Second, there is a new source of hedging demand. It emerges if return realizations provide news that shift the interval of equity premia. Portfolio choice optimally takes into account the effects of news on future confidence.

The direction of hedging depends on how news affects confidence. In Epstein & Schneider (2007), learning about premia gives rise to a contrarian hedging demand if the empirical mean equity premium is low. Intuitively, agents with a low empirical estimate know that a further low return realization may push them towards nonparticipation, and hence a low return on wealth (formally this is captured by a U-shaped value function). To insure against this outcome, they short the asset.

The paper also shows that, quantitatively, learning about the equity premium can generate a significant trend towards stock market participation and investment, in contrast to results with Bayesian learning. The reason lies in the first order effect of uncertainty on investment. Roughly, learning about the premium shrinks the interval of possible premia and thus works like an increases in the mean premium, rather than just a reduction in posterior variance, which tends to be 2nd order.

Campanale (2010) builds a multiple priors model of learning over the life cycle. Investors learn from experience by updating from signals received over their life cycle. He calibrates the model and quantitatively evaluates its predictions for participation and investment patterns by age in the US Survey of Consumer Finances. In particular, he shows that the first order effects of uncertainty help rationalize moderate stock market participation rates and conditional shares with reasonable participation costs. In addition, learning from experience helps match conditional shares over the life-cycle.

7. Discipline in quantitative applications

In the portfolio choice examples above as well as in those on asset pricing below, the size of the belief set is critical for the magnitude of the new effects. There are two approaches in the literature to disciplining the belief set. Anderson et al. (2003) propose the use of detection error probability (see also Barillas et al. (2009) for an exposition). While those authors use detection error probabilities in the context of multiplier preferences, the idea has come to be used also to constrain the belief set in multiple-priors. For example, Sbuelz & Trojani (2008) derive pricing formulas with entropy-constrained priors. Gagliardini et al. (2008) show how to discipline such sets of priors by applying the idea of detection probabilities. The basic idea is to permit only beliefs that are statistically close to some reference belief, in the sense that they are difficult to distinguish from the reference belief based on historical data.

A second approach to imposing discipline involves using a model of learning. For example, the learning model of Epstein & Schneider (2007) allows the modeler to start with a large set of priors in a learning model — resembling a diffuse prior in Bayesian learning — and then to shrink the set of beliefs via updating. A difference between the learning and detection probability approach is that in the former the modeler does not have to assign special status to a reference model. This is helpful in applications where learning agents start with little information, for example, because of recent structural change. In contrast, the detection probability approach works well for situations where learning has ceased or slowed down, and yet the true model remains unknown.

8. Representative agent asset pricing

Epstein & Wang (1994, 1995) first studied representative agent asset pricing with multiple priors (Chen & Epstein (2002) characterize pricing in continuous time). A key insight of this work paper is that asset prices under ambiguity can be computed by first finding the most pessimistic beliefs about a claim to aggregate consumption, and then pricing assets under this pessimistic belief. A second point is that prices can be indeterminate. For example, suppose there is an ambiguous parameter in the distribution of asset payoffs, but selecting a worst case belief about the consumption claim does not pin down the parameter. Then a whole family of prices is consistent with equilibrium.

While indeterminacy is an extreme case, the more general point is that a small change in the distribution of consumption can have large asset pricing effects. Ambiguity aversion can thus give rise to powerful amplification effects. For example, Illeditsch (2009) shows how updating from ambiguous signals can give rise to amplification of bad news.

Epstein & Schneider (2008) consider the effect of learning, with a focus on the role of signals with ambiguous precision. They show that such signals induce an asymmetric response to news — bad news is taken more seriously than good news — and contribute to premia for idiosyncratic volatility as well as negative skewness in returns. Williams (2009) provides evidence that in times of greater uncertainty in the stock market the reaction to earnings announcements is more asymmetric.

Another key property of ambiguous signals is that the anticipation of poor signal quality lowers utility. As a result, a shock that lowers the quality of future signals can lower asset prices. In contrast, in a Bayesian setting the anticipation of less precise future signals does not change utility or prices as long as the distribution of payoffs has not changed. Epstein & Schneider (2008) use a quantitative model to attribute some of the price drop after 9/11 to the discomfort market participants felt because they had to process unfamiliar signals. These results are related to the literature on “information uncertainty” in accounting. For example, Autore et al. (2009) consider the failure of Arthur Anderson as an increase in (firm-specific) ambiguity about AA’s clients and document how the price effect of this shock depended on the availability of firm-specific information.

There are now a number of quantitative studies that apply the recursive multiple-priors model to different asset markets. Trojani & Vanini (2002) revisit the equity premium puzzle. Sbuelz and Trojani (2008) consider predictability of excess stock returns. Jeong et al. (2009) estimate a model of stock returns, also with an emphasis on time variation in equity premia. Drechsler (2008) studies the joint behavior of equity returns and option prices. Both Jeong et al. and Drechsler use a general specification of RMP with separate parameters for risk aversion and substitution as in Epstein & Zin (1989) and thus allow for the interaction of ambiguity and “long run risk”.

Ilut (2009) addresses the uncovered interest parity puzzle in foreign exchange markets using a model of regime switching under ambiguity. Gagliardini et al. (2008) and Ulrich (2009) consider the term structure of interest rates, focusing on ambiguity about real shocks and monetary policy, respectively. Boyarchenko (2009) studies credit risk in corporate bonds.

9. Heterogenous agent models of trading and valuation

Recent work has explored heterogeneous agent models where some agents have multiple-priors. Epstein & Miao (2003) consider an equilibrium model in which greater ambiguity about foreign as opposed to domestic securities leads to a home-bias. Several models center on portfolio inertia as discussed above. Mukerji & Tallon (2001) show that ambiguity can endogenously generate an incomplete market structure. Intuitively, if ambiguity is specific to the payoff on a security, then no agent may be willing to take positions in a security with sufficiently ambiguous payoffs. Mukerji & Tallon (2004) build on this idea to explain the scarcity of indexed debt contracts with ambiguity in relative prices. Easley & O’Hara (2009) consider the welfare effects of financial market regulation in models where multiple-priors agents choose in which markets to participate.

A shock to the economy that suddenly increases ambiguity perceived by market participants can drive widespread withdrawal from markets, that is, a “freeze”. This is why the multiple-priors model has been used to capture the increase in uncertainty during financial crises (Caballero & Krishnamurthy 2008, Guidolin & Rinaldi 2009, Routledge & Zin 2009). Uhlig (2010) considers the role of ambiguity aversion in generating bank runs.

In heterogeneous agent models, prices generally depend on the entire distribution of preferences. An important point here is that if only some agents become more ambiguity averse, this may not increase premia observed in the market. The reason is that the more ambiguity averse group might leave the market altogether, leaving the less ambiguity averse agents driving prices (Trojani and Vanini 2004, Cao et al. 2005, Chapman & Polkovnichenko 2009, Ui 2009). Condie (2008) considers conditions under which ambiguity averse agents affect prices in the long run if they interact with SEU agents.

A number of papers have recently studied setups with ambiguity averse traders and asymmetric information. Condie & Ganguli (2009) show that if an ambiguity averse investor has private information, then portfolio inertia can prevent the revelation of information by prices even if there is the same number of uncertain fundamentals and prices. Ozsoylev & Werner (2009) and Caskey (2009) study the response of prices to shocks when ambiguity averse agents interact with SEU traders and noise traders. Mele & Sangiorgi (2009) focus on the incentives for information acquisition in markets under ambiguity.


David Ahn, Syngjoo Choi, Douglas Gale, and Shachar Kariv. 2009. Estimating ambiguity aversion in a portfolio choice experiment. Unpublished manuscript, Berkeley.
Evan Anderson, Lars Peter Hansen, and Thomas Sargent. 2003. A quartet of semigroups for model specification, robustness, prices of risk and model detection. Journal of the European Economic Association, vol. 1, pages 68-123.
Don Autore, Randall Billingsley, and Meir Schneller. 2009. Information uncertainty and auditor reputation, Journal of Banking and Finance, vol. 33, pages 183-92.
Nina Boyarchenko. 2009. Ambiguity, information quality and credit risk. Unpublished manuscript, University of Chicago.
Francisco Barillas, Lars Peter Hansen, and Thomas Sargent. 2009. Doubts or variability?, Journal of Economic Theory, vol. 144, pages 2388-418.
Peter Bossaerts, Paolo Ghirardato, Serena Guarnaschelli, and William Zame. 2010. Ambiguity in asset markets: theory and experiment, Review of Financial Studies, vol. 23, pages 1325-59.
Ricardo Caballero, and Arvind Krishnamurthy. 2008. Collective risk management in a flight to quality episode, Journal of Finance, vol. 63, pages 2195-230.
Claudio Campanale. 2010. Learning, ambiguity and life-cycle portfolio allocation, Review of Economic Dynamics, in press.
Henry Cao, Tan Wang, and Harold Zhang. 2005. Model uncertainty, limited market participation, and asset prices, Review of Financial Studies, vol. 18, pages 1219-51.
Henry Cao, Bing Han, David Hirshleifer, and Harold Zhang. 2007. Fear of the Unknown: Familiarity and Economic Decisions, unpublished manuscript, University of North Carolina.
Judson Caskey. 2009. Information in equity markets with ambiguity averse investors, Review of Financial Studies, vol. 22, pages 3595-627.
David Chapman, and Valery Polkovnichenko. 2009. First-order risk aversion, heterogeneity and asset market outcomes, Journal of Finance, vol. 64, pages 1863-87.
Zengjing Chen, and Larry Epstein. 2002. Ambiguity, risk and asset returns in continuous time, Econometrica, vol. 70, pages 1403-43.
Hui Chen, Nengjiu Ju, and Jianju Miao. 2009. Dynamic asset allocation with ambiguous return predictability, Boston University Economics working paper 2009-015.
Scott Condie. 2008: Living with ambiguity: prices and survival when investors have heterogeneous preferences for ambiguity, Economic Theory, vol. 36, pages 81-108.
Scott Condie, and Jayant Ganguli. 2009. Ambiguity and partially-revealing rational expectations equilibria. Unpublished manuscript, University of Cambridge.
James Dow, and Sergio Werlang. 1992. Uncertainty aversion, risk aversion and the optimal choice of portfolio, Econometrica, vol. 60, pages 197-204.
Itamar Drechsler. 2008. Uncertainty, time-varying fear, and asset prices. Unpublished manuscript, Stern School of Business, New York University.
David Easley, and Maureen O’Hara. 2009. Ambiguity and nonparticipation: the role of regulation, Review of Financial Studies, vol. 22, pages 1817-43.
Daniel Ellsberg. 1961. Risk, ambiguity and the Savage axioms. Quarterly Journal of Economics, vol. 75, pages 643-69.
Larry Epstein, and Jianjun Miao. 2003. A two-person dynamic equilibrium under ambiguity, Journal of Economic Dynamics and Control, vol. 27, pages 1253-88.
Larry Epstein, and Martin Schneider. 2003a. Recursive multiple-priors, Journal of Economic Theory, vol. 113, pages 1-31.
Larry Epstein, and Martin Schneider. 2003b. IID: independently and insitiguishably distributed, Journal of Economic Theory, vol. 113, pages 32-50.
Larry Epstein, and Martin Schneider. 2007. Learning under ambiguity, Review of Economic Studies, vol. 74, pages 1275-303.
Larry Epstein, and Martin Schneider. 2008. Ambiguity, information quality and asset pricing, Journal of Finance, vol. 63, pages 197-228.
Larry Epstein, and Martin Schneider. 2010. Ambiguity and asset markets, Unpublished manuscript, Stanford University.
Larry Epstein, and Tan Wang. 1994. Intertemporal asset pricing under Knightian uncertainty, Econometrica, vol. 62, pages 283-322.
Larry Epstein, and Tan Wang. 1995. Uncertainty, risk-neutral measures and security price booms and crashes, Journal of Economic Theory, vol. 67, pages 40-82.
Larry Epstein, and Stanley Zin. 1989. Substitution, risk aversion and the temporal behavior of consumption and asset returns: a theoretical framework, Econometrica, vol. 57, pages 937-69.
Patrick Gagliardini, Paolo Porchia, and Fabio Trojani. 2009. Ambiguity aversion and the term structure of interest rates, Review of Financial Studies, vol. 22, pages 4157-88.
Lorenzo Garlappi, Raman Uppal, and Tan Wang. 2007. Portfolio selection with parameter and model uncertainty: a multi-prior approach, Review of Financial Studies, vol. 20, pages 41-81.
Itzhak Gilboa, and David Schmeidler. 1989. Maxmin expected utility with non-unique priors, Journal of Mathematical Economics, vol. 18, pages 141-53.
Massimo Guidolin, and Francesca Rinaldi. 2009. A simple model of trading and pricing risky assets under ambiguity: any lessons for policy makers. Federal Reserve Bank of St. Louis working paper 2009-020.
Takashi Hayashi. 2005. Intertemporal substitution, risk aversion and ambiguity aversion, Economic Theory, vol. 25, pages 933-56.
Philipp Illeditsch. 2009. Ambiguous information, risk aversion and asset pricing. Unpublished manuscript, Wharton.
Cosmin Ilut. 2009: Ambiguity aversion: implications for the uncovered interest rate parity puzzle. Unpublished manuscript, Duke University.
Daehee Jeong, Hwagyun Kim, ans Joon Park. 2009. Does ambiguity matter? estimating asset pricing models with multiple-priors recursive utility. Unpublished manuscript, Texas A&M University.
Antonio Mele, and Francesco Sangiorgi. 2009. Ambiguity, information acquisition and price swings in asset markets, Financial Markets Group discussion paper 633, London School of Economics.
Jianjun Miao. 2009: Ambiguity, risk and portfolio choice under incomplete information. Annals of Economics and Finance, vol. 10, pages 257-79.
Sujoy Mukerji, and Jean-Marc Tallon. 2001. Ambiguity aversion and incompleteness of financial markets, Review of Economic Studies, vol. 68, pages 883-904.
Sujoy Mukerji, and Jean-Marc Tallon. 2004. Ambiguity aversion and the absence of indexed debt, Economic Theory, vol. 24, pages 665-85.
Han Ozsoylev, and Jan Werner. 2009. Liquidity and asset prices in rational expectations equilibrium with ambiguous information, Unpublished manuscript, University of Minnesota.
Bryan Routledge, and Stanley Zin. 2009. Model uncertainty and liquidity, Review of Economic Dynamics, vol. 12, pages 543-66.
Alessandro Sbuelz, and Fabio Trojani. 2008. Asset prices with locally-constrained-entropy recursive multiple-priors utility, Journal of Economic Dynamics and Control, vol. 32, pages 3695-717.
David Schmeidler. 1989. Subjective probability and expected utility without additivity, Econometrica, vol. 57, pages 571-87.
Mark Schroder, and Costis Skiadas. 1999. Optimal consumption and portfolio selection with stochastic differential utility, Journal of Economic Theory, vol. 89, pages 68-126.
Costis Skiadas. 2008. Dynamic porfolio choice and risk aversion. In Financial Engineering, Vol. 15, ed. JR Birge, V Linetsky, pp. 789-843. New York, Elsevier.
Fabio Trojani, and Paolo Vanini. 2002. A note on robustness in Merton’s model of intertemporal consumption and portfolio choice, Journal of Economic Dynamics and Control, vol. 26, pages 423-35.
Fabio Trojani, and Paolo Vanini. 2004. Robustness and ambiguity aversion in general equilibrium, Review of Finance, vol. 8, pages 279-324.
Harald Uhlig. 2010. A model of a systemic bank run, Journal of Monetary Economics, vol. 57, pages 78-96.
Takashi Ui. 2009. The ambiguity premium vs the risk premium under limited market participation, Unpublished manuscript, Yokohama National University.
Maxim Ulrich. 2009. Inflation ambiguity and the term structure of arbitrage-free U.S. government bonds. Unpublished manuscript, Columbia University.
Christopher Williams. 2009. Asymmetric responses to good and bad news: an empirical case for ambiguity. Unpublished manuscript, University of Michigan.
Volume 11, Issue 1, November 2009

Rasmus Lentz on Heterogeneity in the Labor Market

Rasmus Lentz is Associate Professor of Economics at the University of Wisconsin-Madison. His research interests lie in Labor Economics. Lentz’s RePEc/IDEAS entry.

1. Introduction

I will in this article take the opportunity to describe two projects that I am currently engaged in with Dale T. Mortensen and Jesper Bagger, respectively. They are part of a common research agenda that I view as an exploration of the impact of heterogeneity in the labor market.I have adopted a view of the labor market where productive resources are allocated to firms subject to frictions. Both workers and firms come in a wide range of productive capabilities. Workers are engaged in a perpetual search for higher wages and in the process they move between jobs so as to improve their productivity. At any point in time, the empirically observed large number of job-to-job transitions is a (possibly noisy) reflection of the labor market’s reallocation of resources in the direction of greater productivity.

High and low productivity firms co-exist in an uneasy relationship where the high productivity firms are expanding their scale of operations and employment of workers at the expense of the less productive firms, thereby increasing aggregate productivity. The selection into the most productive firms is limited by frictions in the expansion and maintenance of scale; research and development to expand demand for the firm’s output and/or output capacity are costly activities, and so is the effort to hire and retain workers in the labor market.

Wages reflect productive heterogeneity of both workers and firms, labor market frictions, and since wages are a primary driver of flows also the particular joint distribution of worker and firm types over matches that the market is implementing. The production function is both the key determinant of returns to worker and firm heterogeneity, and the allocation of worker and firm types over matches.

The measurement of heterogeneity’s impact on labor market outcomes allows quantification of the returns to for example human capital accumulation and job search. It is at the core of the evaluation of policies that impact the labor market’s ability to implement efficient allocation of workers to firms. Given frictional job search, the labor market may not achieve the efficient match allocation. Policies that affect the strength of frictions can impact aggregate productivity through their impact on allocation. Furthermore, as we emphasize in Lentz and Mortensen (2008a) aggregate labor productivity growth is in part a result of more productive firms making scale investments that crowd out less productive firms. We refer to this channel as the selection effect. In Lentz and Mortensen (2008a), we find that 54% of Danish productivity growth comes from the selection effect. Labor market policy can impact aggregate productivity growth through this channel if it impacts the mechanisms by which the labor market reallocates workers from less to more productive firms. The latter point applies more broadly to any policy that has a disparate impact on the expected profitability of scale investments across firm types.

In my ongoing agenda on firm heterogeneity and productivity with Dale T. Mortensen we study selection in isolation from allocation. One can well imagine the introduction of allocation considerations in the analysis, although at substantial technical cost. In my work with Jesper Bagger labor market frictions impact both allocation and selection.

In the following, I initially discuss measurement concerns that are common to the two projects. I then proceed to first discuss my project on firm heterogeneity, productivity and labor market friction with Dale T. Mortensen. Then, I discuss my project on sorting and wage dispersion with Jesper Bagger.

2. Measurement

Along with the agenda follows a measurement challenge which typically becomes a major topic of its own. In both of the projects I discuss below, we are currently in the process of estimation. I use Danish matched employer-employee micro panel data. Similar data are available for the United States through the US Census. The fundamental observation in the data is a match between a worker ID and firm ID. Along with this observation follows a record of match specific observations like for instance the start and end dates of the match, and wages. The ID’s are constant over time allowing a record of a worker’s match history and the same for each individual firm. In addition to the match core is a record of possibly time varying worker and firm characteristics. In the case of the Danish data, the entire population of matches is observed from 1980 to date. A similar wealth of data is available for the United States. Needless to say, these are remarkable data but they remain indirect reflections of the key objects of interest. Hence, I approach the data with the help of explicit model structures. The structure provides a lens through which I view the data. From an estimation point of view, it is a way of stating maintained identifying assumptions.Estimation is done by indirect inference. If we could estimate by maximum likelihood, we would. However, the models do not produce likelihood expressions that are practically implementable. Furthermore, a maximum likelihood estimation strategy requires constant access to the data throughout the estimation process and because data access is limited due to confidentiality requirement, computation must therefore be done on servers of the statistical agency that hosts the data. For obvious reasons, statistical agencies typically have computation solutions that are focused on data hosting and access. Less attention is paid to raw computation power and clusters for parallel computing. This is not a good environment for numerically intensive model solving tasks such as those I am facing.

Indirect inference provides a feasible estimation strategy. In addition, it has a few practical advantages as well. First, through the specification of the auxiliary model, it allows a focus on the particular aspects of the data that the model is supposed to speak to. Of course, the freedom of choice of auxiliary model involves the risk of leaving out relevant information in the data, and so care must be taken in this step. Second, the auxiliary model can be designed so that the statistics involved are not subject to the data confidentiality restrictions and can therefore be extracted from the servers of the statistical agency. Estimation can subsequently be done on the researcher’s preferred computation solution. This is really practical. It also broadens data access to researchers without access to the actual confidential micro data – as long as the specified auxiliary model also provides identification in these other cases.

Finally, by including existing reduced form approaches to the question at hand in the auxiliary model, indirect inference allows an easy bridge between the model estimation results and existing reduced form studies. While the existing studies will typically not be actual reduced forms for the model in question, they nevertheless often times contain valuable identifying information. And in the case where they do not help identification, that is an important point as well since the interest in the reduced form typically comes from the conviction that it identifies key points of interest.

3. Firm Heterogeneity, Productivity, and the Labor Market

The Danish micro panel data reveal a number of stylized facts: At any point in time, there is great measured labor productivity dispersion across firms. More productive firms pay higher wages, they are larger in terms of output and to some extent also in terms of input. It is a general feature in these kinds of data that the relationship between firm output and productivity is robustly positive, but the relationship between productivity and input size can be weak. Labor productivity is persistent but not permanent. Firms tend to be born small and they tend to die small. The distribution of labor force size across firms is left skewed with a thick right tail. Workers tend to move in the direction of higher wages.In my work with Dale T. Mortensen on firm heterogeneity and productivity we establish a framework consistent with the data that explicitly connects labor market frictions with the determination of aggregate productivity. The model is a modification of the general equilibrium model of firm dynamics in Lentz and Mortensen (2008a), which builds on Klette and Kortum (2004).

Firms produce intermediary goods. Each intermediary good has a demand that is determined through the aggregation of intermediary goods into a final consumption good. The production of an intermediary good requires labor and firms differ from each other in their labor productivity. It is assumed that production is constant returns to scale in labor. A firm can expand its scale of operations by undertaking a costly product innovation effort which according to a stochastic arrival process yields a new intermediary product which I will also refer to as a product line. Firms can have multiple product lines.

Labor is obtained from the labor market subject to frictions. Matches are a result of costly search and recruitment effort by both workers and firms. Each product line operates its own hiring process and sets wages according to a Stole and Zwiebel (1996) bargaining mechanism. In this wage setting mechanism, each worker bargains with the firm as if the worker is the marginal worker. By assumption worker reallocation between product lines within a firm is subject to the same frictions as those of the overall labor market.

A firm is fully characterized by its labor productivity type and its product portfolio, including the labor force size state of each product line. A firm is born with a single product line as a result of entry effort by a potential entrant. Upon entry, the firm immediately learns its productivity type. A firm exits upon the destruction of its final product. A firm’s type is persistent but need not be permanent.

More productive firms have greater expected profits from scale expansion than less productive firms. Consequently, they choose greater product innovation rates. A product line is destroyed according to the same obsolescence rate regardless of its inventor, and so on average more productive firms obtain greater scale (number of product lines) than less productive firms.

The differential scale expansion rates across firms is at the core of the selection contribution to productivity. Because more productive firms expand at a greater rate, in steady state they employ a greater share of productive resources compared to their birth distribution representation. In this case, the selection effect contributes positively to productivity as the more productive firms crowd out the less productive ones. In Lentz and Mortensen (2008a) we estimate a growth version of this model without labor market frictions on Danish firm panel data. We find the selection effect to be a very important source of productivity growth. In the counterfactual where the distribution of productive resources over firm types is set according to the type distribution at birth rather than that in steady state, productivity growth is less than half.

The impact of labor market friction on the selection effect turns out to be non-trivial. Firm size is in the model constrained by current product demand and labor market frictions. For some firm types, product demand is the more important constraint, for others labor market frictions play a greater role. Therefore, a policy that reduces the level of friction will impact the strength of the selection effect through a disparate impact on firm types. As a side note, this is also an example of an environment where it is crucial to correctly model heterogeneity. A representative firm model completely misses this point.

A product line’s labor force size follows a stochastic birth-death process. Workers are added as a result of recruitment activity and they are lost to exogenous separation and to quits to other firms. Broadly speaking, a more productive firm has a greater return to recruitment than a less productive firm. In combination with a higher match acceptance rate by workers, a more productive firm has a greater hiring rate. The more productive firm also tends to lose workers to other firms at a lower rate. Therefore, absent demand constraints, more productive firms will on average be larger. A reduction in labor market friction will unambiguously strengthen this pattern and the impact on the selection effect would be unambiguously positive.

The interaction with demand constraints complicates matters. If greater productivity does not increase a product line’s frictionless labor demand level much, then it is possible to find an environment where labor force size is primarily demand constrained for high productivity firms and primarily labor friction constrained at the low productivity end. A friction reduction will in such an environment do little to labor demand at the high productivity end but expand labor force size at the low end. This would in isolation weaken the selection effect and could pave the way for the somewhat counterintuitive result that a labor market friction reduction lowers aggregate productivity. I emphasize this complication not because I have any particular reason to believe that it is empirically relevant, nor do I know it to be irrelevant. Rather, I want to highlight that the evaluation of policy instruments and counterfactuals depends crucially on the particular model parameter specification. Hence, the obvious value of fully estimated model.

We are currently working with two versions of the model that differ in the firm’s product pricing mechanism. In one version, product pricing is a result of Betrand competition between the innovating firm and a competitive fringe that can also produce the product but at a productivity disadvantage. One interpretation of the competitive fringe is home production within households. We describe this version of the model in detail in Lentz and Mortensen (2008a). In this case, the marginal productivity of a worker within a product line is constant up to the point where product demand is exhausted. As a result, worker reallocation is purely driven by a desire to move up the product line productivity ladder.

In the other version, product pricing is set by monopoly pricing and the marginal productivity of a worker within a product line is decreasing in the line’s labor force size. In this case, worker reallocation is not just from low to high productivity product lines, but also from well staffed lines to newly created ones that have yet to staff up. Labor market friction and the degree of substitutability between intermediary products determine the extent to which marginal worker productivity is equalized across product lines.

We are in the process of estimating the model and will subsequently explore the link between labor market policies and counterfactuals on aggregate productivity.

4. Sorting, Labor Market Flows and Wages

My project with Jesper Bagger focuses on the measurement of the impact of worker and firm heterogeneity on wages in an environment with labor market frictions and possible sorting. The project is also directly concerned with the measurement of sorting itself.Worker heterogeneity is modelled as a simple single dimensional characteristic referred to as skill. Similarly, firms are characterized by a single dimensional productivity index. For the sake of simplicity, it is assumed that firm production is additively separable across matches. This is clearly an assumption that must be relaxed as the literature moves forward, but for now it allows a relatively simple discussion of the mapping between match production function characteristics and the joint distribution of worker skill and firm productivity over matches. It is assumed that productive heterogeneity is absolute meaning that for any given firm type, a more skilled worker is more productive than a less skilled worker. Similarly for firm productivity.

There is positive complementarity between worker skill and firm productivity if the match production function is supermodular in skill and productivity. In this case, the sum of production from two matches where a high skill worker is matched with a high productivity firm in one match and a low skill worker is matched with a low productivity firm in the other exceeds the output sum of the two matches where you match the high skill worker with the low productivity firm and the low skill worker with high productivity firm. There are negative complementarities in production if the production function is submodular. In this case, the inequality in the example above is reversed, that is, matching opposites produces more than matching likes.

The studies of the partnership model in Becker (1973) and subsequently with matching frictions in Shimer and Smith (2000) emphasize the connection between matching function complementarities and sorting patterns in the equilibrium match distribution. Absent frictions, production function supermodularity (submodularity) induces positive (negative) sorting. Matching frictions complicate matters somewhat. Shimer and Smith (2000) show that log-supermodularity and log-submodularity of the production function are sufficient for positive and negative sorting, respectively. The partnership model takes as given a fixed population of heterogeneous agents. They can match with only one agent at a time. In Shimer and Smith (2000), matched agents cannot search while matched. In their ongoing projects where they apply the partnership model to the study of wages and sorting, Lise, Meghir and Robin (2008) and de Melo (2008) relax this assumption on the worker side of the market. In his study of replacement hiring and wages, Bobbio (2009) relaxes this assumption on both sides of the market. The partnership model’s assumption of scarcity in matching opportunities is a key source of discriminating behavior. In order to accept a match opportunity, it has to compensate the agent for the loss of value from the meeting process while matched. The application of the partnership model to multi-worker firms typically assumes that each position in the firm has its own hiring process that produces meetings that apply only to the position in question.

In Lentz (2010), I set forth an on-the-job search model where sorting can arise as a result of search intensity choice variation across worker types. I show that if the match production function is supermodular, more skilled workers have relatively greater gains from outside job opportunities, they consequently search harder and in a stochastic dominance sense end up matched with more productive firms. That is, positive sorting. In the case where the match production function is submodular, negative sorting obtains.

Unlike the partnership model, firms are non-discriminatory as they are unconstrained in matching opportunities due to the assumption of constant returns to scale. Each firm has a central hiring process that produces meetings. If a firm decides to match with a worker, it does not reduce the value of the hiring process because it always has room for any additional match opportunity the process produces. If workers were to receive job opportunities at the same rate regardless of skill level and employment state, this environment would produce no sorting regardless of the match production function characteristics. This is exactly the case in Postel-Vinay and Robin (2002). Workers, of course can only match with one firm at a time, but since they receive job opportunities at the same rate while matched as they do unmatched, they too are non-discriminatory. Allowing workers to choose the amount of resources they dedicate to the creation of meetings through their choice of search intensity brings back the possibility of sorting.

The sorting by search intensity model and the partnership model represent two benchmark views of the firm’s role in the determination of sorting in the labor market. In the partnership model, firms are highly discriminatory since they are for the purpose of sorting just like single worker firms. In the sorting by search intensity model firms are completely non-discriminatory due to complete absence of match opportunity scarcity. Both views have obvious merit and underscore the importance of a continued push towards a deeper understanding of the firm in labor market research.

In my work with Jesper Bagger, we build an empirical general equilibrium model of sorting and wages based on the sorting by search intensity mechanism. We assume wage bargaining as in Dey and Flinn (2005) and Cahuc, Postel-Vinay and Robin (2006). In this model workers move up the firm productivity ladder through the offer accumulation process. As the worker accumulates offers, she also accumulates bargaining power since wages are effectively set through bargaining with a worker’s outside option of full surplus extraction with the second best job offer during the employment spell in question. For a given worker-firm match, job separation and worker search intensity are jointly efficient.

The match production function translates worker skill and firm productivity indices into output. It is the production function that determines the productive returns to both worker skill and firm productivity. It is also a key determinant of allocation patterns. Hence, model estimation can in many ways be thought of as a structural production function estimation. In most employer-employee data sets, the Danish one included, we only have output measures at the firm level. At the firm level, output is a convolution of the firm productivity effect and the skill effects of all of its workers. However, the data contain wage observations at the match level. Insofar that wages reflect the characteristics of the match production function, one can use wages for identification of the production function. One notable candidate is the log wage decomposition in Abowd, Kramarz and Margolis (1999), where unobserved individual worker and firm wage effects are identified in addition to the impact of observed worker characteristics. The identification strategy relies on the assumption that log wages be an additive and monotone function of the worker and firm wage effects.

Both the sorting by search intensity model and the partnership model produce a wage function that relates worker and firm characteristics to average match wage realizations. As it turns out, in contrast to the match production function, the average match wage realization is not a monotone function of worker skill and firm productivity once sorting is allowed. The ongoing sorting and wage projects based on the partnership model are finding a similar result, although through a substantially different mechanism. Needless to say, this throws quite a lot of sand into the gears of an identification strategy based primarily on something like the Abowd, Kramarz and Margolis (1999) wage decomposition. For example, all of the mentioned projects on sorting and wages emphasize that it is perfectly possible to have an estimated negative correlation between worker and firm wage effects in an environment characterized by positive complementarities in production and an associated positive sorting between worker skill and firm productivity in the match distribution.

Eeckhout and Kircher (2009) and de Melo (2008) propose identification strategies for the strength of sorting based on the idea of comparing variance of worker types within firms to that of the overall population. The approaches are useful advances, however, the strategies do not identify the type of sorting and in addition the identification of worker types may be quite sensitive to the particular modelling framework at hand. So, more information must be brought to bear. In Bagger and Lentz (2008) we propose one identification strategy that combines the observation of unemployment and employment durations with the observed job flows in and out of firms. The type of sorting is revealed by correlating observed unemployment duration with a measure of a worker’s position in the skill hierarchy. In the model, high skill workers have short durations when there are positive complementarities in production and long durations when the complementarities are negative. The firm productivity hierarchy is identified by observing a firm’s relative inflow of job-to-job transitions to its outflow of job-to-job transitions. This measure stems from an ongoing project I am engaged in with Chris Taber and Rune Vejlin where job-to-job transitions are viewed as a possibly noisy revelation of a worker’s preferences over the two firms involved. Identification of worker skill is facilitated by the identification of the productivity hierarchy. The use of worker flow and duration data for the purpose of identifying match allocation and heterogeneity is sensible but the information that is extracted from flows and durations is typically quite model sensitive. A major challenge moving forward is to formulate identification strategies that are robust across modelling frameworks.

We are currently estimating the model and exploring additional identification strategies.


Abowd, John M., Francis Kramarz, and David N. Margolis (1999). “High wage workers and high wage firms,” Econometrica vol. 67(2), pages 251-334.
Becker, Gary S. (1973). “A theory of marriage: Part I,” The Journal of Political Economy vol. 81(4), pages 813-846.
Bobbio, Emmanuele (2009). “Replacement hiring and wages,” Working Paper, University of Wisconsin-Madison.
Cahuc, Pierre, Fabien Postel-Vinay, and Jean-Marc Robin (2006). “Wage bargaining with on-the-job search: Theory and evidence,” Econometrica vol. 74(2), pages 323-364.
de Melo, Rafael Lopes (2008). “Sorting in the labor market: Theory and measurement,” Yale Working Paper.
Dey, Matthew S. and Christopher J. Flinn (2005). “An equilibrium model of health insurance provision and wage determination,” Econometrica vol. 73(2), pages 571-627.
Eeckhout, Jan and Philipp Kircher (2009). “Identifying sorting – in theory,” PIER Working Paper 09-007
Klette, Tor Jakob and Samuel Kortum (2004). “Innovating firms and aggregate innovation,” Journal of Political Economy vol. 112(5), pages 986-1018.
Lentz, Rasmus (2010). “Sorting by search intensity,” Forthcoming in Journal of Economic Theory.
Lentz, Rasmus and Dale T. Mortensen (2008a). “An empirical model of growth through product innovation,” Econometrica vol. 76(6), pages 1317-1373.
Lentz, Rasmus and Dale T. Mortensen (2008b). “Labor market friction, firm heterogeneity, and aggregate employment and productivity,” Working Paper, University of Wisconsin-Madison.
Lentz, Rasmus, Christopher Taber and Rune Vejlin (2009). “Sources of Wage Inequality,” Working Paper, University of Wisconsin-Madison.
Lise, Jeremy, Costas Meghir, and Jean-Marc Robin (2008). “Matching, sorting, and wages,” University College London Working Paper.
Postel-Vinay, Fabien and Jean-Marc Robin (2002). “Equilibrium wage dispersion with worker and employer heterogeneity,” Econometrica vol. 70(6), pages 2295-2350.
Shimer, Robert and Lones Smith (2000). “Assortative matching and search,” Econometrica vol. 68(2), pages 343-369.
Stole, Lars A. and Jeffrey Zwiebel (1996). “Intra-firm bargaining under non-binding contracts,” Review of Economic Studies vol. 63(3), pages 375-410.
Volume 10, Issue 2, April 2009

Marco Bassetto on the Quantitative Evaluation of Fiscal Policy Rules

Marco Bassetto is a Senior Economist in the Economic Research Department at the Federal Reserve Bank of Chicago. He is interested in political-economy models of fiscal policy and in applications of game theory to the analysis of macroeconomic policy more in general. This piece reflects the personal views of the author and not necessarily those of the Federal Reserve Bank of Chicago or the Federal Reserve System. Bassetto’s RePEc/IDEAS entry.

1. Introduction

In 2009, the federal government is poised to run the biggest peacetime deficit in the history of the United States (both in absolute value and as a fraction of gross domestic product, or GDP). Current projections suggest that large deficits will persist in future years, considerably raising the debt/GDP ratio and putting additional strains on future public finances, which will soon also be challenged by the retirement of the baby boomers.These developments are likely to rekindle debate about the desirability of imposing restrictions on government indebtedness. Constraints on deficit financing are the norm for state and local governments in the United States, and they are part of the European Stability and Growth Pact (SGP) to which eurozone countries have committed.

There is a large political-economy literature on government deficits and debt. On the theoretical side, most papers derive qualitative predictions from stylized models. On the empirical side, many papers have studied the consequences of different fiscal constraints on spending and debt (see, e.g., Poterba, 1994 and 1995, Bohn and Inman, 1996); these papers provide quantitative answers, but they do not contain a model that can be used for welfare considerations, or to extrapolate to fiscal institutions that have not been used in the past.

Few papers have attempted to bridge the gap, developing quantitative theoretical models that can be used to study the welfare properties of different fiscal restrictions. As an example, Krusell and Ríos-Rull (1999) have studied the dynamics of government redistribution under a balanced budget, as a function of the frequency with which government decisions are taken.

In this piece, I review some recent quantitative contributions that deal with fiscal deficits and debt, and I discuss open questions that warrant future consideration.

In the first set of papers, a balanced-budget restriction (BBR) is necessarily desirable, and the research question is whether public investment should be subject to the BBR in the same way as ordinary government expenses. The second set of papers abstracts from government investment, but introduces a cost of enacting a BBR, through the inability to smooth tax rates in response to shocks. It then becomes possible to discuss under what conditions a BBR actually improves welfare.

2. Does public investment deserve special treatment?

One of the main complaints about the original form of the European SGP concerned the lack of special provisions for public investment (see, e.g., Monti, 2005). Its reform in 2005 heeded these criticisms, and now “policies to foster research and development and innovation” are taken into account in evaluating whether a deficit is truly excessive (European Council on the Stability and Growth Pact, 2005, article 1).Similarly, all U.S. states can borrow to pay for long-term capital projects. They follow what is known in public finance as the “golden rule,” whereby a jurisdiction should balance its operating budget, but should be able to borrow to pay for capital improvements. This rule has a long tradition both in theory and actual policy, and is mostly justified on the grounds of “fairness”: The operating budget is assumed to benefit current residents, who should thus bear its cost, while public improvements offer long-run benefits to future generations, which implies that it is fair to also ask them to share the burden by using debt financing.

How important was the 2005 reform of the SGP for restoring appropriate incentives to invest in public infrastructure? If a balanced-budget amendment were included in the U.S. Constitution, would public capital deserve special treatment? What other features of the environment are relevant in assessing the quantitative impact of different provisions? We look for the answers to these questions in a series of recent papers.

In Bassetto with Sargent (2006), we introduce the framework of analysis and apply it to the Unites States. In this research, we consider an economy populated by overlapping-generations of potentially mobile households, in which government spending is chosen period by period by current residents. In their decisions, voters only take into account their own present and future costs and benefits, while they neglect those that will accrue to other future residents (new people coming of age or new immigrants).

The government produces two types of public goods: One is durable, while the other is not. The environment is such that a BBR necessarily yields a Pareto-efficient choice for nondurable public goods: all households alive are assumed to benefit in the same way, and to also pay taxes in the same amount. A BBR forces current households to pay exactly for the services they get from the government, and yields correct incentives. The same does not happen for public investment, since current investment will have long-lasting benefits.

We analyze a constitutional restriction on government indebtedness that features two key parameters:
a. The fraction of government investment that can be excluded from the deficit count (e.g., 100% according to the golden rule) and
b. The maturity structure of debt, which measures how fast newly incurred debt has to be repaid.

Two relevant conflicts emerge in the determination of public investment: the first among current voters, who are heterogeneous by age and thus face different mortality and mobility profiles, and the second between current voters and future residents. With a growing population, the second effect always dominates under a pure BBR, leading to underinvestment: the current voters fully take into account the immediate cost, but they only partially internalize future benefits. Under further mild restrictions on the demographic structure and/or the maturity of debt, we obtain the intuitive result that allowing some issuance of debt alleviates the underinvestment.

In our quantitative calibration, we assume that the government is allowed to issue long-term debt that has to be repaid gradually over time through a sinking fund. This is a common practice among U.S. states. For this case, we establish the following results.

a. The golden rule, with 100% deficit financing of public capital, tends to perform very well. The precise amount of deficit financing that exactly yields an efficient outcome is not affected much by the demographic details.

b. When the constitutional restriction is far away from the optimum, demographics are important for the magnitude of the resulting distortions. This is not surprising, since demographics are what drives the economy away from Ricardian equivalence in our context.

c. When the borrowing limit treats public capital and nondurable public consumption in the same way, we find much bigger distortions at the state level than at the federal level. At the state level, people discount future costs and benefits because of mobility more than mortality: at most ages, the hazard of moving out of state is much higher than the hazard of death. By contrast, the hazard of moving out of the United States is negligible.

The quantitative results thus suggest that the current pattern of U.S. institutional restrictions is well matched to its theoretical benefits: the golden rule is practiced by the states, where benefits are likely to be large, but not at the federal level, where benefits would not be as prominent.

In Bassetto and Lepetyuk (2007), we apply the same model to European data. As expected, the costs of not including an investment exemption in the SGP turn out to be modest: European countries are about as far away from Ricardian equivalence as the U.S. federal government, with a somewhat higher hazard of emigration offsetting lower population growth.

More surprisingly, we find that the golden rule performs rather poorly in the context of the SGP, generating distortions from overinvestment that are about as big as those for underinvestment in the original version of the SGP, which treated operating and capital expenses symmetrically. This is because the SGP only counts interest payments against a country’s deficit allowance, allowing indefinite rollover of debt principal. Thus, under the golden rule the additional taxes needed to pay for public investment would be shifted into the future much more than the benefits from the investment. Two possible solutions to this problem are as follows:
a. excluding less than 100% of investment from the deficit count (in our numerical results, about 50% turns out to be appropriate); and
b. excluding net, rather than gross,investment from the deficit count. By including depreciation in the deficit count, this strategy is equivalent to forcing a gradual repayment of the debt that is issued to finance public investment. The drawback of this strategy is that depreciation is difficult to measure, opening a new margin to skirt the rules.

In ongoing work (Bassetto, 2009), I extend the analysis to account for the possibility of endogenous mobility, as well as different tax bases. This extension of the research is particularly important to understand which rules are best suited for local communities, where the household location decision is much more likely to be affected by local amenities and taxes.

Starting from Tiebout (1956), there is a large literature in local public finance that considers how endogenous location affects voters’ incentives. One of the central themes in this literature is capitalization: local amenities and debt are likely to be reflected in the property prices. The theoretical literature (see, e.g., the survey by Mieszkowski and Zodrow, 1989) has analyzed in detail the environments that are more or less conducive to capitalization. Most of these papers consider static environments, with a few considering overlapping-generations of households living for two periods; thus they are difficult to use for quantitative policy analysis. There is also a vast empirical literature that has tried to estimate the magnitude of capitalization.

I develop a dynamic model with long-lived agents, in which the parameters of the model can be more easily related to empirical counterparts, to deliver quantitative predictions about the effects of different policy rules on the efficiency of government spending.

When the tax base is income, endogenous mobility creates two opposing forces on the voters’ incentive to provide public capital. First, a congestion externality is exacerbated: when additional public capital makes a location more attractive, more people move to that location, free-riding on the original investment and diluting its benefits for the original residents. Second, capitalization mitigates the externality: the increased demand for living in the location raises property prices, which benefits the original residents (assumed to own their house). Thus, it is important whether equilibrium adjustments mainly occur through quantity (population size) or through price.

Early quantitative results hint that the price adjustment will be insufficient to provide appropriate incentives for local public investment. An explicit rule that favors capital investment is thus called for. Alternatively, zoning restrictions are needed to drastically limit adjustment in population size.

3. Should we impose a BBR on the federal government?

Answering this question is one of the themes in recent work by Battaglini and Coate (2008a, 2008b) and Azzimonti, Battaglini, and Coate (2008). In their work, in each period the public sector can use its resources in two different ways: by providing public goods or by redistributing resources toward favored groups (“pork-barrel spending”). Public revenues come from a distortionary tax on labor, and the government has access to risk-free borrowing and lending, but cannot issue state-contingent debt. In each period, each group (“district”) has one representative in the policy-making body (“Congress”), and a random coalition forms and makes a decision.In this environment, debt is potentially beneficial for tax-smoothing considerations, such as in Barro (1979) and Aiyagari et al. (2002). However, access to debt is also a potential source of inefficiency, since the partisan nature of some policies introduces a deficit bias akin to what Alesina and Tabellini (1990) and Tabellini and Alesina (1990) describe. Specifically, in each period, the coalition in power has the opportunity to appropriate government funds and redistribute them to its own constituents. This is ex ante undesirable, since it involves raising revenues with distortionary taxes and rebating the proceeds to (a random group of) taxpayers. However, ex post, the transfers may be beneficial to the group in power at the expense of the others. Running deficits constrains future coalitions, which may redistribute government funds in ways that the current coalition finds undesirable.

Battaglini and Coate (2008a, 2008b) prove that the economy will necessarily alternate between two regimes:
a. “Responsible policy-making,” when the marginal distortions from taxation are sufficiently high as to discourage diversion of public funds for redistributive purposes and
b. “Business as usual,” when public resources are less scarce and the coalition in power engages in such targeted spending.

Responsible policy-making will prevail when the economy inherits a high level of public debt, or when it faces an adverse shock such as a high need for the general public good (e.g., during a war). When the adverse shock ends, the debt level gradually drifts lower, until it reaches a level at which business as usual restarts.

An important observation is that a BBR is a cure for one of the symptoms of inefficiency, but not for its source. While a deficit bias obviously disappears under a BBR, pork-barrel spending does not. In a calibrated example, Azzimonti, Battaglini, and Coate (2008) show that the prevalence of pork-barrel spending actually increases under a BBR, since the governing coalitions are no longer subject to the fiscal discipline imposed by servicing large amounts of debt. This insight potentially applies to many other environments, and serves as a warning that curing deficits simply by banning them may cause undesirable consequences unless we have a clear understanding of the political frictions that generate Pareto-dominated outcomes.

In ongoing work, Azzimonti, Battaglini, and Coate (2008) evaluate quantitatively the consequences of a balanced-budget amendment to the U.S. constitution. Their preliminary results show that the welfare consequences depend on the initial level of debt. When the government is not initially subject to a BBR and debt is at any of the values in the support of the associated ergodic distribution, introducing a BBR would never be desirable.

Azzimonti, Battaglini and Coate’s calibration struggles to match the pattern of peacetime deficits, since the shock-absorbing role of government debt is minor in response to typical business-cycle shocks. This may be of concern because the cyclical behavior of spending is used to identify the magnitude of political distortions. Nonetheless, the match to the actual variability of spending and debt is quite good when the possibility of large shocks such as World War II is introduced, and their work represents an important step in developing a dynamic quantitative model of the costs of partisan policymaking.

4. Where should we go next?

The papers described in the previous sections are but one step in bringing quantitative economic modeling to the optimal design of fiscal institutions. Future work will have to develop in three dimensions:

a. Robustness

The previous analysis relies on specific political-economic frictions. To what extent do the implications generalize to other settings? As an example, let me briefly speculate on the robustness of the results about the golden rule.

It is straightforward to see that the rule would be much more beneficial if we assumed that operating budgets are subject to a deficit bias arising from partisan policymaking, while public investment is purely for the common good, as in Peletier, Dur, and Swank (1999), Azzimonti (2004), or Battaglini and Coate (2007). However, this assumption is at odds with the observation that “pork projects” are often capital items (e.g., the now infamous “bridge to nowhere”).

Consider instead the following scenario, vaguely inspired by work of Rogoff and Sibert (1988), Rogoff (1990), and Besley and Smart (2007). Suppose that it takes time for voters to correctly assess the benefits of a long-term project (e.g., investment in renewable energy resources). Then, in the short run, it is difficult for the voters to distinguish the farsighted politicians, who are able to discern good projects, from the incompetent ones, who may pick projects more or less at random. This difficulty may bias policymaking to short-term projects, for which competence may be easier to signal to voters. Is this an important quantitative force? Only by developing models that are more detailed will we be able to gain confidence in the robustness of the institutional recommendations.

b. Analysis of other fiscal institutions

In this discussion, I have only addressed two specific questions. In practice, there are of course countless other dimensions of fiscal institutions worth considering. Taking again inspiration from current events, the stimulus package signed into law by President Obama on February 17 contains substantial transfers from the federal government to state governments. Moreover, federal matching is a standard feature for some expense items (such as interstate highways) but not in others (education). How large should a federal match be, and in what circumstances should it be granted? Are externalities from public goods quantitatively more important for this question, or is it more important to pay attention to insurance and discipline (see, e.g., Persson and Tabellini, 1996a and 1996b, or Sanguinetti and Tommasi, 2004)?

These questions are important not just for the United States, since transfers from the central government to regional/provincial governments are or have been prominent in a number of countries (e.g., Argentina, Brazil, or Italy).

c. Tax base

Should we rely more or less on property taxes, rather than income taxes, to finance government expenditures? Two provocative papers by Rangel (2005) and Conley and Rangel (2001) argue that land taxes (based on pure acreage, not value) would be very beneficial for intertemporal incentives. As we discuss in Bassetto (2009), the drawback of pure land taxes is that they would be unable to generate substantial revenues without dragging the value of the marginal land to zero, at which point the scheme unravels. Does this imply that we should move towards income or sales taxes? Or should we instead consider property taxes, which may have beneficial capitalization effects but distort capital accumulation?

d. Intergenerational accounting

In the works cited previously, what represents a deficit is clearly defined, and government debt captures well the intertemporal effects of fiscal policy. Yet Auerbach and Kotlikoff (along with various coauthors) have forcefully argued for intergenerational accounting as a more comprehensive and appropriate measure (see, e.g., Auerbach, Gokhale, and Kotlikoff, 1991 and 1994, and Kotlikoff, 1992).

In the context of distortionary taxation, a similar point is made formally in Bassetto and Kocherlakota (2004): When the government has the power to tax (or subsidize) past income, the same allocation can be supported by arbitrary paths for government debt (for an application to Social Security, see Grochulski and Kocherlakota, 2007). This is particularly an issue in models of “new dynamic public finance,” where the fiscal distortions arise purely out of asymmetric information between the private sector and the fiscal authority. In these papers, the ability to tax past income is always present, and the deficit path may be correspondingly indeterminate.

Several papers have looked at the political-economy of intergenerational accounting, particularly from the perspective of social security (see, e.g., Cooley and Soares, 1996, Galasso, 1999, Song, Storesletten, and Zilibotti, 2007, and Bassetto, 2008). The introduction of a balanced-budget restriction would most likely interact with the considerations raised in these papers.

e. Timing of institutional reforms

Policy choices are endogenous in the work described previously, but institutional constraints are taken as given, and the goal of the research is to assess the welfare properties of imposing alternative restrictions on fiscal policy. A separate but important issue is when an institutional reform takes place, and how. In the case of U.S. states, the introduction of balanced-budget requirements dates back to the aftermath of the state defaults of the 1840s (see, e.g., Secrist, 1914). These constitutional reforms took place at a time when access to borrowing for states was severely disrupted; indeed, a renewed commitment to fiscal responsibility could be viewed as a way of restoring access to credit markets. This is but one example of a general pattern, whereby major fiscal reforms often follow a public finance crisis (for some other examples, see Sargent, 1983a and 1983b). The largely ineffective Gramm-Rudman-Hollings Act of 1985 could also be seen in this light – it was a preventative measure that was enacted out of concern for the consequences of the then-unprecedented deficits of the Reagan era.

While these considerations warrant a more systematic analysis, they suggest to me that now may be the perfect time for economists to engage in a debate over the fiscal institutions that will serve the United States for the next generation and beyond.


Aiyagari, Rao, Albert Marcet, Thomas J. Sargent, and Juha Seppälä, 2002. “Optimal Taxation without State-Contingent Debt,” Journal of Political Economy, vol. 110(6), pp. 1220-1254.
Alesina, Alberto, and Guido Tabellini, 1990. “A Positive Theory of Fiscal Deficits and Government Debt,” Review of Economic Studies, vol. 57(3), pp. 403-414.
Auerbach, Alan J., Jagadeesh Gokhale, and Laurence J. Kotlikoff, 1991. “Generational Accounts: a Meaningful Alternative to Deficit Accounts,” in: “Tax Policy and the Economy,” (D. Bradford, ed.), MIT Press, vol. 5, pp. 55-110.
Auerbach, Alan J., Jagadeesh Gokhale, and Laurence J. Kotlikoff, 1994. “Generational Accounting: A Meaningful Way to Evaluate Fiscal Policy,” Journal of Economic Perspectives, vol. 8(1), pp. 73-94.
Azzimonti, Marina, 2004. “On the Dynamic Inefficiency of Governments,” mimeo, University of Texas.
Azzimonti, Marina, Marco Battaglini, and Stephen Coate, 2008. “Analyzing the Case for a Balanced Budget Amendment to the U.S. Constitution,” mimeo, University of Texas, Princeton University, and Cornell University.
Barro, Robert J., 1979. “On the Determination of the Public Debt,” Journal of Political Economy, vol. 87(4), pp. 940-971.
Bassetto, Marco, 2008. “Political Economy of Taxation in an Overlapping-Generations Economy,” Review of Economic Dynamics, vol. 11(1), pp. 18-43.
Bassetto, Marco, 2009. “Public Investment and Budget Rules for State vs. Local Governments,” mimeo, Federal Reserve Bank of Chicago.
Bassetto, Marco, and Narayana Kocherlakota, 2004. “On the Irrelevance of Government Debt when Taxes are Distortionary,” Journal of Monetary Economics, vol. 51(2), pp. 299-304.
Bassetto, Marco, and Vadym Lepetyuk, 2007. “Government Investment and the European Stability and Growth Pact,” NBER Working Paper, n. 13200.
Bassetto, Marco, with Thomas J. Sargent, 2006. “Politics and Efficiency of Separating Capital and Ordinary Government Budgets,” Quarterly Journal of Economics, vol. 121(4), pp. 1167-1210.
Battaglini, Marco, and Stephen Coate, 2007. “Inefficiency in Legislative Policy-Making: A Dynamic Analysis,” American Economic Review, vol. 97(1), pp. 118-149.
Battaglini, Marco, and Stephen Coate, 2008a. “A Dynamic Theory of Public Spending, Taxation, and Debt,” American Economic Review, vol. 98(1), pp. 201-236.
Battaglini, Marco, and Stephen Coate, 2008b. “Fiscal Policy over the Real Business Cycle: A Positive Theory,” NBER Working Paper, n. 14047.
Besley, Timothy, and Michael Smart, 2007. “Fiscal Restraints and Voter Welfare,” Journal of Public Economics, vol. 91(3-4), pp. 755-773.
Bohn, Henning, and Robert P. Inman, 1996. “Balanced-Budget Rules and Public Deficits: Evidence from the U.S. States,” Carnegie-Rochester Conference Series on Public Policy, vol. 45, pp. 13-76.
Conley, John P., and Antonio Rangel, 2001. “Intergenerational Fiscal Constitutions: How to Protect Future Generations Using Land Taxes and Federalism,” NBER Working Paper, n. 8394.
Cooley, Thomas F., and Jorge Soares, 1999. “A Positive Theory of Social Security Based on Reputation,” Journal of Political Economy, vol. 107(1), pp. 135-160.
European Council on the Stability and Growth Pact, 2005. Council Regulation No. 1056/2005.
Galasso, Vincenzo, 1999. “The U.S. Social Security System: What Does Political Sustainability Imply?” Review of Economic Dynamics, vol. 2(3), pp. 698-730.
Grochulski, Borys, and Narayana R. Kocherlakota, 2007. “Nonseparable Preferences and Optimal Social Security Systems,” Minnesota Economics Research Reports, n.1.
Kotlikoff, Laurence J., 1992. “Generational Accounting: Knowing who Pays, and when, for what we Spend,” Macmillan, Free Press.
Krusell, Per, and José-Víctor Ríos-Rull, 1999. “On the Size of U.S. Government: Political Economy in the Neoclassical Growth Model,” American Economic Review, vol. 89(5), pp. 1156-1181.
Mieszkowski, Peter, and George R. Zodrow, 1989. “Taxation and the Tiebout Model: The Differential Effects of Head Taxes, Taxes on Land Rents, and Property Taxes,” Journal of Economic Literature, vol. 27(3), pp. 1098-1146.
Monti, Mario, 2005. “Toughen up the Reform Agenda and Make it Count,” Financial Times, March 22, p. 17.
Peletier, Ben D., Robert A. J. Dur, and Otto H. Swank, 1999. “Voting on the Budget Deficit: Comment,” American Economic Review, vol. 89(5), pp. 1377-1381.
Persson, Torsten, and Guido Tabellini, 1996. “Federal Fiscal Constitutions: Risk Sharing and Moral Hazard,” Econometrica, vol. 64(3), pp. 623-646.
Persson, Torsten, and Guido Tabellini, 1996. “Federal Fiscal Constitutions: Risk Sharing and Redistribution,” Journal of Political Economy, vol. 104(5), pp. 979-1009.
Poterba, James M., 1994. “State Responses to Fiscal Crises: The Effects of Budgetary Institutions and Politics,” Journal of Political Economy, vol. 102(4), pp. 799-821
Poterba, James M., 1995. “Capital Budgets, Borrowing Rules, and State Capital Spending,” Journal of Public Economics, vol. 56(2), pp. 165-187.
Rangel, Antonio, 2005. “How to Protect Future Generations Using Tax Base Restrictions,” American Economic Review, vol. 95(1), pp. 314-346.
Rogoff, Kenneth, 1990. “Equilibrium Political Budget Cycles,” American Economic Review, vol. 80(1), pp. 21-36.
Rogoff, Kenneth, and Anne Sibert, 1988. “Elections and Macroeconomic Policy Cycles,” Review of Economic Studies, vol. 55(1), pp. 1-16.
Sanguinetti, Pablo, and Mariano Tommasi, 2004. “Intergovernmental Transfers and Fiscal Behavior Insurance versus Aggregate Discipline,” Journal of International Economics, vol. 62(1), pp. 149-170.
Sargent, Thomas J., 1983a. “The Ends of Four Big Inflations,” in: “Inflation: Causes and Effects,” (R. E. Hall, ed.), The University of Chicago Press, pp. 41-97.
Sargent, Thomas J., 1983b. “Stopping Moderate Inflations: The Methods of Poincaré and Thatcher,” in: “Inflation, Debt and Indexation,” (R. Dornbusch and M. H. Simonsen, eds.), MIT Press, pp. 54-98.
Secrist, Horace, 1914. “An economic analysis of the constitutional restrictions upon public indebtedness in the United States,” Bulletin of the University of Wisconsin. Economics and political science series, vol. 8, n. 1.
Song, Zheng, Kjetil Storesletten, and Fabrizio Zilibotti, 2007. “Rotten Parents and Disciplined Children: A Politico-Economic Theory of Public Expenditure and Debt,” mimeo, Fudan University, University of Oslo, and University of Zurich.
Tabellini, Guido, and Alberto Alesina, 1990, “Voting on the Budget Deficit,” American Economic Review, vol. 80(1), pp. 37-49.
Tiebout, Charles M., 1956. “A Pure Theory of Local Public Expenditures,” Journal of Political Economy, vol. 64(5), pp. 416-424.

Volume 10, Issue 1, November 2008

Ricardo Lagos on Liquidity and the Search Theory of Money

Ricardo Lagos is Associate Professor of Economics at New York University. He is interested in monetary economics, especially the theory of search in money. Lagos’s RePEc/IDEAS entry.

1. Introduction

There is no ambiguity among economists regarding what it means for an asset to be risky, or for markets to be complete. There seems to be, however, no definition of “liquidity” that is generally agreed upon. The notion of liquidity is sometimes used as an attribute of an asset, e.g., U.S. Treasuries are considered to be more liquid than equity shares. The notion of liquidity is often also used to describe the state or nature of a market, e.g., the market for municipal bonds is commonly regarded as illiquid. Sometimes researchers describe economic agents as being “liquidity constrained,” to mean that the agents face binding borrowing constraints. In what follows, I will focus on the first two notions of liquidity.

In financial economics, the liquidity of assets and markets is associated with the cost of trading. An asset is considered to be liquid if trading it entails relatively low transaction costs, e.g., transaction taxes, brokerage fees, or bid-ask spreads. A market is regarded as liquid if individual traders can find a counterpart for trade relatively quickly, and if the out-of-pocket costs involved in consummating trades are relatively small. There is a vast literature in finance that uses liquidity differences measured by differences in transaction costs to rationalize various asset-pricing puzzles, i.e., asset-return differentials that seem too large to be accounted for by the differences in the stochastic properties of the flows of payments that the assets represent. (For an extensive list of references, see Amihud et al., 2005.)

In monetary economics, “liquidity” refers to the degree to which an asset is useful as a medium of exchange. An asset is illiquid if it cannot be used as means of payment in quid pro quo trades. In particular, the Search Theory of Money–by which I mean the class of models that use search theory to provide micro foundations for monetary exchange that was pioneered by Kiyotaki and Wright (1989)–is built around the premise that assets can be valued not only for the intrinsic value of the real payoffs they represent, but also for their usefulness in the mechanism of exchange. This approach has deepened our understanding of the nature of monetary exchange by making explicit the frictions–e.g., specialization patterns, the configuration of the decentralized exchange mechanism, information structure, and so on–that make monetary exchange an equilibrium. In other words, this approach has proven useful for explaining the grandfather of all asset pricing puzzles: the existence of fiat money; an asset that is a formal claim to nothing yet sells at a positive price. Despite the evident conceptual connection and the potential for cross-fertilization, the Search Theory of Money and the mainstream asset-pricing literature have managed to stay disconnected for many years.

In the sections that follow, I will review some of my recent research and an ongoing research agenda, parts of which I have pursued, or am currently pursuing, with Guillaume Rocheteau, Pierre-Olivier Weill, and Randy Wright. In Sections 2-5 I will survey several papers that represent an effort to develop models in which, much as in the Search Theory of Money, financial assets are valued not only as claims to streams of consumption goods but also for their usefulness in the mechanism of exchange–i.e., for their moneyness, or exchange liquidity. In Section 6 I focus on the notion of transaction liquidity associated with transaction costs that is used in the financial literature, and review two papers that represent an effort to trace this notion of liquidity back to the microstructure of the market in which the assets are traded.

2. From indivisibility and upper bounds to Euler equations

The approach to monetary economics that started with Kiyotaki and Wright (1989) consists of using search theory to provide an explicit model of the type of decentralized trading activity that can give rise to a meaningful role for a medium of exchange. This literature made significant progress along several dimensions, but for a number of years, the depth of the analysis and the breadth of its fundamental insights were limited by stark modeling restrictions on asset holdings. Specifically, in order to keep the endogenous distribution of money holdings manageable, agents were typically restricted to hold either 0 units or 1 unit of an indivisible asset. These restrictions meant that agents never faced a standard portfolio problem leading to standard Euler equations, namely, the basic building block of any modern theory that–much like search-theoretic models–seeks to explain asset prices and asset demand patterns.

In “A Unified Framework for Monetary Theory and Policy Analysis” (hereafter LW), Randy Wright and I propose a search-based framework that combines some features of search models, such as an explicit mathematical formulation of the decentralized trading and the price-setting mechanisms, with some features of competitive models. Specifically, agents sometimes trade in a decentralized manner as in search theory–bilaterally, at prices determined by bargaining–and sometimes as in competitive theory–with the market, at market clearing prices. There are at least two important benefits from taking this step from pure search theory toward competitive theory. First, it becomes relatively easy to integrate search-based micro foundations for money demand with the rest of macroeconomic theory. For example, some real-world markets may be better approximated by competitive markets, so it may be convenient in applications to be able to incorporate a segment of competitive trades into our search-based theories. Second, it turns out that under certain conditions on preferences (quasi-linearity in one of the goods that is traded competitively), allowing agents periodic access to competitive markets implies that the model remains tractable–even if we work with divisible money and allow agents to carry any nonnegative amount. (Quasi-linearity eliminates wealth effects in the demand for money, which simplifies the dynamics of the endogenous distribution of money holdings. In the simplest version, all agents who trade in the competitive market choose to carry the same money balances into the next round of decentralized trade, therefore periodically, the endogenous distribution of money holdings becomes degenerate. This allows for sharp analytic results, and makes the framework easy to work with. An alternative approach was proposed by Shi, 1997, who develops a tractable search model with divisible money that relies on a large-household construct to avoid distributional issues.)

Just as incorporating a competitive segment brings the search theory of money closer to mainstream macroeconomic theory, relaxing the stark restrictions on money holdings implies that the search-theoretic models can now deliver standard Euler equations. This brings the field within a step of mainstream asset-pricing theory. The missing step is a meaningful portfolio choice problem; something that requires introducing financial assets that agents can hold alongside money balances.

3. A first look at competing assets: money and capital

Initially, the new search-theoretic literature with divisible money and unrestricted holdings tended to shy away from formulations in which the role of money as a medium of exchange could be challenged by other assets. This issue was circumvented either by assuming that money is the only asset (e.g., Lagos and Wright, 2003, Lagos and Rocheteau, 2005), or by assuming that assets other than money simply cannot be used in exchange (e.g., Aruoba and Wright, 2003). The implicit presumption being, perhaps, that in the face of competition from other assets, money would be driven out of circulation, or rendered “inessential” (a term used by monetary theorists to mean that the set of Pareto optimal allocations implementable by a monetary equilibrium is no larger than the set of Pareto optimal allocations implementable by a nonmonetary equilibrium).

In “Money and Capital as Competing Media of Exchange,” Guillaume Rocheteau and I build on LW and consider a model where real assets (reproducible capital goods) can compete with fiat money as a medium of exchange. Our theory allows agents to choose which assets to exchange in decentralized trades and imposes no restrictions on their portfolios. We establish that a monetary equilibrium exists if and only if money is essential, and offer a condition on fundamentals under which this is the case. The condition states that money is essential when the capital stock that a social planner would choose to accumulate is smaller than the stock of assets that agents need to conduct transactions. In the nonmonetary equilibrium, this liquidity shortage manifests itself as a premium on the rate of return on the assets that can be used as a medium of exchange, and this premium induces agents to over-accumulate capital. Capital plays two roles in this economy: it has a productive role and it serves as a medium of exchange in decentralized trades. The introduction of fiat money helps to disentangle the productive use of capital from its liquidity use, and induces agents to reduce the inefficiently high stock of capital goods. In the monetary equilibrium, money has the same rate of return as capital since both assets can be used in decentralized trade and agents can exploit arbitrage opportunities in the centralized market. We find that when a monetary equilibrium exists, the policy of contracting the money supply at the rate of time preference is optimal.

4. Exchange liquidity and the asset-pricing puzzles

In “Asset Prices and Liquidity in an Exchange Economy,” I develop an asset-pricing model in which financial assets are valued for their exchange liquidity–the extent to which they are useful in facilitating exchange–as well as for being claims to streams of consumption goods. I use the theory to study the implications of this liquidity channel for average asset returns, the equity-premium puzzle and the risk-free rate puzzle. I consider a real LW economy with two assets: a one-period government-issued risk-free real bill (a “bond”), and an equity share that represents the bearer’s ownership of a “Lucas tree” and confers him the right to collect a stochastic stream of real dividends. The model can be thought of as a version of Mehra and Prescott (1985), but extended to incorporate some trades that take place in a decentralized manner, away from competitive markets. As in the prototypical search model of money, agents face quid pro quo constraints in decentralized trades.

In the basic formulation, assets differ only in the stochastic properties of their payoffs, and agents are free to choose which assets to use as means of payment in decentralized trades. The theory unambiguously predicts that someone testing an agent’s Euler equation for the risk-free bill using its measured rate of return would find that, at the margin, this agent can gain from transferring consumption from the future to the present. That is, there would appear to be a risk-free rate puzzle. I also find that, at least qualitatively, the theory may also be consistent with an equity premium in excess of the risk premium that compensates equity holders for bearing undiversifiable aggregate risk. I calibrate the model economies and study the extent to which they are able to generate average equity returns and risk-free rates that are in line with U.S. data. Mehra and Prescott’s test of their theory essentially consisted of experimenting with different values of the curvature of the agent’s utility function (call it sigma) to find the values for which the average risk-free rate and equity premium in the model matched those in the U.S. economy. I carry out a similar exercise.

First, I consider a baseline economy in which agents are free to use bonds and equity shares in all decentralized trades. I find that for relatively low values of sigma, the liquidity mechanism is inactive and the equilibrium is the one in Mehra-Prescott. For larger values of sigma (equal to or greater than 8) equity shares and bills are valuable in decentralized exchange. This additional motive for holding the assets lowers the return on equity and the risk-free rate from what they would be in the Mehra-Prescott economy, and brings them closer to the data. There is a precise sense in which even if shares are just as useful as bonds for exchange purposes, quantitatively, the model performs better than the Mehra-Prescott frictionless benchmark. For example, with standard constant relative risk aversion preferences, it takes a value of sigma of about 10 for the model to be consistent with asset return data in the Hansen-Jagannathan sense (as opposed to a value of sigma above 20 in Mehra-Prescott). Despite equity shares and bonds being equally acceptable in decentralized exchange, the model is capable of increasing the size of the equity premium somewhat relative to the Mehra-Prescott benchmark. The reason is that equity is a worse hedge against the risk of facing binding trading constraints in the decentralized market than bonds (trading constraints tend to bind more in states where the equity return is low).

Equity and bonds are equally liquid (equally useful to finance decentralize trades) in the baseline model. In order to assess the extent to which liquidity differences (differences in acceptability) can magnify the return differential between equity and bonds, I also analyze specifications in which exogenous restrictions, which can be interpreted as arising from institutional or legal arrangements, give bonds an advantage over equity as a medium of exchange. Specifically, I consider the case in which equity shares cannot be used in a fraction theta of decentralized exchanges (theta =0 is the case with no exogenous liquidity differences analyzed previously). For a calibrated version of this model, I formulate the following question: For a given value of sigma, how large does theta (the relative illiquidity of equity) have to be for the model to generate an average yearly risk-free rate of 1% and an equity premium that matches the long-term average for the U.S. economy? The answer is, quite small: If one allows for the fact that bonds may be slightly better suited than equity shares to play the medium-of-exchange role, then the model is able to match the historical average return to equity and the risk-free rate for the United States with values of sigma between 3 and 5.

I take these results as an indication that prying deeper into the microeconomics of the decentralized exchange process can add to our understanding of how asset prices and returns are determined in actual economies. The quantitative results also highlight the importance of a fundamental question: why is asset X more generally accepted or better suited to function as a medium of exchange than asset Y? The finding that small differences in the acceptability of an asset can generate relatively large return differentials underscores the importance of tackling this question. Some research along these lines is already underway. For example, Kim and Lee (2008), Lester et al. (2008), and Rocheteau (2008) are exploring the possibility that differences in acceptability may arise due to a moral hazard problem in an environment where some assets are more susceptible to counterfeiting than others. Lagos and Rocheteau (2008) are focusing on the differences in acceptability that arise from an adverse selection problem due to the fact that some agents may be better informed about the return characteristics of certain assets than other agents. Nosal and Rocheteau (2008) are exploring trading mechanisms that may give some assets an advantage in exchange as in Zhu and Wallace (2007).

5. Asset prices, exchange liquidity, and monetary policy

The work described in the previous section studies the implications of exchange liquidity for real asset returns in economies with no money. Since much of the existing work on asset pricing abstracts from monetary considerations, this seemed like a natural starting point. However, given the emphasis on exchange liquidity, it would be odd to neglect fiat money–the quintessential medium of exchange–indefinitely. For one thing, the primary role of fiat money is precisely to provide exchange liquidity, so to the extent that the valuations of other financial assets have a liquidity component, the interactions between these other assets and money through the agents’ portfolio choices should not be ignored. Also, by setting monetary policy, governments can affect real money balances and in this way supply the economy with the liquidity it needs to lubricate the mechanism of decentralized exchange. So again, to the extent that the valuations of financial assets have a liquidity component, monetary policy will be a key determinant of their (real) measured returns.

In “Some Results on the Optimality and Implementation of the Friedman Rule in the Search Theory of Money,” I consider a physical environment similar to the one described in the previous section, but replace the one-period government-issued risk-free real bill with government-issued fiat money. In this context, I show that the quantities in a monetary equilibrium are Pareto optimal if and only if the nominal interest rate, i.e., the marginal (indirect) utility of holding an additional dollar, is constant and equal to zero. Thus, a monetary authority that wishes to maximize welfare ought to follow Milton Friedman’s prescription that monetary policy should be conducted with the objective of inducing a zero nominal interest rate. I characterize a large family of deterministic monetary policies that implement Milton Friedman’s prescription, in the sense that these policies are consistent with the existence of a monetary equilibrium with zero nominal interest rates. This family of optimal policies is defined by two properties: (i) the money supply must be arbitrarily close to zero for an infinite number of dates, and (ii) asymptotically, on average, the growth rate of the money supply must be at least as large as the rate of time preference. Interestingly, even though the agents’ liquidity needs are stochastic in this environment (because equity, whose price is stochastic, can be used alongside money in decentralized trades) this is the same class of monetary policies that implements the Friedman rule in the context of deterministic cash-in-advance economies, as shown by Cole and Kocherlakota (1998) and Wilson (1979).

Under an optimal policy, the quantity of real money balances is large enough so that agents’ liquidity needs are satiated, so the real equity price and return are independent of monetary and liquidity considerations. The monetary equilibrium under an optimal monetary policy also exhibits some peculiarities: the price level is indeterminate, and the inflation rate can be independent of the path of the money supply, as was emphasized by Cole and Kocherlakota (1998) in the context of their deterministic cash-in-advance economy. Some may find the failure of the quantity theory and the ensuing price-level indeterminacy unappealing if the model is to be used for applied research. One way to eschew these issues, is to consider a perturbation of a certain class of optimal policies that implements a constant but positive nominal interest rate. A policy that targets a constant nonzero nominal rate in this stochastic environment, however, will typically involve a stochastic monetary policy rule. This is the direction I pursue in “Asset Prices, Liquidity, and Monetary Policy in an Exchange Economy” to study the positive implications of monetary policy for asset prices and returns. The analysis provides insights on how monetary policy must be conducted in order to support a recursive monetary equilibrium with a constant nominal interest rate (with the Pareto optimal equilibrium in which the nominal rate is zero as a limiting case): The growth rate of the money supply must be relatively low in states in which the real value of the equilibrium equity holdings is below average. Something similar happens with the implied inflation rate: it is relatively low between state x and a next-period state x’, if the realized real value of the equilibrium equity holdings in state x’ is below its state-x conditional expectation.

I also find that on average, liquidity considerations can introduce a negative relationship between the nominal interest rate (and the inflation rate) and real equity returns. Intuitively, since agents are free to use any combination of assets for exchange purposes, even if the equity yields a real and exogenous dividend stream, part of the equity return will be linked to its liquidity return, and this liquidity return in turn depends on the quantity of real money balances–which is a function of the inflation rate. On average, if the rate of inflation is higher, real money balances are lower, and the liquidity return on equity rises, which causes its price to rise and its real measured rate of return (dividend yield plus capital gains) to fall. This type of logic could perhaps help to rationalize the fact that historically, real stock returns and inflation have been negatively correlated–an observation long considered anomalous in the finance literature (e.g., Fama and Schwert, 1977).

The model has a number of implications for the time-paths of output, inflation, interest rates, equity prices, and equity returns, and it would be interesting to explore these implications further. For example, even though variations in aggregate output are effectively exogenous under the types of monetary policies considered, for some parametrizations the theory produces a negative correlation between the inflation rate and the growth rate of output–a short-run “Phillips curve” –but one that is entirely generated by a monetary policy designed to provide liquidity in an economy with stochastic liquidity needs.

6. Transaction liquidity and the structure of financial markets

In the introductory section I mentioned that in finance, the liquidity of assets and markets is associated to the cost of trading: this transaction liquidity is, loosely speaking, the ability to trade cheaply. Central to this literature is the notion that actual financial trade is not costless and seamless as in competitive theory. To capture the idea that trade is not costless, much of the work in this area maintains the competitive market structure, but incorporates transaction costs of various forms (e.g., fixed costs of trading, or costs that are proportional to the size of the trade). In many of these models, transaction costs affect asset prices because in equilibrium, investors must be compensated for bearing these costs. Hence for any given dividend flow that the asset generates, transaction costs lower the asset price and increase the asset return, i.e., higher transaction costs reduce the transaction liquidity of the asset.

A recent related strand of work in theoretical finance started by Duffie et al. (2005) subscribes to the notion of market liquidity as trading costs, but goes deeper into the nature of these trading costs by building explicit models of the mechanism of exchange in financial markets. The starting point is the observation that many financial securities (e.g., unlisted stocks, currencies, derivatives, corporate bonds, municipal bonds, federal funds) are traded in over-the-counter (OTC) markets. The defining feature of OTC markets is that they have no formal organization: unlike organized securities exchanges, OTC markets are completely decentralized and do not operate in a particular location at set times. An agent wishing to trade a security in an OTC market is confronted with two fundamental trading frictions: he must first search for a counterpart, and once a potential counterpart has been found, the two parties will typically negotiate the terms of the trade to share the gains.

Duffie et al. (2005) show that a search-based model of an OTC market can parsimoniously rationalize standard measures of transaction liquidity discussed in the finance literature, such as trade volume, bid-ask spreads, and trading delays. A virtue of their formulation is that it is analytically tractable, so all these mechanisms can be well understood. The literature spurred by Duffie et al. (2005), however, keeps the framework tractable by imposing a stark restriction on asset holdings: agents can only hold either 0 units or 1 unit of the asset.

In “Liquidity in Asset Markets with Search Frictions,” Guillaume Rocheteau and I develop a search-based model of trade in an OTC market with no restrictions on investors’ asset holdings. The model is close in structure and spirit to Duffie et al. (2005): there are two types of agents, investors and dealers. The asset is only held by investors (they can hold any nonnegative position), and their idiosyncratic willingness to hold the asset changes over time, which creates a motive for trade among investors. Trades are intermediated by dealers, and investors contact dealers at random times, with the period of time preceding a trade interpreted as an execution delay. We find that as a result of the restrictions they impose on asset holdings, existing search-based theories of trade in OTC markets neglect a critical feature of illiquid markets, namely, that market participants can mitigate trading frictions by adjusting their asset positions to reduce their trading needs.

The key theoretical observation is that an investor’s asset demand in an OTC market depends not only on his valuation for the asset at the time of the trade, but also on his expected valuation over the holding period until his next opportunity to trade. A reduction in trading frictions (e.g., a reduction in the average time it takes for an investor to contact a dealer) makes investors less likely to remain locked into an undesirable asset position and therefore induces them to put more weight on their current valuation. As a result, a reduction in trading frictions induces an investor to demand a larger asset position if his current valuation is relatively high, and a smaller position if it is relatively low, which tends to increase the spread of the distribution of asset holdings. We find that this effect is a key channel through which trading frictions determine trade volume, bid-ask spreads, and trading delays–the dimensions of transaction liquidity that search-based theories of financial intermediation are designed to explain.

In “Search in Asset Markets: Market Structure, Liquidity, and Welfare,” Guillaume Rocheteau and I consider a version of this model with free entry of dealers as a way to endogenize trading delays. We show that when interacted with investors’ unrestricted asset holding decisions, the dealers’ incentives to make markets generate a liquidity externality that can give rise to multiple steady states. This finding suggests that all the symptoms of an illiquid market–large spreads, small trade volume, and long trading delays–can simultaneously arise as a self-fulfilling phenomenon in asset markets with an OTC structure.

In many financial markets, the search-for-a-counterpart problem is alleviated by dealers who trade assets from their own inventories. During market crashes, for instance, it can take a long time for an investor to find a counterpart for trade, either because of the technological limitations of order-handling systems or, as in OTC markets, due to the decentralized nature of the trading process. In these circumstances, liquidity provision by dealers (in the sense of their alleviating the investors’ search problem by becoming themselves a counterpart for trade) can become critical, as shown by Weill (2007). In “Crashes and Recoveries in Illiquid Markets,” Guillaume Rocheteau, Pierre-Olivier Weill and I extend the model in “Liquidity in Asset Markets with Search Frictions” to allow dealers to accumulate asset inventories. We use the theory to study the equilibrium and the socially optimal inventory policies of dealers during a market crash, which we model as a temporary negative shock to investors’ willingness to hold the asset, followed by a (possibly stochastic) recovery path.

Our model can rationalize why dealers intervene in some crises and withdraw in others. We derive conditions under which dealers will find it in their interest to provide liquidity in the aftermath of a crash, as well as conditions under which their incentives to provide liquidity are consistent with market efficiency. We relate the liquidity provision by dealers to the details of the market structure, e.g., dealers’ degree of market power or the extent of the search frictions (the average length of time it takes for an investor to contact a dealer), and the characteristics of the crash, such as the severity and persistence of the shock to investors’ demands.

We find that the amount of liquidity provided by dealers following a crash varies nonmonotonically with the magnitude of search frictions. When search frictions are small, investors with higher-than-average utility for assets become more willing to hold larger-than-average positions and absorb more of the selling pressure coming from investors whose demands for the asset are lower than normal. In some cases, the former are so willing to buy large quantities of the asset from the other investors, i.e., so willing to serve as a counterpart for trade, that dealers don’t find it profitable to step in. If, on the contrary, search frictions are large enough, dealers do not accumulate inventories either, but for a different reason: Trading frictions reduce the investors’ need for liquidity provision by dealers. Indeed, in order to reduce their exposure to the search frictions, investors choose to take less extreme asset positions, so the problem of finding a counterpart for trade becomes less relevant. In fact, it is possible that the investors reduce their trading needs so much that dealers don’t find it profitable to accumulate inventories following a crash. Thus, if one considers a spectrum of asset markets ranging from those with very small search frictions, such as the New York Stock Exchange (NYSE), to those with severe search frictions, such as the corporate bond market, one would expect to see dealers accumulate more asset inventories during a crash in markets which are in the intermediate range of the spectrum.

7. Concluding remarks

A single underlying theme runs through the work I have reviewed in the preceding sections: in many instances, the demand for an asset (and consequently the asset price and return) depends not only on the demand for the fundamentals that the asset represents, but also on the nature of the mechanism of exchange through which the asset is traded. Financial economists associate the “mechanism of exchange” to the microstructure of the market where the asset trades, and call the asset “liquid” if it can be traded cheaply in terms of time, and out-of-pocket costs. Monetary theorists associate the “mechanism of exchange” to the explicit microeconomic process through which goods and the assets used to pay for those goods flow between buyers and sellers, and call an asset “liquid” if it is generally accepted and used in this exchange process.

On the one hand, by conceptualizing financial assets in the way monetary theorists think of fiat money, we can develop theories of liquidity that afford new insights into the fundamental features of assets and markets that can make some assets useful in the mechanism of exchange, and hence more prone to exhibit returns that exceed their fundamental valuations. A better understanding of the deeper determinants of the liquidity component of asset valuations can shed new light on a number of asset-pricing anomalies, as well as on the role that monetary policy plays, and the role it ought to play, in the determination of asset prices. On the other hand, the finance microstructure perspective reviewed in Section 6, formalizes some of the key micro elements of the exchange process in actual financial markets, which include trading delays, bilateral decentralized exchange, and other distinctively non-Walrasian elements, much like those which characterize the stylized “decentralized market” of the macro models in Sections 2-5. It seems to me that incorporating these microstructure considerations into those macro models would be a fertile avenue for future research. The hope I hold for this research agenda, is that by continuing to develop the association between the monetary and the financial perspectives on liquidity, we may be able to make progress on some deeper questions, such as which assets are better suited to satisfy the quid pro quo constraints in the Search Theory of Money, and why certain assets seem more prone to be traded in frictional market structures than others.


Amihud, Yakov, Haim Mendelson, and Lasse H. Pedersen, 2005. “Liquidity and Asset Prices,” Foundations and Trends in Finance, vol. 1(4), pages 269-364.
Aruoba, S. Boragan, and Randall Wright, 2003. “Search, Money, and Capital: A Neoclassical Dichotomy,” Journal of Money, Credit, and Banking, vol. 35(6), pages 1085-1105.
Cole, Harold L., and Narayana Kocherlakota, 1998. “Zero Nominal Interest Rates: Why They’re Good and How to Get Them,” Federal Reserve Bank of Minneapolis Quarterly Review, vol. 22(2), pages 2-10.
Duffie, Darrell, Nicolae Garleanu, and Lasse Heje Pedersen, 2005. “Over-the-Counter Markets,” Econometrica, vol. 73(6), pages 1815-1847.
Fama, Eugene F., and William G. Schwert, 1977. “Asset Returns and Inflation,” Journal of Financial Economics, vol. 5(2), pages 115-146.
Kim, Young Sik, and Manjong Lee, 2008. “Recognizability and Liquidity,” Working paper.
Kiyotaki, Nobuhiro, and Randall Wright, 1989. “On Money as a Medium of Exchange,” Journal of Political Economy, vol. 97(4), pages 927-954.
Lagos, Ricardo, 2006. “Asset Prices and Liquidity in an Exchange Economy,” Federal Reserve Bank of Minneapolis Staff Report 373.
Lagos, Ricardo, 2008a. “Some Results on the Optimality and Implementation of the Friedman Rule in the Search Theory of Money,” Working paper.
Lagos, Ricardo, 2008b. “Asset Prices, Liquidity, and Monetary Policy in an Exchange Economy,” Working paper.
Lagos, Ricardo, and Guillaume Rocheteau, 2005. “Inflation, Output, and Welfare,” International Economic Review, vol. 46(2), pages 495-522.
Lagos, Ricardo, and Guillaume Rocheteau, 2007. “Search in Asset Markets: Market Structure, Liquidity, and Welfare,” American Economic Review (Papers and Proceedings), vol. 97(2), pages 198-202.
Lagos, Ricardo, and Guillaume Rocheteau, 2008a. “Money and Capital as Competing Media of Exchange,” Journal of Economic Theory, vol. 142(1), pages 247-258.
Lagos, Ricardo, and Guillaume Rocheteau, 2008b. “The Informational Foundations of Asset Liquidity,” Working paper.
Lagos, Ricardo, and Guillaume Rocheteau, forthcoming. “Liquidity in Asset Markets with Search Frictions,” Econometrica.
Lagos, Ricardo, Guillaume Rocheteau, and Pierre-Olivier Weill, 2007. “Crashes and Recoveries in Illiquid Markets,” Federal Reserve Bank of Cleveland Working paper 0708.
Lagos, Ricardo, and Randall Wright, 2003. “Dynamics, Cycles and Sunspot Equilibria in `Genuinely Dynamic, Fundamentally Disaggregative’ Models of Money,” Journal of Economic Theory, vol. 109(2), pages 156-171.
Lagos, Ricardo, and Randall Wright, 2005. “A Unified Framework for Monetary Theory and Policy Analysis,” Journal of Political Economy, vol. 113(3), pages 463-484.
Lester, Benjamin, Andrew Postlewaite and Randall Wright, 2008. “Information, Liquidity and Asset Prices,” PIER Working paper, 08-039.
Lucas, Robert E., Jr., 1978. “Asset Prices in an Exchange Economy,” Econometrica, vol. 46(6), pages 1426-1445.
Mehra, Rajnish, and Edward C. Prescott, 1985. “The Equity Premium: A Puzzle,” Journal of Monetary Economics, vol. 15(2), pages 145-161.
Nosal, Ed, and Guillaume Rocheteau, 2008. “Pairwise Trade, Asset Prices, and Monetary Policy,” Working paper.
Rocheteau, Guillaume, 2008. “Information and Liquidity: A Discussion,” Working paper.
Shi, Shouyong, 1997. “A Divisible Search Model of Fiat Money,” Econometrica, vol. 64(1), pages 75-102.
Weill, Pierre-Olivier, 2007. “Leaning Against the Wind,” Review of Economic Studies, vol. 74(4), pages 1329-1354.
Wilson, Charles, 1979. “An Infinite Horizon Model with Money,” in: Jerry R. Green and José A. Scheinkman (eds.), In General Equilibrium, Growth, and Trade, pages 79-104. New York: Academic Press.
Zhu, Tao, and Neil Wallace, 2007. “Pairwise Trade and Coexistence of Money and Higher-Return Assets,” Journal of Economic Theory, vol. 133(1), pages 524-35.

Volume 9, Issue 2, April 2008

Sydney Ludvigson on Empirical Evaluation of Economic Theories of Risk Premia

Sydney Ludvigson is the William R. Berkley Term Associate Professor at the Department of Economics, New York University. She is interested in asset valuation, equity premia and consumption smoothness. Ludvigson’s RePEc/IDEAS entry.

 What explains the behavior of risk premia in stock and bond markets, both over time and cross-sectionally across classes of assets? For academic researchers, the progression of empirical evidence on these questions has presented a continuing challenge to asset pricing theory and an important road map for future inquiry. For investment professionals, finding practical answers to these questions is the fundamental purpose of financial economics, as well as its principal reward.To address these questions, economists need to develop theoretical models of risk. Once such models have been developed, formal statistical analysis is required to assess how well these models fit the data, and to provide independent estimates of the theories’ key parameters. In this essay, I describe work that aims to build our understanding of the ways in which modern-day asset pricing theories are related to asset pricing facts established from historical data, to estimate the models’ key parameters, and to formally evaluate the extent to which leading theories are successful in explaining the facts. The general approach is a multifarious one that involves both formal econometric estimation as well as simulation analyses directed at particular questions of interest. The approach is summarized in three articles, numbered below for ease of reference:
  • [1] “Euler Equation Errors” (with Martin Lettau).
  • [2] “An Estimation of Economic Models with Recursive Preferences” (with Xiaohong Chen and Jack Favilukis).
  • [3] “Land of Addicts? An Empirical Investigation of Habit-Based Asset Pricing Models” (with Xiaohong Chen).

Relating Asset Pricing Theories to Asset Pricing Facts

Previous research shows that the standard, representative agent, consumption-based asset pricing theory based on constant relative risk aversion utility fails to explain the average returns of risky assets. (For example, Hansen and Singleton (1982); Ferson and Constantinides (1991); Hansen and Jagannathan (1991); Cochrane (1996); Kocherlakota (1996)) One aspect of this failure, addressed in [1], is the large unconditional Euler equation errors that the model generates when evaluated on cross-sections of stock returns. Euler equation errors are statistical discrepancies between a theory’s prediction about the dynamic behavior of expected discounted asset returns and that implied by observable data. In [1], we present evidence on the size of these errors and show that they remain economically large even when preference parameters are freely chosen to maximize the model’s chances of fitting the data. Thus, unlike the equity premium puzzle of Mehra and Prescott (1985), the large Euler equation errors cannot be resolved with high values of risk aversion.To explain why the standard model fails, we need to develop alternative models that can rationalize its large Euler equation errors. Yet surprisingly little research has been devoted to assessing the extent to which newer consumption-based asset pricing theories–those specifically developed to address empirical limitations of the standard consumption-based model–can explain its large Euler equation errors. Unconditional Euler equation errors can be interpreted economically as pricing errors; thus we use the terms “Euler equation error” and “pricing error” interchangeably.

The research in [1] makes three contributions. First, we show that leading consumption-based asset pricing theories resoundingly fail to explain the mispricing of the standard consumption-based model. Specifically, we investigate four models at the vanguard of consumption-based asset pricing and show that the benchmark specification of each of these theories counterfactually implies that the standard model has negligible Euler equation errors when its parameters are freely chosen to fit the data. This anomaly is striking because early empirical evidence that the standard model’s Euler equations were violated provided much of the original impetus for developing the newer models we investigate here.

Second, we show that the leading asset pricing models we study fail to explain the mispricing of the standard model because they fundamentally mischaracterize the joint behavior of consumption and asset returns in recessions, when aggregate consumption is falling. In the model economies, realized excess returns on risky assets are negative when consumption is falling, whereas in the data they are often positive.

Our third contribution is to suggest one specific direction along which the current models can be improved, based on a time-varying, state-dependent correlation between stockholder and aggregate consumption growth. Specifically, we show that a stylized model in which aggregate consumption growth and stockholder consumption growth are highly correlated most of the time, but have low or negative correlation in recessions, produces violations of the standard model’s Euler equations and departures from joint lognormality of aggregate consumption growth and asset returns that are remarkably similar to those found in the data.

Why should we care about the ability of leading consumption-based asset pricing models to explain the failure of the standard consumption-based model? To motivate the importance of these findings for consumption-based asset pricing theory, it is helpful to consider, by way of analogy, the literature on the value premium puzzle in financial economics. In this literature, the classic Capital Asset Pricing Model (CAPM) resoundingly fails to explain the high average excess returns of value stocks, resulting in a value premium puzzle (Fama and French (1992, 1993)). It is well accepted that a fully successful theoretical resolution to this puzzle must accomplish two things: (i) it must provide an alternative theory to the CAPM that explains the high average returns of value stocks, and (ii) it must explain the failure of the CAPM to rationalize those high returns.

Analogously, the large empirical Euler equation errors of the standard consumption-based model place additional restrictions on new consumption-based models: not only must such models have zero pricing errors when the Euler equation is correctly specified according to the model, they must also produce large pricing errors when the Euler equation is incorrectly specified using power utility and aggregate consumption. To understand why the classic consumption-based model is wrong, alternative theories must generate the same large Euler equation errors that we observe in the data for this model.

Our analysis employs simulated data from several contemporary consumption-based asset pricing theories expressly developed to address empirical limitations of the standard consumption-based model. Clearly, it is not possible to study an exhaustive list of all models that fit this description; thus we limit our analysis to four that both represent a range of approaches to consumption-based asset pricing, and have received significant attention in the literature. These are: the representative agent external habit-persistence paradigms of (i) Campbell and Cochrane (1999) and (ii) Menzly, Santos and Veronesi (2004), (iii) the representative agent long-run risk model based on recursive preferences of Bansal and Yaron (2004), and (iv) the limited participation model of Guvenen (2003). Each is an explicitly parameterized economic model calibrated to accord with the data, and each has proven remarkably successful in explaining a range of asset pricing phenomena that the standard model fails to explain.

We show that some of these models can explain why we obtain implausibly high estimates of risk aversion and the subjective rate of time-preference when freely fitting aggregate data to the Euler equations of the standard consumption-based model. But, none can explain the large unconditional Euler equation errors associated with such estimates for plausibly calibrated sets of asset returns. Indeed, the asset pricing models we consider counterfactually imply that parameter values can be found for which the unconditional Euler equations of the standard consumption-based model are exactly satisfied.

The work in [1] diagnoses this result by showing that each of the four models studied satisfy sufficient conditions under which parameter values can always be found such that the Euler equations of the standard model will be exactly satisfied. The economically important condition satisfied by each model is that realized excess returns on risky assets are negative whenever consumption growth is sufficiently negative. We show that such a condition is violated in the data.

We close the paper by turning our attention to stylized models with limited stockmarket participation. When limited participation is combined with a time-varying, state-dependent correlation between stockholder and aggregate consumption, consumption-based asset pricing theories come much closer to rationalizing the large Euler equation errors of the standard paradigm that in large part motivated the search for newer models in the first place.

Econometric Modeling of Asset Pricing Models

A large and growing body of theoretical work in macroeconomics and finance models the preferences of economic agents using a recursive utility function of the type explored by Epstein and Zin (1989, 1991) and Weil (1989) (See for example Campbell (1993, 1996); Tallarini (2000); Campbell and Viceira (2001); Bansal and Yaron (2004); Colacito and Croce (2005); Bansal, Dittmar and Kiku (2007); Campbell and Vuolteenaho (2004); Gomes and Michaelides (2005); Krueger and Kubler (2005); Hansen, Heaton and Li (2005); Kiku (2005); Malloy, Moskowitz and Vissing-Jorgensen (2005); Campanale, Castro and Clementi (2007); Croce (2006); Bansal, Dittmar and Lundblad (2005); Croce, Lettau and Ludvigson (2007); Hansen and Sargent (2006), Piazzesi and Schneider (2006)). One reason for the growing interest in such preferences is that they provide a potentially important generalization of the standard power utility model discussed above, first investigated in classic empirical studies by Hansen and Singleton (1982, 1983). The salient feature of this generalization is a greater degree of flexibility as regards attitudes towards risk and intertemporal substitution. Specifically, under the recursive representation, the coefficient of relative risk aversion need not equal the inverse of the elasticity of intertemporal substitution (EIS), as it must in time-separable expected utility models with constant relative risk aversion. This degree of flexibility is appealing in many applications because it is unclear why an individual’s willingness to substitute consumption across random states of nature should be so tightly linked to her willingness to substitute consumption deterministically over time, as it must in standard models of preferences.Despite the growing interest in recursive utility models, there has been a relatively small amount econometric work aimed at estimating the relevant preference parameters and assessing the model’s fit with the data. As a consequence, theoretical models are often calibrated with little econometric guidance as to the value of key preference parameters, the extent to which the model explains the data relative to competing specifications, or the implications of the model’s best-fitting specifications for other economic variables of interest, such as the return to the aggregate wealth portfolio or the return to human wealth. The purpose of [2] is to help fill this gap in the literature by undertaking a formal econometric evaluation of the Epstein-Zin-Weil (EZW) recursive utility model.

If recursive preferences are of growing interest, why has there been so little formal econometric work evaluating these models? In its most general form, the EZW model is extremely challenging to evaluate empirically. The EZW recursive utility function is a constant elasticity of substitution (CES) aggregator over current consumption and the expected discounted utility of future consumption. This structure makes estimation of the general model difficult because the intertemporal marginal rate of substitution is a function of the unobservable continuation value of the future consumption plan. The common approach in the literature is to make one of a number of simplifying assumptions that effectively reduce the continuation value function to an observable variable. For example, one approach to this problem, based on the insight of Epstein and Zin (1989), is to exploit the relation between the continuation value and the return on the aggregate wealth portfolio. To the extent that the return on the aggregate wealth portfolio can be measured or proxied, the unobservable continuation value can be substituted out of the marginal rate of substitution and estimation can proceed using only observable variables (e.g., Epstein and Zin (1991)). Unfortunately, the aggregate wealth portfolio represents a claim to future consumption and is itself unobservable. Moreover, given the potential importance of human capital and other nontradable assets in aggregate wealth, its return may not be well proxied by observable asset market returns.

These difficulties can be overcome in specific cases of the EZW recursive utility model. For example, if the EIS is restricted to unity and consumption follows a loglinear time-series process, the continuation value has an analytical solution and is a function of observable consumption data (e.g., Hansen, Heaton and Li (2005)). Alternatively, if consumption and asset returns are assumed to be jointly lognormally distributed and homoskedastic (or if a second-order linearization is applied to the Euler equation), the risk premium of any asset can be expressed as a function of covariances of the asset’s return with current consumption growth and with news about future consumption growth (e.g., Restoy and Weil (1998), Campbell (2003)). In this case, the model’s cross-sectional asset pricing implications can be evaluated using observable consumption data and a model for expectations of future consumption.

While the study of these specific cases has yielded a number of important insights, there are several reasons why it may be desirable to allow for more general representations of the model, free from tight parametric or distributional assumptions. First, an EIS of unity implies that the consumption-wealth ratio is constant, contradicting statistical evidence that it varies considerably over time. Lettau and Ludvigson (2001a) argue that a cointegrating residual for log consumption, log asset wealth, and log labor income should be correlated with the unobservable log consumption-aggregate wealth ratio, and find evidence that this residual varies considerably over time and forecasts future stock market returns. See also recent evidence on the consumption-wealth ratio in Hansen, Heaton, Roussanov and Lee (2007) and Lustig, Van Nieuwerburgh and Verdelhan (2008). Moreover, even first-order expansions of the EZW model around an EIS of unity may not capture the magnitude of variability of the consumption-wealth ratio (Hansen, Heaton, Roussanov and Lee (2007)). Second, although aggregate consumption growth itself appears to be well described by a lognormal process, empirical evidence suggests that the joint distribution of consumption and asset returns exhibits significant departures from lognormality (Lettau and Ludvigson (2005)). Third, Kocherlakota (1990) points out that joint lognormality is inconsistent with an individual maximizing a utility function that satisfies the recursive representation used by Epstein and Zin (1989, 1991) and Weil (1989).

To overcome these issues, in [2] we employ a semiparametric estimation technique that allows us to conduct estimation and testing of the EZW recursive utility model without the need to find a proxy for the unobservable aggregate wealth return, without linearizing the model, and without placing tight parametric restrictions on either the law of motion or joint distribution of consumption and asset returns, or on the value of key preference parameters such as the EIS. We present estimates of all the preference parameters of the EZW model, evaluate the model’s ability to fit asset return data relative to competing asset pricing models, and investigate the implications of such estimates for the unobservable aggregate wealth return and human wealth return.

To avoid having to find a proxy for the return on the aggregate wealth portfolio, we explicitly estimate the unobservable continuation value of the future consumption plan. By assuming that consumption growth falls within a general class of stationary, dynamic models, we may identify the state variables over which the continuation value is defined. However, without placing tight parametric restrictions on the model, the continuation value is still an unknown function of the relevant state variables. Thus the key to our approach is that the unknown continuation value function is estimated nonparametrically, in effect allowing the data to dictate the shape of the function. The resulting empirical specification for investor utility is semiparametric in the sense that it contains both the finite dimensional unknown parameters that are part of the CES utility function (risk aversion, EIS, and subjective time-discount factor), as well as the infinite dimensional unknown continuation value function.

Using quarterly data on consumption growth, assets returns and instruments, our empirical results indicate that the estimated relative risk aversion parameter is high, ranging from 17-60, with higher values for the representative agent version of the model than the representative stockholder version. The estimated elasticity of intertemporal substitution is typically above one, and differs considerably from the inverse of the coefficient of relative risk aversion. In addition, the estimated aggregate wealth return is found to be weakly correlated with the CRSP value-weighted stock market return and much less volatile, implying that the return to human capital is negatively correlated with the aggregate stock market return. This later finding is consistent with results in Lustig and Van Nieuwerburgh (2005), discussed further below. In data from 1952 to 2005, we find that an SMD estimated EZW recursive utility model can explain a cross-section of size and book-market sorted portfolio equity returns better than the time-separable, constant relative risk aversion power utility model and better than the Lettau and Ludvigson (2001b) scaled consumption CAPM model, but not as well as purely empirical models based on financial factors such as the Fama and French (1993) three-factor model. These results are encouraging for the recursive utility framework, because they suggest that the model’s ability to fit the data is in a comparable range with other models that have shown particular success in explaining the cross-section of expected stock returns.

A similar semiparameteric approach is taken in [3] to study an entirely different class of asset pricing models, namely those in which investors are presumed to have a consumption “habit.” According to these theories of aggregate stock market behavior, assets are priced as if there were a representative investor whose utility is a power function of the difference between aggregate consumption and a “habit” level, where the habit is some function of lagged and (possibly) contemporaneous consumption. Unfortunately, theory does not provide precise guidelines about the parametric functional relationship between the habit and aggregate consumption. As a consequence, there is substantial divergence across theoretical models in how the habit stock is specified to vary with aggregate consumption. As for the EZW model, the fundamental problem is the unobservability of some function that is crucial to the success of the model, in this case the habit function. [3] both develops and applies the formal econometric techniques required to estimate the habit function and to formally test important aspects of habit-based models. While many theoretical papers have offered calibrated versions of the habit, the econometric estimation and testing of these models that we propose is new. If habit formation is actually present in the manner suggested by these many influential theoretical papers, then estimating it freely should produce a theoretically plausible functional form. [3] studies the ability of a general class of habit-based asset pricing models to match the conditional moment restrictions implied by asset pricing theory. Instead of testing a particular model of habit formation, our semiparameteric approach allows us to treat the functional form of the habit as unknown, and to estimate it along with the rest of the model’s parameters. This approach allows us to empirically evaluate a number of interesting hypotheses about the specification of habit-based asset pricing models that have not been previously investigated, and to formally test the framework’s ability to explain stock return data relative to other models that have proven empirically successful.

Using this methodology, we empirically investigate a number of hypotheses about the specification of habit-based asset pricing models that have not been previously investigated. One hypothesis concerns whether the habit is better described as a linear or nonlinear function. We develop a statistical test of the hypothesis of linearity and find that the functional form of the habit is better described as nonlinear rather than linear.

A second hypothesis concerns the distinction between “internal” and “external” habit formation. About half of the theoretical papers cited above investigate models of internal habit formation, in which the habit is a function of the agent’s own past consumption. The rest investigate models of external habit formation, in which the habit depends on the consumption of some exterior reference group, typically per capita aggregate consumption. Abel (1990) calls external habit formation “catching up with the Joneses.” Determining which form of habit formation is more empirically plausible is important because the two specifications can have dramatically different implications for optimal tax policy and welfare analysis (Ljungqvist and Uhlig (2000)), and for whether habit models can explain long-standing asset-allocation puzzles in the international finance literature (Shore and White (2002)). To address this issue, we derive a conditional moment restriction that nests the internal and external nonlinear habit function, under the assumption that both functions are specified over current and lagged consumption with the same finite lag length. Our empirical results indicate that the data are better described by internal habit formation than external habit formation.

The SMD approach also allows us to assess the quantitative importance of the habit in the power utility specification. Our empirical results suggest that the habit is a substantial fraction of current consumption–about 97 percent on average–echoing the specification of Campbell and Cochrane (1999) in which the steady-state habit-consumption ratio exceeds 94 percent. The SMD estimated habit function is concave and generates positive intertemporal marginal rate of substitution in consumption. The SMD estimated subjective time-discount factor is around 0.99 and the estimated power utility curvature parameter is about 0.80 for three different combinations of instruments and asset returns.

Finally, we undertake a statistical model comparison analysis. Because our habit-based asset pricing model makes some parametric assumptions that may not be fully accurate (e.g., it maintains the power utility specification), and because the SMD-estimated nonparametric habit function contains lagged consumption of only finite lag length, the implied Stochastic Discount Factor (SDF) should be best viewed as a proxy to the true unknown SDF. Thus, we evaluate the SMD-estimated habit model and several competing asset pricing models by employing the model comparison distance metrics recommended in Hansen and Jagannathan (1997) (the so-called HJ distance and the HJ+ distance), where all the models are treated as SDF proxies to the unknown truth. In particular, the SMD-estimated internal habit model is compared to (i) the SMD-estimated external habit model, (ii) the three-factor asset pricing model of Fama and French (1993), (iii) the “scaled” consumption Capital Asset Pricing Model (CAPM) of Lettau and Ludvigson (2001b), (iv) the classic CAPM of Sharpe (1964) and Lintner (1965), and (v) the classic consumption CAPM of Breeden (1979) and Breeden and Litzenberger (1978). Doing so, we find that a SMD-estimated internal habit model can better explain a cross-section of size and book-market sorted equity returns, both economically and in a statistically significant way, than the other five competing models. These results are particularly encouraging for the internal habit specification, since the Fama and French (1993) three-factor model and the Lettau and Ludvigson (2001b) scaled consumption CAPM have previously displayed relative success in explaining the cross-section of stock market portfolio returns.

The Future Research Agenda

I am currently working on several projects that extend the analyses on equity markets described above to study housing markets, risk premia in housing assets, and the relationship of these variables to aggregate consumer spending. One line of work (joint with Christopher Mayer of Columbia University) concerns the role of risk premia in U.S. housing markets. Existing empirical work in the housing literature has assumed that housing risk premia are constant. Yet there are plenty of reasons to investigate whether this assumption is plausible. Indeed, the unprecedented surge in U.S. house prices that preceded the recent mortgage crisis appears, anecdotally, to have been driven by a decline in market participants’ assessment of the riskiness of these assets. We are currently investigating whether risk premia in the U.S. housing market vary across metropolitan areas and assessing the extent to which particular models of risk can account for that variation.A closely related theoretical project with Stijn Van Nieuwerburgh of the Stern School at NYU and Jack Favilukis of London School of Economics explores the effects of changing collateral constraints from housing assets on aggregate consumer spending. It is often presumed that changes in such collateral constraints will have a large affect on aggregate consumer spending, especially if financial markets are incomplete and agents cannot perfectly insure idiosyncratic shocks to their labor income or housing wealth. In this work we show that, even when markets are incomplete, the theoretical basis for such a large and direct linkage between consumer spending and housing wealth is unclear. Although fluctuations in housing collateral constraints do affect some household’s ability to borrow and consume, in general equilibrium fluctuations in housing collateral affect households’ ability to share risks with one another, and therefore affect the cross-sectional distribution of consumption, but may have very little affect on the size of the overall consumption pie, that is on aggregate consumption. We develop and solve a general equilibrium model to measure the theoretical marginal propensity to consume out of housing wealth and to assess the impact of changing collateral constraints on aggregate consumption. One important question we intend to address is to what extent risk premia adjust versus quantities (aggregate consumption). We solve for optimal portfolio decisions of such heterogeneous households who face housing collateral constraints, and determine the equilibrium housing returns they give rise to.


Andrew Abel, 1990. “Asset Prices under Habit Formation and Catching Up with the Joneses,” American Economic Review, v. 80(2), p. 38-42.
Ravi Bansal & Amir Yaron, 2004. “Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles,” Journal of Finance, v. 59(4), p. 1481-1509.
Ravi Bansal, Robert Dittmar & Christian Lundblad, 2005. “Consumption, Dividends, and the Cross Section of Equity Returns,” Journal of Finance, v. 60(4), p. 1639-1672.
Ravi Bansal, Robert Dittmar & Dana Kiku, 2007. “Cointegration and Consumption Risks in Asset Returns,” NBER Working Paper 13108.
Douglas Breeden, 1979. “An intertemporal asset pricing model with stochastic consumption and investment opportunities,” Journal of Financial Economics, v. 7(3), p. 265-296.
Douglas Breeden & Robert Litzenberger, 1978. “Prices of State-contingent Claims Implicit in Option Prices,” Journal of Business, v. 51(4), p. 621-51.
Claudio Campanale, Rui Castro & Gian Luca Clementi, 2007. “Asset Pricing in a Production Economy with Chew-Dekel Preferences,” Working Paper 07-07, Rimini Centre for Economic Analysis.
John Campbell, 1993. “Intertemporal Asset Pricing without Consumption Data,” American Economic Review, v. 83(3), p. 487-512.
John Campbell, 1996. “Understanding Risk and Return,” Journal of Political Economy, v. 104(2), p. 298-345.
John Campbell, 2003. “Consumption-based asset pricing,” in: G. Constantinides, M. Harris & R. Stulz (ed.), Handbook of the Economics of Finance, volume 1, chapter 13, p. 803-887, Elsevier.
John Campbell & John Cochrane, 1999. “Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior,” Journal of Political Economy, v. 107(2), p. 205-251.
John Campbell & Luis Viceira, 2001. “Strategic Asset Allocation: Portfolio Choice for Long-Term Investers,” London, UK: Oxford University Press.
John Campbell & Tuomo Vuolteenaho, 2004. “Bad Beta, Good Beta,” American Economic Review, v. 94(5), p. 1249-1275.
John Cochrane, 1996. “A Cross-Sectional Test of an Investment-Based Asset Pricing Model,” Journal of Political Economy, v. 104(3), p. 572-621.
Riccardo Colacito & Mariano Croce, 2005. “Risks For The Long Run And The Real Exchange Rate,” 2005 Meeting Papers, 794, Society for Economic Dynamics.
Mariano Croce, 2006. “Welfare Costs, Long Run Consumption Risk, and a Production Economy,” 2006 Meeting Papers, 582, Society for Economic Dynamics.
Mariano Croce, Martin Lettau & Sydney Ludvigson, 2007. “Investor Information, Long-Run Risk, and the Duration of Risky Cash-Flows,” NBER Working Paper 12912.
Larry Epstein & Stanley Zin, 1989. “Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework,” Econometrica, v. 57(4), p. 937-69.
Larry Epstein & Stanley Zin, 1991. “Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis,” Journal of Political Economy, v. 99(2), p. 263-86.
Eugene Fama & Kenneth French, 1992. “ The Cross-Section of Expected Stock Returns,” Journal of Finance, v. 47(2), p. 427-65.
Eugene Fama & Kenneth French, 1993. “Common risk factors in the returns on stocks and bonds,” Journal of Financial Economics, v. 33(1), p. 3-56.
Wayne Ferson & George Constantinides, 1991. “Habit persistence and durability in aggregate consumption: Empirical tests,” Journal of Financial Economics, v. 29(2), p. 199-240.
Francisco Gomes & Alexander Michaelides, 2005. “Optimal Life-Cycle Asset Allocation: Understanding the Empirical Evidence,” Journal of Finance, v. 60(2), p. 869-904.
Fatih Guvenen, 2003. “A Parsimonious Macroeconomic Model for Asset Pricing: Habit Formation or Cross-sectional Heterogeneity?,” RCER Working Paper 499, University of Rochester.
Lars Peter Hansen & Kenneth Singleton, 1982. “Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models,” Econometrica, v. 50(5), p. 1269-86.
Lars Peter Hansen & Kenneth Singleton, 1983. “Stochastic Consumption, Risk Aversion, and the Temporal Behavior of Asset Returns,” Journal of Political Economy, v. 91(2), p. 249-65.
Lars Peter Hansen & Ravi Jagannathan, 1997. “ Assessing Specification Errors in Stochastic Discount Factor Models,” Journal of Finance, v. 52(2), p. 557-90.
Lars Peter Hansen & Ravi Jagannathan, 1991. “Implications of Security Market Data for Models of Dynamic Economies,” Journal of Political Economy, v. 99(2), p. 225-62.
Lars Peter Hansen & Thomas Sargent, 2006. “Fragile Beliefs and the Price of Model Uncertainty.” Unpublished mimeo, New York University.
Lars Peter Hansen, John Heaton & Nan Li, 2005. “Consumption Strikes Back?: Measuring Long-Run Risk,” NBER Working Paper 11476.
Lars Peter Hansen, John Heaton, Junghoon Lee & Nikolai Roussanov, 2007. “Intertemporal Substitution and Risk Aversion,” in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, volume 6, chapter 61, Elsevier.
Dana Kiku, 2005. “Is the Value Premium a Puzzle?” Unpublished mimeo, Duke University.
Narayana Kocherlakota, 1990. “ Disentangling the Coefficient of Relative Risk Aversion from the Elasticity of Intertemporal Substitution: An Irrelevance Result,” Journal of Finance, v. 45(1), p. 175-90.
Narayana Kocherlakota, 1996. “The Equity Premium: It’s Still a Puzzle,” Journal of Economic Literature, v. 34(1), p. 42-71.
Dirk Krueger & Felix Kubler, 2006. “Pareto-Improving Social Security Reform when Financial Markets are Incomplete!?,” American Economic Review, v. 96(3), p. 737-755.
Martin Lettau & Sydney Ludvigson, 2001. “Consumption, Aggregate Wealth, and Expected Stock Returns,” Journal of Finance, v. 56(3), p. 815-849.
Martin Lettau & Sydney Ludvigson, 2001. “Resurrecting the (C)CAPM: A Cross-Sectional Test When Risk Premia Are Time-Varying,” Journal of Political Economy, v. 109(6), p. 1238-1287.
Martin Lettau & Sydney Ludvigson, 2005. “Euler Equation Errors,” NBER Working Paper 11606.
John Lintner, 1965. “Security Prices, Risk and Maximal Gains from Diversification,” Journal of Finance, v. 20, p. 587-615.
Lars Ljungqvist & Harald Uhlig, 2000. “Tax Policy and Aggregate Demand Management under Catching Up with the Joneses,” American Economic Review, v. 90(3), p. 356-366.
Hanno Lustig & Stijn Van Nieuwerburgh, 2005. “The Returns on Human Capital: Good News on Wall Street is Bad News on Main Street,” NBER Working Paper 11564.
Hanno Lustig, Stijn Van Nieuwerburgh & Adrien Verdelhan, 2008. “The Wealth-Consumption Ratio,” NBER Working Paper 13896.
Christopher Malloy, Tobias Moskowitz & Annette Vissing-Jorgensen, 2005. “Long-Run Stockholder Consumption Risk and Asset Returns,” unpublished mimeo, University of Chicago, Graduate School of Business.
Rajnish Mehra & Edward Prescott, 1985. “The equity premium: A puzzle,” Journal of Monetary Economics, v. 15(2), p. 145-161.
Lior Menzly, Tano Santos & Pietro Veronesi, 2004. “Understanding Predictability,” Journal of Political Economy, v. 112(1), p. 1-47.
Monika Piazzesi & Martin Schneider, 2006. “Equilibrium Yield Curves,” NBER Working Paper 12609.
Fernando Restoy & Philippe Weil, 1998. “Approximate Equilibrium Asset Prices,” NBER Working Paper 6611.
William F. Sharpe, 1964. “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk,” Journal of Finance, v. 19, p. 425-444.
Stephen H. Shore & Joshua S. White, 2002. “External Habit Formation and the Home Bias Puzzle.” Unpublished mimeo, Harvard University.
Tallarini Jr., Thomas D., 2000. “Risk-sensitive real business cycles,” Journal of Monetary Economics, v. 45(3), p. 507-532.
Weil, Philippe, 1989. “The equity premium puzzle and the risk-free rate puzzle,” Journal of Monetary Economics, v. 24(3), p. 401-421.

Volume 9, Issue 1, November 2007

Amir Yaron on Lifetime Inequality and Long Run Risks and Asset Pricing

 Amir Yaron is Associate Professor of Finance at the Wharton School of Business, University of Pennsylvania and Faculty Research Associate at the NBER. He is interested in macrofinance, in particular studying aggregate and individual sources of risks. Yaron’s RePEc/IDEAS entry.

My research is at the intersection of macroeconomics and finance. An ongoing challenge in macroeconomics and finance is to identify the important sources of risks that individuals and firms face and how these in turn affect allocations and prices. These risks might include, for example, aggregate productivity shocks, uninsurable individual labor risk, and/or financial frictions faced by both individuals and firms. My research identifies and measures a subset of these risks, and analyzes how they map into observable quantities such as consumption and prices.I would like to describe two research programs which at first may appear somewhat remote, but at least from my perspective, do ultimately have a common intersection point. The first area departs from the representative agent paradigm and analyzes issues such as consumption behavior, portfolio choices, risk sharing, inequality and equilibrium prices in environments where agents face uninsurable idiosyncratic labor market risk. Most of this research has been with Chris Telmer and Kjetil Storesletten. In this research line there are two interrelated questions: (i) what are the properties of idiosyncratic earnings shocks and (ii) what are their quantitative ramifications for allocations, risk sharing, inequality, and ultimately asset pricing? Since Kjetil described most of it in his newsletter contribution, I will proceed to discuss some recent work with Mark Huggett and Gustavo Ventura that tries to embed these risks within models of human capital. The second area focuses on my recent work with Ravi Bansal on aggregate models that feature Long Run Risks for understanding the sources of fluctuations of asset prices.

Human Capital and Lifetime Inequality

Much of my current research in this area is channeled to endogenize, to some degree, idiosyncratic earnings risks. Currently, the common approach to modern versions of the life-cycle, permanent-income hypothesis, is to specify earnings and wages as exogenous random processes. This approach has dominated the literature on consumption, savings, and wealth distribution as well the literature on social security and income tax reform.Our research program asks to what extent differences in individual conditions at the start of economic life contribute to the dynamics of earnings inequality over the life cycle. In this context, we revisit issues regarding the quantitative importance of earnings shocks during agents’ working years for lifetime inequality and welfare. That is, we ask to what degree is lifetime inequality due to differences across people established early in life as opposed to differences in luck experienced over the lifetime? Among initial conditions, individual differences established early in life, which ones are the most important?

Answers to these questions should shed light on several important issues. This analysis can provide quantitative information on the relative importance of the many policies directed at modifying or at providing insurance for initial conditions (e.g. public education) against those directed at shocks over the lifetime (e.g., unemployment insurance programs). A discussion of lifetime inequality cannot proceed far without discussing which type of initial condition is the most critical for determining how one fares in life. Finally, a useful framework for answering these questions should also be central in the analysis of a wide range of policies considered in macroeconomics, public finance and labor economics. In particular, many of the current policy analyses are done with an exogenous earnings or wage processes. These policy experiments do not change, by construction, the earnings process and thus changes are mainly operative through various risk sharing channels. However, when human capital is endogenous, such policy experiments can alter the incentives to acquire human capital and therefore change the earnings profiles themselves, and potentially result in large welfare gains/losses.

In Huggett, Ventura and Yaron (2006), we first take an extreme view, abstract from idiosyncratic risk altogether, and ask whether the process for endogenous accumulation of human capital can induce sufficient transition dynamics over the life-cycle to allow such a model to match salient features of the earnings distribution. We focus on the age profiles for the mean, Gini and skewness of earnings. Surprisingly, the richness of these dynamics can accommodate many features of the earnings distribution. We show that a benchmark human capital model (the Ben-Porath (1967) model) in which agents are different in learning ability and initial human capital can replicate these earning properties. The distributions for initial human capital and ability to learn have the property that learning ability must substantively differ across agents and that learning ability and initial human capital are positively correlated.

The model implies, however, that over time both individual earnings levels and growth rates are strongly positively autocorrelated. Evidence from US data shows that earnings growth rates are negatively correlated. This, in conjunction with related evidence on consumption inequality as in Storesletten, Telmer and Yaron (2004) and Deaton and Paxson (1994), suggests an important role for persistent idiosyncratic shocks. Moreover, based on the human capital view, observed earnings fluctuations are a mixture of exogenous shocks and investment in human capital–making inference regarding earnings shocks difficult.

To address these issues in Huggett, Ventura and Yaron (2007), we extend the human capital model to include idiosyncratic shocks to human capital. In order to identify the shocks empirically, we exploit the fact that toward the end of (working) life agents no longer invest in human capital and thus first differences in wages will reveal the shock process. Given this process and observed initial conditions for wealth, we solve for the best (joint log-normal) distribution for learning ability and initial human capital that allows the model to fit various earnings facts. The model suggests that most (around 60 to 70%) of the variation in life time utility (or wealth) are attributable to initial conditions as opposed to shocks. Among initial conditions, variation in initial human capital is substantially more important than variation in learning ability or initial wealth for determining how an agent fares in life.

In the model there are two offsetting forces which together account for the increase in earnings dispersion. One force is that agents differ in learning ability. Agents with higher learning ability have steeper mean earnings profiles than low ability agents, other things equal. This mechanism is supported by the literature, see Card (1999), on the shape of the mean age-earnings profiles by years of education. It is also supported by the work of Lillard and Weiss (1979), Baker (1997) and closely related to the recent work of Guvenen (2007). These authors estimate a statistical model of earnings and find important permanent differences in individual earnings growth rates. The other force is that agents differ in idiosyncratic human capital shocks received over the lifetime.

Future work entails important analysis both in terms of data and models. One important issue stems from the fact that some of the known stylized facts have ‘changed’. For example, the quantitative magnitude of the rise in consumption inequality, found say in Deaton and Paxson (1994) and which is so important for interpreting the role of shocks and market insurance, seems to have diminished with the recent samples. These results seem to also be more sensitive to whether one treats the data using cohort or time effects. There are several important efforts trying to address these issues by contemplating various structural changes, data collection issues, etc. (see Heathcote, Storesletten and Violante (2004) and Attanasio, Battistin and Ichimura (2004)). These are important measurement issues as they clearly affect our inference and modeling choices.

We are currently working on several extensions and applications of our framework. In particular, we are investigating issues related to taxation and social insurance in the presence of human capital acquisition and idiosyncratic risk. The analysis should reveal whether the explicit consideration of human capital accumulation is quantitatively important for some policy experiment and whether the conclusions are different from those that arise using exogenous wage or earnings framework. To get a better handle on the shocks to human capital it would be interesting to link our framework more directly to the literature on unemployment durations–the latter presumably affects the degree to which human capital depreciates. This can be a fruitful ground for better understanding the mapping from job loss duration and shocks to human capital. Another potentially important area is distinguishing between general human capital and schooling. We plan to extend our framework to allow for discrete schooling choice early in life. This extension can be important for differentiating the effects of skilled and unskilled exposure to these human capital shocks. Finally, in the background, many models assume agents (and their employer) know their ability type. It can be potentially interesting to extend our framework to allow for learning. Recent work by Guvenen and Smith (2007) seems to indicate that this can be an interesting channel for quantitatively interpreting the data.

Long Run Risks

A fundamental question both macro and finance academics seek to understand is what causes asset prices to fluctuate and what risks warrant significant risk premia? In general, fluctuations in asset prices can be attributed either to changes in costs of capital or to changes in expected cash flows. However, the conventional wisdom about cash flows, be it consumption growth or dividends growth, is that for all practical purposes they are i.i.d. This view leaves fluctuations in expected cash flows no role in explaining asset prices. As a result, much attention in this literature has focused on changes in the costs of capital. In general equilibrium, such changes are often accommodated by fluctuations in risk preferences.In Bansal and Yaron (2004), we challenge this view by refocusing attention to cash flows. We model consumption and dividend growth rates as containing (i) a small persistent expected growth rate component, and (ii) fluctuating volatility–which captures time-varying economic uncertainty and in the presence of the Epstein and Zin (1989) preferences leads to fluctuations in costs of capital/expected returns. We show that this specification for consumption and dividends is consistent with observed annual consumption and dividend data. Our model captures the intuition that financial markets dislike economic uncertainty, and fluctuating growth prospects are important for asset valuations. Shocks to expected growth alter expectations about future economic growth not only for short horizons but also for the very long run. Agents demand large equity risk premia as they fear that a reduction in economic growth prospects or a rise in economic uncertainty will lower equilibrium consumption, wealth and asset prices. This is distinct from habits-based models in which almost all asset price fluctuations are attributable to time variation in risk premium due to altering risk aversion. Hence, in these models fluctuations in corporate profits (or dividends) do not play a significant role in determining asset prices.

The Long Run Risks model relies on generalized recursive preferences (e.g., Kreps and Porteus (1978), Epstein and Zin (1989), Weil (1989)), which provide a separate role for relative risk aversion and the intertemporal elasticity of substitution (IES). In this framework, a restriction on preferences arises if agents are to explicitly fear (in the sense of lowering prices) adverse movements in expected growth and economic volatility. The restriction is that the IES be greater than one and that agents prefer early resolution of uncertainty (the risk aversion be larger than the reciprocal of the IES). Risk premia in this model are determined by three distinct sources of risk: transient, long-run, and volatility (economic uncertainty) risks, whereas in the standard time separable CRRA preferences the latter two risks simply have zero market prices of risk.

We use econometric techniques to show that the cash flow process, which contains in addition to an i.i.d component a small persistent component, is essentially indistinguishable in finite samples from a pure i.i.d process. Nonetheless, this process results in profoundly different asset pricing implications. Although, the innovations in expected cash flows are relatively small, it is their long-lasting feature that requires risk compensation and leads to large reaction in the price-dividend ratio and ex-post equity return and, consequently, the risk-premium on the asset. We show that risks related to varying growth prospects and fluctuating economic uncertainty can indeed quantitatively justify the observed equity premium, the level of the risk free rate, and the ex-post volatilities of the market return, risk free rate and the price-dividend ratio. The model implies time varying risk premia and, as in the data, that market return volatility is stochastic.

The Long Run Risks framework has already received quite a bit of attention and has been a useful framework for thinking about asset pricing. There is an extensive ongoing body of research examining various extensions to other assets markets. For example, to further evaluate the empirical implications of long-run risks model, Bansal, Dittmar and Lundblad (2005) measure cash-flows of different portfolios (value, growth, size, etc.) and show that differences in magnitude of the long-run response of cash-flows to consumption shocks can empirically account for differences in expected returns across assets. They show how to use cointegration to measure long-run consumption risks in cash flows, and document, that this goes quite a long way in explaining differences in mean returns. There is an ongoing discussion on understanding the precision of various approaches to measuring the long-run cash flow responses to consumption shocks, see for example Hansen, Heaton and Li (2005).

In a more recent work, Bansal, Kiku and Yaron (2007), we focus directly on a relatively rich menu of asset returns and show how to estimate the long-run risks model using the more standard Euler equation-GMM based approach such as in Hansen and Singleton (1982). The difficulty in applying the standard GMM techniques is that the intertemporal marginal rate of substitution contains the unobservable return on wealth. We circumvent this by exploiting the dynamics of aggregate consumption growth and the model’s Euler restrictions to solve for the unobserved return on the claim over the future consumption stream. We show that quantitatively the long-run risks model can successfully account for the market, value, and size sorted returns. Although we initially find low estimates of the IES and large risk aversion coefficients, we show via simulations that finite sample and time-averaging effects (the latter emanating from averaged annual data but monthly decision interval) lead to a downward bias in the IES estimate and a upward bias of the risk aversion coefficient–reconciling many of the previous findings in this literature. After accounting for these effects, the model generates many of the appropriate asset pricing results at reasonable values of risk aversion and IES. The empirical evidence in this paper highlights, again, the importance of low-frequency movements and time-varying uncertainty in economic growth for understanding risk-return trade-offs in financial markets.

One of the important channels of the Long-Run Risks model is the role of time variation in cash flow volatility. There is ample evidence of time variation in market returns at least at high frequency and also to some extent over business cycles. A question that naturally arises is whether there is a detectable component for these effects in consumption, dividends and earnings, the data that researchers in this area often use. In Bansal, Khatchatrian and Yaron (2005), we provide extensive empirical evidence supporting this channel of fluctuating economic uncertainty. We use data from the U.S. and several other countries to show that economic uncertainty (measured by consumption and earnings volatility) sharply predicts and is predicted by price-dividend and price-earnings ratios. Our evidence shows that a rise in economic uncertainty leads to a fall in asset prices, and that high valuation ratios predict low subsequent economic uncertainty. This latter finding is consistent with a long-lasting uncertainty channel, but is inconsistent with the standard formulation in which consumption growth is i.i.d and homoskedastic.

Views regarding the sources of variation of asset markets are often shaped via a decomposition of the variation of the price-dividend ratio. Interpreting this decomposition is intimately related to whether one views asset market fluctuations as driven by variation in discount rates or by changes in expected cash flows. This view turns out to depend on the type of cash flow one chooses to focus on. For example, in Bansal, Khatchatrian and Yaron (2005) we show that there is a strong positive relation between aggregate earnings growth and asset prices. This evidence suggests that broadening the notion of cash flows provides a different view about the sources of asset price fluctuations, and that the focus on dividends (which are somewhat less predictable) may have led researchers to dismiss the cash flow channel prematurely. Furthermore, in Bansal and Yaron (2006), we show that the price-dividend ratio decomposition critically hinges on whether one analyzes price and dividend per share or total dividend and total market capitalization. Broadly, the difference between these two cash flow measures captures equity investment from the non financial corporate sector to the corporate sector via issuances, and payments by the non-financial corporate sector to the private sector via repurchases. While there is no theoretical reason to impose cointegration between dividend per-share and consumption or output, macroeconomic restrictions suggest that total payouts ought to be cointegrated with consumption. This is indeed the case in the data, and estimation which imposes this restriction for aggregate payouts seems to support a view in which about 50% of the variation in valuation ratios are attributable to expected growth and the remaining to discount rates. Furthermore, a variant of the Long Run Risk model that imposes this cointegration restriction generates comparable results. These issues highlight the importance of examining and modeling cash flow dynamics. For example, models focusing on production, which typically impose cointegation, have the difficult task of endogenously generating the joint dynamics of consumption and dividends–features that are so critical for the purpose of asset pricing evaluations. Related issues arise when thinking about how cash flows of firms, sectors, portfolios and aggregate quantities relate. Future research will clearly have to explore these dimensions of the data and models will need to address them in a more consistent manner.

Long Run Risks is an exciting area and there are now several researchers and papers that use features of the Long Run Risks framework or extend it to address various issues and markets. These include research on foreign exchange markets, the term structure of interest rates, credit spreads, derivative markets, the recent rise in the stock market and the great moderation, cost of business cycles, cointegration and portfolio choice, the value premium, production economies with long run risks, heterogeneous agents, robust control and learning, inflation risk premia, and housing. I believe these lines of research will remain fruitful and contribute toward our understanding of economic risks.


Attanasio, Orazio, Erich Battistin and Hidehiko Ichimura, 2004, What Really Happened To Consumption Inequality in the U.S.?, Working paper, NBER 10038.
Baker, Michael, 1997, Growth-rate Heterogeneity and the Covariance Structure of Life Cycle Earnings, Journal of Labor Economics 15(2), 338-375.
Bansal, Ravi, Robert F. Dittmar and Christian Lundblad, 2005, Consumption, Dividends, and the Cross-section of Equity Returns, Journal of Finance 60(4), 1639-1672.
Bansal, Ravi, Varoujan Khatchatrian and Amir Yaron, 2005, Interpretable Asset Markets?, European Economic Review 49(3), 531-560.
Bansal, Ravi, Dana Kiku and Amir Yaron, 2007, Risks for the Long Run: Estimation and Inference, Working paper, University of Pennsylvania.
Bansal, Ravi, and Amir Yaron, 2004, Risks for the Long Run: A potential Resolution of Asset Pricing Puzzles, Journal of Finance 59(4), 1481-1509.
Bansal, Ravi, and Amir Yaron, 2006, The Asset Pricing-Macro Nexus and Return-Cash Flow Predictability, Working paper, The Wharton School, University of Pennsylvania.
Ben-Porath, Yoram, 1967, The Production of Human Capital and the Life Cycle of Earnings, Journal of Political Economy 75(4I), 352-365.
Card, David, 1999, The Causal Effect of Education on Earnings, In Orley Ashenfelter and David Card, editors, Handbook of Labor Economics, Volume 3, (Elsevier, Amsterdam).
Deaton, Angus, and Christina Paxson, 1994, Intertemporal Choice and Inequality, Journal of Political Economy 102(3), 437-467.
Epstein, Larry G., and Stanley E. Zin, 1989, Substitution, Risk Aversion, and the Intertemporal Behavior of Consumption and Asset Returns: A Theoretical Framework, Econometrica 57(4), 937-969.
Guvenen, Fatih, 2007, Learning your Earning: Are Labor Income Shocks Really Very Persistent?, American Economic Review 97(3), 687-712.
Guvenen, Fatih, and Anthony Smith, 2007, Inferring Labor Income Risk from Economic Choices: An Indirect Inference Approach, Working paper, Yale University. 9
Hansen, Lars Peter, John Heaton and Nan Li, 2005, Consumption Strikes back?, Working paper, NBER, 11476.
Hansen, Lars Peter, and Kenneth Singleton, 1982, Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models, Econometrica 50(5), 1269-1286.
Heathcote, Jonathan, Kjetil Storesletten and Gianluca Violante, 2004, The Cross-Sectional Implications of Rising Wage Inequality in the United States, Discussion paper, CEPR, 4296.
Huggett, Mark, Gustavo Ventura and Amir Yaron, 2006, Human Capital and Earnings Distribution Dynamics, Journal of Monetary Economics 53(2), 265-290.
Huggett, Mark, Gustavo Ventura and Amir Yaron, 2007, Sources of Lifetime Inequality, Working paper, NBER, 13224.
Kreps, David, and Evan Porteus, 1978, Temporal Resolution of Uncertainty and Dynamic Choice Theory, Econometrica 46(1), 185-200.
Lillard, L., and Yoram Weiss, 1979, Components of Variation in Panel Earnings Data: American Scientists 1960-70, Econometrica 47(2), 437-454.
Storesletten, Kjetil, 2003, The Research Agenda: Kjetil Storesletten on Inequality in Macroeconomics, EconomicDynamics Newsletter 5(1).
Storesletten, Kjetil, Chris I. Telmer and Amir Yaron, 2004, Consumption and Risk Sharing Over the Life Cycle, Journal of Monetary Economics 51(3), 609-633.
Weil, Philippe, 1989, The Equity Premium Puzzle and the Risk-free Rate Puzzle, Journal of Monetary Economics 24(3), 401-421.
Volume 8, Issue 2, April 2007

Matthias Doepke on the Transition from Stagnation to Growth

Matthias Doepke is Associate Professor of Economics at UCLA. He is interested in the economic growth and development, demographic change, political economics, and monetary economics. Doepke’s RePEc/IDEAS entry.

The major part of my research is concerned with what may be called the “transition perspective” on economic development. This literature starts from the observation that economic growth is a historically recent phenomenon. Until about 200 years ago, living standards were essentially stagnant in every country in the world. Starting with the industrial revolution in Britain, an increasing number of countries have undergone a transformation from a pre-industrial, stagnant, mostly agricultural economy to a modern society where sustained economic growth is the norm.The transition from stagnation to growth is not simply a matter of increased technical progress or faster capital accumulation, but a sweeping transformation of a diverse set of aspects of the economy and of society. For example, all countries that have successfully developed have also experienced a demographic transition of rapidly falling mortality and fertility rates, a structural transformation from agriculture to industry and services, as well as political changes such as the abolishment of child labor, the introduction of public education, and the expansion of women’s rights.

It is precisely because economically successful countries are so similar to each other in all these dimensions that we think that studying the transition from stagnation to growth is relevant for economic development today. By improving our understanding of this transition, we hope to learn which of the changes that accompany the economic takeoff are essential ingredients in the growth process rather than luxury goods that merely happen to be acquired as economies grow rich. In what follows, I will review my research with a number of coauthors on demographic change, political reforms, and cultural change during the transition and discuss what the findings imply for economic development.

The Demographic Transition

The standard explanation for economic stagnation in the pre-industrial era is the Malthusian income-population feedback. Before industrialization, living standards and population growth were positively related: when food and other resources were plentiful, people had more children, and more children survived to adulthood. This relationship led to a Malthusian trap where productivity improvements increased population density, which, in turn, depressed living standards due to the scarcity of land.Given the central role of population growth in Malthus’ theory, it is no surprise that the first models of the transition from stagnation to growth (such as Galor and Weil 2000 and Hansen and Prescott 2002) focused on the demographic dimension of the transition. In my work on the issue, I concentrate on the question why the speed and timing of fertility decline varies so substantially across countries. For example, after World War II a number of Asian countries such as South Korea needed only thirty years to undergo a demographic shift that in Britain took more than 100 year to complete.

In “Accounting for Fertility Decline during the Transition to Growth” I develop a theory in which (following Hansen and Prescott 2002) the economic takeoff is modeled as an endogenous switch from a land-intensive agricultural technology to a modern industrial technology. Fertility decisions are endogenous, and are subject to a quantity-quality tradeoff. The model generates a transition from Malthusian stagnation to growth accompanied by a demographic transition from high to low fertility.

The theory points to government policies that affect the opportunity cost of education as a key determinant of demographic change during development. In particular, the speed and timing of fertility decline is highly reactive to education subsidies and child labor restrictions. Comparing across policies, child labor regulations turns out to have larger effects than education policies. This is due to the fact that before industrialization, working children used to provide a substantial fraction of the overall income of the typical family. As a consequence, forgone child-labor income turns out to be the main component of the overall opportunity cost of education.

In addition to influencing fertility decisions, child labor and education policies also have a major impact on the evolution of inequality. The inequality effects are large because of the impact of government policies on the fertility differential between the rich and the poor. If poor unskilled parents have many children who themselves receive little education, the fraction of unskilled workers in the economy will tend to increase, which puts further downward pressure on the wages of the unskilled. The relationship of inequality, differential fertility, and economic growth is analyzed in more detail in “Inequality and Growth: Why Differential Fertility Matters” (with David de la Croix). The paper shows that it is not overall population growth, but the distribution of fertility within the population which matters most for growth. In other words, who is having the children is more important than how many children there are overall.

Political Reform: Child Labor and Public Education

The finding that social policies can have a large impact on economic outcomes in a country undergoing the transition from stagnation to growth leads to the question of what determines if and when these policies are adopted. Consider the case of child labor laws. The first countries to successfully develop all introduced a set of policies that outlawed most child labor in the late nineteenth century (in addition to direct child labor restrictions, compulsory schooling laws also played a major role). In contrast, unregulated child labor continues to be widespread in many developing countries.What determines whether a country adopts child labor laws, and why are differences in child labor regulation so persistent? One possibility, of course, is that ruling out child labor is socially optimal at some stage of development. However, in “Origins and Consequences of Child Labor Restrictions: A Macroeconomic Perspective,” Dirk Krueger and I argue that this is unlikely to be the case; while child labor may lead to specific inefficiencies, a child labor ban is generally not the best policy to address these inefficiencies. The alternative is a political-economy explanation for the existence of child labor laws, which is the angle that Fabrizio Zilibotti and I pursue in “The Macroeconomics of Child Labor Regulation.”

In our model, the motive that leads to support for child labor restrictions is the drive to limit competition: unskilled workers compete with children in the labor market, and therefore stand to gain from higher wages if child labor is restricted. In this sense, we regard child labor laws as similar to other forms of labor regulation aimed at, say, union outsiders. There is, however, one essential difference: in the case of child labor, the potential competition comes at least partly from inside the unskilled workers’ families. For this reason, workers’ attitudes regarding child labor laws depend not only on the degree to which they compete with children in the labor market, but also on the extent to which their own income relies on child labor.

We examine workers’ political preferences over child labor laws in a framework with endogenous fertility and education decisions. The potential loss of child-labor income is especially severe for workers who have many children. We show that the irreversible nature of fertility decisions can lead to multiple politico-economic steady states. Countries can get locked into an outcome where the average family size is large, households rely on child labor, and public support for child labor regulation is low. Alternatively, there is a regime with small family sizes, high levels of education, and widespread support for regulation. In each case, the existing political regime induces fertility decisions that lock parents into supporting the status quo.

The existence of multiple steady states can explain why in some developing countries a large proportion of children work and political support for the introduction of child labor laws is weak, while other countries at similar stages of development have strict regulations and a low incidence of child labor. Child labor laws are introduced only if an increase in the demand for human capital induces young families to reduce fertility and educate their children. This prediction is consistent with the history of child labor regulation in Britain, where the introduction of regulations in the nineteenth century followed a period of rising wage inequality, and coincided with rapidly declining fertility rates and an expansion of education.

Political Reform: Female Empowerment

In addition to changes in specific laws and regulations, a major political transformation in the course of development is the expansion of economic and political rights. Arguably, the people who experienced the most dramatic improvement in their legal position were married women. In the U.S. and Britain, until the mid-nineteenth century married women had essentially no economic or political rights at all: their entire legal existence was subsumed in marriage, and husbands got to make all the decisions. A married woman could not own property, she could not make a will, she usually could not obtain a divorce, in the case of separation she could not get custody of her children, and she had no right to vote.The legal position of married women started to improve in the second half of the nineteenth century. The reforms started well before women obtained the right to vote, and well before married women’s labor force participation started to rise substantially. In ongoing research with Michèle Tertilt (“Women’s Liberation: What’s in It for Men?”), we examine the reasons behind this transformation from an economic perspective. We focus on the observation that expanding female rights amounted to a voluntary ceding of power on the part of men, who at the time were in firm political control. What, then, are the economic interests of men for sharing power with women?

In our analysis, we interpret women’s rights as a determinant of bargaining power within marriage. The idea put forth in the paper is that from a man’s perspective, there is a tradeoff between the power of one’s own wife and other men’s wives. Men ideally want their wives to have no rights. At the same time, men care about their daughters, and may prefer them to have some power vis-à-vis the future sons-in-law. Moreover, men would like their children (both sons and daughters) to find high-quality spouses. In our theory, an expansion of women’s rights leads to increased investment in children (including future sons- and daughters-in-law), which provides an additional motive for men to support women’s rights.

We show that the strength of men’s incentives for supporting women’s rights depends on the return to education. If parents do not invest into their children’s education, men have little incentive for extending rights. The situation changes when an increase in the demand for human capital induces families to reduce fertility and educate their children. If the return to education is sufficiently high, men stand to benefit from giving equal rights to women, and they will vote for the reforms. These predictions are consistent with the observation that the initial phase of expanding women’s rights in the U.S. and Britain coincided with the main phase of fertility decline and a rapid increase in schooling levels.

Our findings provide a contrast to a recent literature on franchise extension initiated by Acemoglu and Robinson (2000). In their theory, the expansion of political rights is driven by the threat of violence: the elite extend the franchise in order to avert the threat of a revolution. In the case of women’s rights, fear of revolution appears as an unlikely motive for the reforms. Instead, we suggest that changes in the economic environment led to a situation where both men and women stood to gain from an equalized distribution of rights. (Lizzeri and Persico 2004 and Galor and Moav 2006 apply similar arguments to franchise extension and public education funding.)

Political Reform: Property-Rights Institutions

In many developing countries, the institutional framework governing economic life has its roots in the colonial period, when the interests of European settlers clashed with those of the native population or imported slaves. A recent historical and empirical literature documents a reversal of fortune among these former European colonies, i.e., countries that were initially economically successful were overtaken by others (such as the U.S. and Canada) that started out relatively poor (See Sokoloff and Engerman 2000 and Acemoglu, Johnson, and Robinson 2001, 2002).A number of authors argue that this pattern is due to institutions; in particular, institutions that were set up in the initially successful colonies turned out to be a hindrance for development later on. In ongoing research with Andrea Eisfeldt (“Colonies”), we examine this hypothesis in a theoretical framework based on endogenous property rights. In our theory, property rights are represented as a state variable given by the number of people with power in a country, i.e., ‘gun owners.’ Gun owners can protect their own property, they can trade with other gun owners in a standard market economy, and, crucially, they can exploit and expropriate others who do not own guns.

We develop a simple theory of colonization where the colonizing power optimally determines the number of gun-owning settlers to be sent to each colony. Here a colony is characterized by its technology and factor endowments, including the number of (unarmed) locals already present. After the initial colonization stage, political control passes to the gun owners in each colony. The key decision collectively taken by the gun owners is emancipation: they can decide to issue guns to some or all of the oppressed locals and slaves, and thereby issue them with property rights. The incentives for doing so stem from the fact that free labor is complementary to physical capital, which, in turn, is owned by the existing gun owners.

Optimal colonization leads to an initial outcome where income per capita is highest in the colonies with the highest ratio of the unarmed to gun-owning settlers. Subsequently, capital accumulation leads to a rise of the industrial sector, with an associated increase in the demand for free labor. In the long run, full emancipation takes place in all colonies. Emancipation proceeds faster, however, in colonies that start out with relatively few oppressed. Intuitively, people whose property rights are protected accumulate more capital, which in turn makes it attractive to issue even more property rights in the future in order to raise the return on this capital. The result is a reversal of fortune: Through faster emancipation, the initially poor colonies overtake the richer colonies in terms of income per capita.

Cultural Change

One of the puzzles posed by the British industrial revolution is the observation that the land-owning upper class was not able to maintain its relative economic position in society, and was instead overtaken by entrepreneurs and capitalists who, for the most part, rose from the middle classes. Many observers of the time linked this outcome to differences in values, attitudes, and ultimately preferences across social classes. Building on this hypothesis, in “Occupational Choice and the Spirit of Capitalism” Fabrizio Zilibotti and I develop a theory of preference formation that is rooted in the rational choice paradigm, and ask whether such a theory can help explain the success and failure of different social classes in the industrialization period.In our theory, altruistic parents strive to shape their children’s preferences in a way that best fits with their future material circumstances. We focus on two key aspects of preferences: the rate of time preference (patience) and the taste for leisure (or, conversely, work ethic). Parental investments in patience interact with the occupational choice of the child. Lifetime earnings are relatively flat in some occupations, while high returns are achieved only late in life in others, in particular those requiring the acquisition of skills. A parent’s incentive for investing in a child’s patience increases in the steepness of the child’s future income profile. Parental investments in their children’s taste for leisure hinge on the role of labor effort. Parents who expect their children to be wholly reliant on labor income will tend to instill them with a strong work ethic, i.e., a tolerance for hard work and a reduced taste for leisure. In contrast, parents who anticipate their children to be rentiers with ample free time will teach them to appreciate refined leisure activities, from performing classical music to hunting foxes.

The theory can account for the reversal in the economic fortunes of different social classes at the time of the industrial revolution. For centuries, members of the pre-industrial middle class—artisans, craftsmen, and merchants—had to sacrifice consumption and leisure in their youths to acquire skills. Artisans, for instance, could become prosperous masters of their professions only after undergoing lengthy stages of apprenticeship and journeymanship. We argue that in response to this economic environment, the middle classes developed a system of values and preferences centered on parsimony, work ethic, and delay of gratification. For the landed upper class, in contrast, neither work ethics nor patience were particularly valuable, because the members of this class could rely on fairly stable rental incomes from their estates. As a result, the landowning elite cultivated refined tastes for leisure and grew less future-oriented.

In the pre-industrial era, these differences in preferences and values had limited consequences. However, patience and work ethics became a key asset—a “spirit of capitalism”—when opportunities of economic advancement through entrepreneurship and investment arose at the outset of the industrial revolution. In an already stratified society, it was members of the patient, hard-working middle class who made the most of the new opportunities and ultimately gained economic ascendancy over the landed elite.


One of the byproducts of the literature on the transition to growth is a new and, I think, highly productive exchange of ideas between growth theorists and economic historians. Starting from a situation where most variables of interest were contained in the Penn World Tables, theorists have considerably expanded their view of what matters for economic development, and are now doing research on many aspects of political and social change that were not traditionally in the realm of growth theory.Ultimately, we hope that by studying the transition from stagnation to growth in the countries that successfully completed the transition, we will be able to learn more about why some countries fail to develop successfully even today. From this perspective, a recurring theme in the research described above is the role of human capital as a catalyst for economic and social change. Most importantly, we believe that increased demand for human capital changed the nature of the family, with investment in children steadily gaining in importance. In addition to affecting family decisions such as fertility, this process also shifted political preferences for policies such as child labor regulation, public education, and women’s rights. Similarly, we interpret the divergent success of the upper and the middle class in the course of the industrial revolution as a consequence of human capital investment, although here the investment is in preferences or values of varying economic usefulness rather than in productive knowledge itself. Taken together, these findings suggest that the direct productivity effect may be only a small part of the overall contribution of human capital to a successful transition from stagnation to growth.


Acemoglu, Daron, Simon Johnson, and James A. Robinson. 2001. “The Colonial Origins of Comparative Development: An Empirical Investigation.” American Economic Review 91(5): 1369-401.
Acemoglu, Daron, Simon Johnson, and James A. Robinson. 2002. “Reversal of Fortune: Geography and Institutions in the Making of the Modern World Income Distribution.” Quarterly Journal of Economics 117(4): 1231-94.
Acemoglu, Daron, and James Robinson. 2000. “Why Did the West Extend the Franchise? Democracy, Inequality and Growth in Historical Perspective.” Quarterly Journal of Economics 115(4): 1167-1199.
Becker, Gary S., Kevin M. Murphy, and Robert Tamura. 1990. “Human Capital, Fertility, and Economic Growth.” Journal of Political Economy 98(5):S12-37.
de la Croix, David, and Matthias Doepke. 2003. “Inequality and Growth: Why Differential Fertility Matters.” American Economic Review 93(4): 1091-1113.
de la Croix, David, and Matthias Doepke. 2006. “To Segregate or to Integrate: Education Politics and Democracy.” CEPR Discussion Paper 5799.
Doepke, Matthias. 2004. “Accounting for Fertility Decline during the Transition to Growth.” Journal of Economic Growth 9(3): 347-383.
Doepke, Matthias. 2005. “Child Mortality and Fertility Decline: Does the Barro-Becker Model Fit the Facts?” Journal of Population Economics 18(2): 337-366.
Doepke, Matthias, and Andrea Eisfeldt. 2007. “Colonies.” Unpublished manuscript, UCLA and Northwestern University.
Doepke, Matthias, and Dirk Krueger. 2006. “Origins and Consequences of Child Labor Restrictions: A Macroeconomic Perspective.” NBER Working Paper 12665.
Doepke, Matthias, and Michele Tertilt. 2007. “Women’s Liberation: What’s in It for Men?” Unpublished manuscript, UCLA and Stanford University.
Doepke, Matthias, and Fabrizio Zilibotti. 2005. “The Macroeconomics of Child Labor Regulation.” American Economic Review 95(5): 1492-1524.
Doepke, Matthias, and Fabrizio Zilibotti. 2007. “Occupational Choice and the Spirit of Capitalism.” NBER Working Paper 12917.
Galor, Oded, and Omer Moav. 2006. “Das Human-Kapital: A Theory of the Demise of the Class Structure.” Review of Economic Studies 73(1): 85-117.
Galor, Oded, and David N. Weil. 2000. “Population, Technology, and Growth, From Malthusian Stagnation to the Demographic Transition and Beyond.” American Economic Review 90(4): 806-28.
Hansen, Gary D., and Edward C. Prescott. 2002. “Malthus to Solow.” American Economic Review 92(4): 1205-17.
Lizzeri, Alessandro, and Nicola Persico. 2004. “Why Did the Elites Extend the Suffrage? Democracy and the Scope of Government with an Application to Britain’s Age of Reform.” Quarterly Journal of Economics 119(4): 707-65.
Lucas, Jr., Robert E. 2002. “The Industrial Revolution: Past and Future.” In Lectures on Economic Growth, Harvard University Press.
Sokoloff, Kenneth L., and Stanley L. Engerman. 2000. “Institutions, Factor Endowments, and Paths of Development in the New World.” Journal of Economic Perspectives 14(3): 217-32.

Volume 8, Issue 1, November 2006

Jesús Fernández-Villaverde and Juan F. Rubio-Ramírez on Estimating DSGE Models

Jesús Fernández-Villaverde and Juan F. Rubio-Ramírez are both Associate Professors of Economics at Duke University. They have written several papers about how to take dynamic general equilibrium models to the data. Fernández-Villaverde’s RePEc/IDEAS entry and Rubio-Ramírez’s RePEc/IDEAS entry.

Our research agenda has focused on the estimation of dynamic stochastic general equilibrium (DSGE) models. In particular, we have worked on the likelihood-based approach to inference.DSGE models are the standard tool of quantitative macroeconomics. We use them to organize our thinking, to measure the importance of different phenomena, and to provide policy prescriptions. However, since Kydland and Prescott’s immensely influential 1982 paper, the profession has fought about how to take these models to the data. Three issues are at stake: first, how to determine the values of the parameters that describe preferences and technology (the unfortunately named “structural” parameters); second, how to measure the fit of the model; and third, how to decide which of the existing theories better accounts for the observed data.

Kydland and Prescott proposed to “calibrate” their model, i.e., to select parameter values by matching some moments of the data and by borrowing from microeconomic evidence. Calibration was a reasonable choice at the time. Macroeconomists were unsure about how to compute their models efficiently, a necessary condition to perform likelihood-based inference. Moreover, even if economists had known how to do so, most of the techniques required for estimating DSGE models using a likelihood approach did not exist. Finally, as recalled by Sargent (2005), the early results on estimation brought much disappointment. The models were being blown out of the water by likelihood ratio tests despite the feeling that those models could teach practitioners important lessons. Calibration offered a way out. By focusing only on a very limited set of moments of the model, researchers could claim success and keep developing the theory.

The landscape changed dramatically in the 1990s. There were developments along three fronts. First, macroeconomists learned how to efficiently compute equilibrium models with rich dynamics. There is not much point in estimating very stylized models that do not even have a remote chance of fitting the data well. Second, statisticians developed simulation techniques like Markov chain Monte Carlo (MCMC), which we require to estimate DSGE models. Third, and perhaps most important, computer power has become so cheap and readily available that we can now do things that were unthinkable 20 years ago.

One of the things we can now do is to estimate non-linear and/or non-normal DSGE models using a likelihood approach. This statement begets two questions: 1) Why do we want to estimate those DSGE models? and 2) How do we do it?

Why Do We Want to Estimate Non-linear and/or Non-normal DSGE Models?

Let us begin with some background. There are many reasons why the likelihood estimation of DSGE models is an important topic. First of all, a rational expectations equilibrium is a likelihood function. Therefore, if you trust your model, you have to trust its likelihood. Second, the likelihood approach provides a coherent and systematic procedure to estimate all the parameters of interest. The calibration approach may have made sense back in the 1980s when we had only a small bundle of parameters to select values for. However, current models are richly parameterized. Neither a loose application of the method of moments (which is what moment matching in calibration amounts to) nor some disparate collection of microeconomic estimates will provide us with the discipline to quantify the behavior of the model. Parameters do not have a life of their own: their estimated values are always conditional on one particular model. Hence, we cannot import these estimated values from one model to another. Finally, the likelihood yields excellent asymptotic properties and sound small sample behavior.However, likelihood-based estimation suffers from a fundamental problem: the need to evaluate the likelihood function of the DSGE model. Except in a few cases, there is no analytical or numerical procedure to write down the likelihood.

The standard solution in the literature has been to find the linear approximation to the policy functions of the model. If, in addition, we assume that the shocks to the economy are normally distributed, we can apply the Kalman filter and evaluate the likelihood implied by the approximated policy functions. This strategy depends on the accuracy of the approximation of the exact policy functions by a linear relation and on the presence of normal shocks. Each of those two assumptions is problematic.

Linear Policy Functions

When we talk about linearization, the first temptation is to sweep it under the rug as a small numerical error. However, the impact of linearization is grimmer than it looks. We explore this assertion in our paper “Convergence Properties of the Likelihood of Computed Dynamic Models”, published in Econometrica and coauthored with Manuel Santos. In that paper, we prove that second order approximation errors in the policy function, like those generated by linearization, have first order effects on the likelihood function. Moreover, we demonstrate that the error in the approximated likelihood is compounded with the size of the sample. Period by period, small errors in the policy function accumulate at the same rate at which the sample size grows. Thus, the approximated likelihood diverges from the exact one as we get more and more observations.We have documented how those theoretical insights are quantitatively relevant for real-life applications. The main piece of evidence is in our paper “Estimating Dynamic Equilibrium Economies: Linear versus Nonlinear Likelihood”, published in the Journal of Applied Econometrics. The paper compares the results of estimating the linearized version of a DSGE model with the results from estimating the non-linear version. In the first case, we evaluate the likelihood of the model with the Kalman filter. In the second case, we evaluate the likelihood with the particle filter (which we will discuss below). Our findings highlight how linearization has a non-trivial impact on inference. First, both for simulated and for U.S. data, the non-linear version of the model fits the data substantially better. This is true even for a nearly linear case. Second, the differences in terms of point estimates, although relatively small in absolute values, have substantive effects on the behavior of the model.

Other researchers have found similar results when they take DSGE models to the data. We particularly like the work of Amisano and Tristiani (2005) and An (2005). Both papers investigate New Keynesian models. They find that the non-linear estimation allows them to identify more structural parameters, to fit the data better, and to obtain more accurate estimates of the welfare effects of monetary policies.

Normal Shocks

The second requirement for applying the Kalman filter to estimate DSGE models is the assumption that the shocks driving the economy are normally distributed. Since nearly all DSGE models make this assumption, this requirement may not look dangerous. This impression is wrong: normality is extremely restrictive.Researchers put normal shocks in their models out of convenience, not for any substantive reason. In fact, fat tails are such a pervasive feature of the data that normality is implausible. More thoughtful treatments of the shocks deliver huge benefits. For example, the fit of an ARMA process to U.S. output data improves dramatically when the innovations are distributed as student-t’s (a density with fat tails) instead of normal ones (Geweke, 1993 and 1994).

A simple way to generate fat tails, and one that captures the evidence of volatility clustering in the data, is to have time-varying volatility in the shocks. Why macroeconomists have not focused more effort on the topic is a puzzle. After all, Engle (1982), in the first work on time-varying volatility, picked as his application of the ARCH model the process for United Kingdom inflation. However, that route was not followed. Even today, and beyond our own work on the issue, only Justiniano and Primiceri (2006) take seriously the idea that shocks in a DSGE model may have a richer structure than normal innovations.

Time-varying volatility of the shocks is not only a device to achieve a better fit, it is key to understanding economic facts. Think about the “Great Moderation.” Kim and Nelson (1999), McConnell and Pérez-Quirós (2000), and Stock and Watson (2002) have documented a decline in the variance of output growth since the mid 1980s. Moreover, there is a narrowing gap between growth rates during booms and recessions. What has caused the change in observed aggregate volatility? Was it due to better conducting of monetary policy by the Fed? Or was it because we did not suffer large shocks like the oil crises of the 1970s? We can answer that question only if we estimate structural models where we let both the monetary policy rule and the volatility of the shocks evolve over time. We will elaborate below on how to explore policy change as a particular case of parameter drifting.

There are two possibilities to introduce time-varying variance in shocks. One is stochastic volatility. The other one is Markov regime-switching models. We have worked more on the first approach since it is easier to handle. However, as we will explain below, we are currently exploring the second one.

A common feature of both stochastic volatility and regime-switching models is that they induce fundamental non-linearities and fat tails. Linearization, by construction, precludes any possibility of assessing time-varying volatility. If we linearize the laws of motion for the shocks, as someone who wanted to rely on the Kalman filter would be forced to do, the volatility terms would drop. Justiniano and Primiceri (2006) have got around that problem by pioneering the use of partially linear models in a specially clever way. Unfortunately, there is only so much we can do even with partially linear models. We need a general procedure to tackle non-linear and/or non-normal problems.

How Do We Do It?

Our previous arguments point out the need to evaluate the likelihood function of the non-linear and/or non-normal solution of DSGE models. But, how can we do that? This is where our paper, “Estimating Macroeconomic Models: A Likelihood Approach,” comes in. This paper shows how a simulation technique known as the particle filter allows us to evaluate that likelihood function. Once we have the likelihood, we can estimate the parameters of the model by maximizing the likelihood (if you are a classical econometrician) or by combining the likelihood with a prior density for the model parameter to form a posterior distribution (if you are a Bayesian one). Also, we can compare how well different economies explain the data with likelihood ratio tests or Bayes factors.The particle filter is a sequential Monte Carlo method that tracks the unobservable distribution of states of a dynamic model conditional on observables. The reason we are keenly interested in tracking such distribution is that, with it, we can obtain a consistent evaluation of the likelihood of the model using a straightforward application of the law of the large numbers.

The particle filter substitutes the population conditional distribution of states, which is difficult if not impossible to characterize, by an empirical distribution generated by simulation. The twist of ingenuity of the particle filter is that the simulation is generated through a device known as sequential importance resampling (SIR). SIR ensures that the Monte Carlo method achieves sufficient accuracy in a reasonable amount of time. Hence, the particle filter delivers the key object that we need to estimate non-linear and/or non-normal DSGE models: an efficient evaluation of the likelihood function of the model.

To illustrate our method, we follow Greenwood, Hercowitz, and Krusell (1997 and 2000). These authors have vigorously defended the importance of technological change specific to new investment goods for understanding postwar U.S. growth and aggregate fluctuations. We estimate a version of their business cycle model. The model has three shocks: to preferences, to neutral technology, and to investment-specific technology. All three shocks display stochastic volatility. Also, there are two unit roots and cointegration relations derived from the balanced growth path properties of the economy. We solve the model using second order approximations and apply the particle filter to evaluate the likelihood function.

The data reveal three facts. First, there is strong evidence for the presence of stochastic volatility in U.S. data. Capturing this phenomenon notably improves the fit of the model. Second, the decline in aggregate volatility has been a gradual trend and not, as suggested by the literature, the result of an abrupt drop in the mid 1980s. The fall in volatility started in the late 1950s, was interrupted in the late 1960s and early 1970s, and resumed around 1979. Third, changes in the volatility of preference shocks account for most of the variation in the volatility of output growth over the last 50 years.

Summarizing, our paper shows how to conduct an estimation of non-linear and/or non-normal DSGE models, that such estimation is feasible in real life, and that it helps us to obtain many answers we could not otherwise generate.

Complementary Papers

Parallel to our main line of estimation of non-linear and/or non-normal DSGE models, we have written other papers that complement our work.The first paper in this line of research is “Comparing Dynamic Equilibrium Economies to Data: a Bayesian Approach,” published in the Journal of Econometrics. This paper studies the properties of the Bayesian approach to estimation and comparison of dynamic economies. First, we show that Bayesian methods have a classical interpretation: asymptotically, the parameter point estimates converge to their pseudotrue values, and the best model under the Kullback-Leibler distance will have the highest posterior probability. Both results hold even if the models are non-nested, misspecified, and non-linear. Second, we illustrate the strong small sample behavior of the approach using a well-known example: the U.S. cattle cycle. Bayesian estimates outperform maximum likelihood, and the proposed model is easily compared with a set of Bayesian vector autoregressions.

A second paper we would like to mention is “A,B,C’s (and D)’s for Understanding VARs”, written with Thomas Sargent and Mark Watson. This paper analyzes the connections between DSGE models and vector autoregressions (VARs), a popular empirical strategy. An approximation to the equilibrium of a DSGE model can be expressed in terms of a linear state space system. An associated linear state space system determines a vector autoregression for observables available to an econometrician. We provide a simple algebraic condition to check whether the impulse response of the VAR resembles the impulse response associated with the economic model. If the condition does not hold, the interpretation exercises done with VARs are misleading. Also, the paper describes many interesting links between DSGE models and empirical representations. Finally, we give four examples that illustrate how the condition works in practice.

In “Comparing Solution Methods for Dynamic Equilibrium Economies”, published in the Journal of Economic Dynamics and Control and joint with Boragan Aruoba, of the University of Maryland, we assess different solution methods for DSGE models. This comparison is relevant because when we estimate DSGE models, we want to solve them quickly and accurately. In the paper, we compute and simulate the stochastic neoclassical growth model with leisure choice by implementing first, second, and fifth order perturbations in levels and in logs, the finite elements method, Chebyshev polynomials, and value function iteration for several calibrations. We document the performance of the methods in terms of computing time, implementation complexity, and accuracy, and we present some conclusions and pointers for future research.

This paper motivated us to think about the possibility of developing new and efficient solution techniques for dynamic models. A first outcome of this work has been “Solving DSGE Models with Perturbation Methods and a Change of Variables,” also published in the Journal of Economic Dynamics and Control. This paper explores the changes of variables technique to solve the stochastic neoclassical growth model with leisure choice. We build upon Kenn Judd’s idea of changing variables in the computed policy functions of the economy. The optimal change of variables for an exponential family reduces the average absolute Euler equation errors of the solution of the model by a factor of three. We demonstrate how changes of variables can correct for variations in the risk level of the economy even if we work with first-order approximations to the policy functions. Moreover, we can keep a linear representation of the laws of motion of the model if we employ a nearly optimal transformation. We finish by discussing how to employ our results to estimate DSGE models

What is Next?

The previous paragraphs were just a summary of the work we have done on the estimation of DSGE models. But there is plenty of work ahead of us.Currently, we are working on a commissioned article for the NBER Macroeconomics Annual. This paper will study the following question: How stable over time are the so-called “structural parameters” of DSGE models? At the core of these models, we have the parameters that define the preferences and technology that describe the environment. Usually, we assume that these parameters are structural in the sense of Hurwicz (1962): they are invariant to interventions, including shocks by nature. Their invariance permits us to exploit the model fruitfully as a laboratory for quantitative analysis. At the same time, the profession is accumulating more and more evidence of parameter instability in dynamic models. We are undertaking the first systematic analysis of parameter instability in the context of a “state of the art” DSGE model. One important application of this research is that we can explore changes in monetary policy over time. If you model monetary policy as a feedback function, you can think about the policy change as a change in the parameters of that feedback function, i.e., as one particular example of parameter drifting.

A related project is our work on semi-nonparametric estimation of DSGE models. The recent DSGE models used by the profession are complicated structures. They rely on many parametric assumptions: utility function, production function, adjustment costs, structure of stochastic shocks, etc. Some of those parametric choices are based on restrictions imposed by the data on theory. For example, the fact that labor income share has been relative constant since 1950s suggests a Cobb-Douglas production function. Unfortunately, many other parametric assumptions are not. Researchers choose parametric forms for those functions based only on convenience. How dependent are our findings on the previous parametric assumptions? Can we make more robust assumptions? Our conversations with Xiaohong Chen have convinced us that this in a worthwhile avenue of improvement. We are pursuing the estimation of DSGE models when we relax parametric assumptions along certain aspects of the model with the method of Sieves, which Xiaohong has passionately championed.

We would also like to better understand how to compute and estimate models with Markov regime-switching. Those models are a nice alternative to stochastic volatility models. They allow for less variation in volatility, hence gaining much efficiency. Also, they may better capture phenomena such as the abrupt break in U.S. interest rates in 1979. Regime-switching models present interesting challenges in terms of computation and estimation.

Finally, we are interested in the integration of microeconomic heterogeneity within estimated DSGE models. James Heckman has emphasized again and again that individual heterogeneity is the defining feature of micro data (see Browning, Hansen, and Heckman, 1999, for the empirical importance of individual heterogeneity and its relevance for macroeconomists). Our macro models need to move away from the basic representative agent paradigm and include richer configurations. The work of Victor Ríos-Rull in this area has been path breaking. Of course, this raises the difficult challenge of how to effectively estimate these economies. We expect to tackle some of those difficulties in the near future.


An, S. (2005). “Bayesian Estimation of DSGE Models: Lessons from Second Order Approximations.” Mimeo, University of Pennsylvania.
Amisano, G. and O. Tristani (2005). “Euro Area Inflation Persistence in an Estimated Nonlinear DSGE Model.” Mimeo, European Central Bank.
Aruoba, S.B., J. Fernández-Villaverde and J. Rubio-Ramí rez (2006). “Comparing Solution Methods for Dynamic Equilibrium Economies.” Journal of Economic Dynamics and Control 30, 2447-2508.
Browning, M., L.P. Hansen, and J.J. Heckman (1999). “Micro Data and General Equilibrium Models.” in: J.B. Taylor and M. Woodford (eds.), Handbook of Macroeconomics, volume 1, chapter 8, pages 543-633 Elsevier.
Fernández-Villaverde, J. and J. Rubio-Ramírez (2004). “Comparing Dynamic Equilibrium Models to Data: A Bayesian Approach.” Journal of Econometrics 123, 153-187.
Fernández-Villaverde, J. and J. Rubio-Ramírez (2005a). “Estimating Dynamic Equilibrium Economies: Linear versus Nonlinear Likelihood.” Journal of Applied Econometrics, 20, 891-910.
Fernández-Villaverde, J. and J. Rubio-Ramírez (2005b). “Estimating Macroeconomic Models: A Likelihood Approach.” NBER Technical Working Paper T0321.
Fernández-Villaverde, J. and J. Rubio-Ramírez (2006). “Solving DSGE Models with Perturbation Methods and a Change of Variables.” Journal of Economic Dynamics and Control 30, 2509-2531.
Fernández-Villaverde, J., J. Rubio-Ramírez, T.J. Sargent, and M. Watson (2006). “A,B,C’s (and D)’s for Understanding VARs.” Mimeo, Duke University.
Fernández-Villaverde, J., J. Rubio-Ramírez, and M.S. Santos (2006). “Convergence Properties of the Likelihood of Computed Dynamic Models.” Econometrica 74, 93-119.
Geweke, J.F. (1993). “Bayesian Treatment of the Independent Student-t Linear Model.” Journal of Applied Econometrics 1993, 8, S19-S40.
Geweke, J.F. (1994). “Priors for Macroeconomic Time Series and Their Application.” Econometric Theory 10, 609-632.
Greenwood, J, Z. Hercowitz, and P. Krusell (1997). “Long-Run Implications of Investment-Specific Technological Change.” American Economic Review 87, 342-362.
Greenwood, J, Z. Hercowitz, and P. Krusell (2000). “The Role of Investment-Specific Technological Change in the Business Cycle.” European Economic Review 44, 91-115.
Hurwicz, L. (1962). “On the Structural Form of Interdependent Systems”. In E. Nagel, P. Suppes, and A. Tarski (eds.), Logic, Methodology and Philosophy of Science. Stanford University Press.
Justiniano A. and G.E. Primiceri (2006). “The Time Varying Volatility of Macroeconomic Fluctuations.” NBER working paper 12022.
Kim, C. and C.R. Nelson (1999) “Has the U.S. Economy Become More Stable? A Bayesian Approach Based on a Markov-Switching Model of the Business Cycle.” Review of Economics and Statistics 81, 608-616.
McConnell, M.M. and G. Pérez-Quirós (2000). “Output Fluctuations in the United States: What Has Changed Since the Early 1980’s?American Economic Review 90, 1464-1476.
Sargent, T.J. (2005). “An Interview with Thomas J. Sargent by George W. Evans and Seppo Honkapohja.” Macroeconomic Dynamics 9, 561-583.
Stock, J.H. and M.W. Watson (2002). “Has the Business Cycle Changed, and Why?NBER Macroeconomics Annual 17, 159-218.

Volume 7, Issue 2, April 2006

Pierre-Olivier Gourinchas on Global Imbalances and Financial Factors

 Pierre-Olivier Gourinchas is Assistant Professor of Economics at the University of California, Berkeley. His main lines of research are on precautionary savings and international financial integration. Gourinchas’ RePEc/IDEAS entry.

Ever since David Hume’s (1752) price-specie flow mechanism, understanding the dynamic process of adjustment of a country’s external balance is one of the most pressing –and vexing– question for international macroeconomists. The modern approach to this issue characterizes the dynamics of external debt as the result of forward-looking savings decisions by households, and investment decisions by firms, in market structures of varying degrees of complexity. As Obstfeld (2001) remarks, “[this approach] provides a conceptual framework appropriate for thinking about the important and interrelated policy issues of external balance, external sustainability and equilibrium real exchange rates”. Yet in most empirical studies, the theory falls short of explaining the dynamics of the current account. External adjustment has been the focus of much discussion recently, given the unprecedented build-up of US external imbalances. The current account deficits of the United States have steadily grown since the mid 1990s, reaching 6.4% of GDP in 2005. This represents the largest deficit in world history in dollar terms. Will such an imbalance be corrected, how and at what horizon?The research agenda I will discuss here today focuses on the historical role of financial variables in this adjustment process. My first line of research –with Hélène Rey from Princeton– shifts the focus of the analysis from the current account to the net and gross international investment positions and the role of valuation effects. My second line of research –with Ricardo Caballero and Emmanual Farhi from MIT– discusses the role of financial development and emphasizes the global supply of financial assets.

In the following discussion, I consider each in turn.

1. The importance of expected valuation effects

The recent wave of financial globalization came with a sharp increase in gross cross-holdings of foreign assets and liabilities (see Lane and Milesi- Ferretti (2006)). Hence, it is quite natural to shift the emphasis to the determinants of a country’s net international investment position (NIIP). Consider the US. Its NIIP is nothing but a leveraged portfolio, short in dollar denominated US assets (US equity, corporate and government debt, inward direct investment etc.) and long in foreign currency denominated foreign assets (Japanese equity, direct investment in China, UK gilts etc.) whose value is affected by fluctuations in assets and currency prices. The upsurge in cross border holdings has therefore opened the door to potentially large wealth transfers across countries, which may alter net foreign asset dynamics. These valuation effects are absent, not only from the standard theory, but also from official statistics since the National Income and Product Accounts and the Balance of Payment report most items in the current account at historical cost. Hence official data give a very approximate and potentially misleading reflection of the change in a country’s true NIIP.Here is a way to think about the orders of magnitude involved: at the end of 2004, the Bureau of Economic analysis reports US gross external assets and liabilities equal respectively to 85% and 107% of US GDP, implying a NIIP of -22% of GDP. That year, the trade deficit on goods and services reached 5.3% of GDP. The standard approach suggests that the US will need to run significant trade surpluses, at some point in the future, to stabilize its external debt. Part of the adjustment, however, may also come from lower returns on US assets held by foreigners, relative to the return on foreign assets held by the US, i.e. a wealth transfer to the US. Since most US liabilities are denominated in US dollars, and approximately 70% of US foreign assets are denominated in foreign currencies, this wealth transfer can take the form of a depreciation of the US dollar. For instance, consider an unexpected 10% depreciation of the US currency. It implies, ceteris paribus, a transfer of 5.9% (0.7*0.85*0.1) of GDP from the rest of the world to the US that would more than cover the trade deficit. Could it be, then, that movements in currency and asset prices contribute systematically to the adjustment process and if so, by how much?

One may be tempted to dismiss even the possibility of such predictable valuation effects. After all, usual interest parity considerations would rule them out: asset and currency prices should be expected to move in such direction as to deliver similar returns, when measured in a common currency. I will return to this important theoretical issue shortly, but I want to concentrate first on what the data have to say.

The first task is to construct accurate measures of a country’s NIIP at market value. In Gourinchas and Rey (2006a), we assemble a quarterly dataset of the US gross foreign asset and liability positions at market value since 1952 disaggregated into four broad asset categories (direct investment, equity, debt and other –mostly bank loans and trade credit), and compute capital gains and total returns on these global portfolios components. This exercise delivers a number of important “stylized facts.” First, it is well known that the investment income balance –the balance of interest, dividends and earnings on direct investment paid to and by the US– has remained positive despite mounting net liabilities. What is less well-known is that the evidence on total return on US external assets and liabilities is consistent with the evidence on yields: since 1952, the US enjoyed an average annual excess return on its gross assets of 2.11%. Moreover, this excess return has increased to 3.32% since the collapse of the Bretton Woods system of fixed exchange rates. About one third of this excess return reflects the role of the US as a world financial intermediary, borrowing mostly in the form of low yield-low risk assets (loans and debt), and investing in high yield-high risks assets (equity and FDI). The remaining two thirds arise from return differentials within asset classes. This reflects mostly the ability of the US to borrow at very low interest rates, a fact sometimes interpreted as evidence of the “exorbitant priviledge” that the US enjoys from its unique position in the international monetary order, as the issuer of the world’s reserve currency.

Gourinchas and Rey (2005) turn to the question of the international adjustment process. We cast the analysis in very general terms, relying simply on a country’s intertemporal external constraint and a no-Ponzi condition, and characterize two adjustment channels. The traditional “trade channel” links current imbalances to future trade surpluses. The novel “valuation channel” shows that expected future excess returns on the NIIP can also potentially contribute to the process of adjustment. Formally, our empirical approach builds on Campbell and Shiller (1988), who look at the adjustment process of the dividend price ratio, or more recently Lettau and Ludvigson (2001), who look at movements in the consumption-wealth ratio. Like these papers, we construct a measure of cyclical external imbalances –akin to the deviation from trend of the ratio of the trade deficit (the flow) to the NIIP (the stock)– and relate it to future expected net exports growth and excess returns. In contrast with these papers, we allow for slow moving structural changes in the data, capturing increasing trade and financial integration. The empirical results indicates that up to 27% of cyclical external imbalances are eliminated via predictable adjustments in future returns, and 64% are eliminated via future improvements in the trade balance, accounting for 91% of the fluctuations in external imbalances. We then turn the argument on its head: if the valuation channel is operative, current cyclical imbalances, properly measured, should predict future excess returns, and possibly future currency movements. There again, we obtain very strong predictability results, from 1 to 16 quarters ahead, both in and out of sample. A global imbalance today strongly predicts future positive excess return on US external assets and a future depreciation of the U.S. dollar. This last result is especially striking: the classic paper of Meese and Rogoff (1983), established that no exchange rate model could significantly outperform the random walk at short to medium horizons. Our results decisively overturn their conclusion.

2. Valuation effects: some elements of theory

It is now time to return to the theory. As mentioned above, the empirical evidence in favor of strong predictable valuation effects is quite puzzling: why would the rest of the world agree to buy US assets (i.e. finance the US current account deficit) if these assets are expected to under-perform?A successful theory will need two critical ingredients: consumption and portfolio home biases. The former implies that a stabilization of the current account must be accompanied by relative price and real exchange rate movements. The latter requires that domestic and foreign assets are imperfect substitute and implies that wealth transfers are accompanied by predictable and partially offsetting exchange rate movements (see Obstfeld (2004)). The connection between consumption and portfolio home biases is an active topic of research (see Obstfeld and Rogoff (2000), Coeurdacier (2005) and Heathcote and Perri (2005)). Under some conditions, home portfolio bias can emerge as a consequence of the tilt in preferences toward the home good.

Gourinchas and Rey (2006b) build on this literature. We consider a two-country Lucas tree economy with complete markets and preferences for the home good (see Kollmann (2006) for a related model). Preliminary results indicate that, in models with perfect risk sharing, external adjustment operates via strong and unexpected valuation effects, but no predictable valuation effects. The intuition for that result is the following: in an endowment economy, efficient risk sharing requires that a country runs a trade deficit when domestic output is relatively low. To do this, the planner’s allocation generates an unexpected valuation gain that offsets current and expected future trade deficits. One way to implement this allocation is for foreigners to hold claims to the domestic tree and vice versa: under reasonable preference assumptions, the negative domestic shock lowers the value of domestic equity relative to foreign equity and generates an unexpected capital loss for foreigners, which turns the domestic country into a net creditor. In the meantime, the decline in the relative supply of the home good requires an instant real appreciation, followed by a subsequent depreciation. Crucially, this expected real depreciation is offset by expected adjustments in asset returns. Therefore it does not generate predictable excess returns nor contributes to the adjustment process.

Looking ahead, the next obvious step is to build general equilibrium models of international portfolio allocation with incomplete markets. I see this as a major task that will close a much needed gap in the literature between effectively complete markets models and the special cases that assume away predictable return or eliminate current account fluctuations (see, inter alia, Baxter and Crucini (1995), Corsetti and Pesenti (2001), Heathcote and Perri (2005), Pavlova and Rigobon (2003), Tille (2005)). One interesting step in that direction is Evans and Hnatkovska (2005).

Along the way, we are witnessing a renewal of interest in the old partial-equilibrium portfolio balance literature of Kouri (1982), and more recently Blanchard Giavazzi and Sa (2005), that generate predictable valuation effects. In these models interest rates are constant and the exchange rate performs the dual role of allocating global portfolios between imperfectly substitutable domestic and foreign assets, and affecting the trade balance through traditional expenditure switching effects. Whether the insights from that literature survive in a modern dynamic global portfolio model is a question of great interest.

3. The global supply of financial assets

Despite extensive debates on the factors behind the current “global imbalances,” few formal structures analyze the joint determination of capital flows and asset returns. In my view, any successful theory should address three stylized facts. The first is the well known increase in current account deficits in the US, offset by surpluses in Europe, Japan and since 1997, emerging and oil producing countries. The second fact, oft cited in recent months, is the stubborn decline in long run world real interest rates. The third fact is the sharp increase in the share of US assets in the financial portfolio of the rest of the world.Caballero, Farhi and Gourinchas (2006) develop a stylized model to account for these three observations. Its key feature is a focus on the ability of different regions to supply tradable financial assets, and how this impacts equilibrium world interest rates and global capital flows.

The model is quite standard, except for two features. First, it assumes that only a fraction of current and future domestic output can be capitalized into tradable financial claims. The present value of the remaining share of output constitutes a non-tradable financial asset. Second, the model is non-ricardian: as in Blanchard (1985) or Weil (1987), current households do not have full rights over the non-tradable asset: some of these rights might belong to future unborn generations. In a ricardian setting, the relative supply of tradable and non-tradable financial assets is irrelevant: an increase in the share of income capitalized into tradable assets increases the supply of those assets but decreases the supply of non-tradable financial assets by the same amount, and hence raises the demand for tradable financial assets one for one. This leaves equilibrium allocations and interest rates unchanged. By contrast, in a non-ricardian setting, an increase in the share of income capitalized into tradable assets increases the total supply of financial assets and affects equilibrium allocations.

The fraction of output that can be attached to tradable financial assets might differ across countries, reflecting different levels of financial development, of protection of property rights, of intermediation capital or of any financial friction.

The model considers what happens when regions that are good asset suppliers experience a sustained growth slowdown (continental Western Europe and Japan in the early 1990s), or when the quality, or acceptance of financial assets deteriorates (emerging Asia and Russia after the Asian crisis). In both cases, the global supply of financial assets declines. This depresses global interest rates, generates persistent capital flows into the US and an offsetting current account deficit. From the good’s market perspective, global declines in the supply of financial assets abroad increases the value of US financial assets, hence US wealth when portfolio are not perfectly diversified. This increases consumption and leads to a trade deficit.

We extend the basic structure along two dimensions. First we allow for domestic and foreign direct investment. Direct investment generates intermediation rents for the US (as documented in Gourinchas and Rey (2006a)) that further relax the US external constraint and finances permanent trade deficits. Second, we introduce heterogeneous goods to discuss real exchange rate determination. The exchange rate patterns generated by the expanded model are consistent with the data, while leaving the broader pattern of capital flows and global returns largely unchanged. In the short run, under the assumption of home consumption bias, the increase in US wealth translates into higher relative demand for US goods and a real exchange rate appreciation. In the long run, we find that the real exchange rate depreciates only moderately.

This line of research highlights the role of financial factors for current imbalances. It indicates that the current configuration of asymmetries is likely to continue until the conditions for the initial imbalances are reversed (higher growth among asset suppliers, Europe and Japan, or financial development among asset demanders, emerging Asia). Along that path, the US may build large net external liabilities. Of course, such leverage is risky. Our framework emphasizes that these risks do not arise unavoidably from the current situation.


Baxter, Marianne and Mario Crucini (1995): “Business Cycles and the Asset Structure of Foreign Trade,” International Economic Review, vol. 36(4), pages 821-54, November.
Blanchard, Olivier (1985): “Debt, Deficits, anf Finite Horizons,” Journal of Political Economy, vol. 93, pp. 223-47.
Blanchard, Olicier, Francesco Giavazzi and Filipa Sa (2005): “International Investors, the U.S. Current Account, and the Dollar,” Economic Activity, Spring.
Caballero, Ricardo, Emmanuel Farhi and Pierre-Olivier Gourinchas (2006): “An Equilibrium Model of “Global Imbalances” and Low Interest Rates,” NBER Working Paper 11996.
Campbell, John and Robert Shiller (1988): “The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors,” Review of Financial Studies, vol. 1, pp. 195-227.
Cœurdacier, Nicolas (2005): “Do trade costs in goods markets lead to home bias in equities?”, mimeo, Paris-Jourdan Sciences Économiques.
Corsetti, Giancarlo and Paolo Pesenti (2001): “Welfare and Macroeconomic Interdependence,” Quarterly Journal of Economics, vol. 116(2), pp. 421-445, May.
Evans, Martin and Viktoria Hnatkovska (2005): “International Capital Flows Returns and World Financial Integration,” NBER working paper 11701.
Gourinchas, Pierre-Olivier and Hélène Rey (2005): “International Financial Adjustment,” NBER working paper 11155.
Gourinchas, Pierre-Olivier and Hélène Rey (2006a): “From World Banker to World Venture Capitalist: US External Adjustment and the Exorbitant Privilege,” in: Richard Clarida (ed.), G7 Current Account Imbalances: Sustainability and Adjustment, The University of Chicago Press, forthcoming.
Gourinchas, Pierre-Olivier and Hélène Rey (2006b): “The Intertemporal Approach to the Financial Account,” mimeo UC Berkeley and Princeton.
Heathcote, Jonathan and Fabrizio Perri (2005): “The international diversification puzzle is not as bad as you think,” mimeo, NYU Stern and Georgetown University.
Hume, David (1752): “On the Balance of Trade,” in: Essays, Moral, Political and Literary, London, Henri Frowde (pub. 1904)
Kollmann, Robert (2005): “International Portfolio Equilibrium and the Current Account,” CEPR working paper 5512.
Kouri, Pentti (1982): “Balance of Payment and the Foreign Exchange Market: A Dynamic Partial Equilibrium Model,” in: J. Bhandari and B. Putnam (eds.), Economic Interdependence and Flexible Exchange Rates, MIT Press, Cambridge MA, pp. 116-156.
Lane, Phillip and Gian Maria Milesi-Ferretti (2206): “A Global Perspective on External Positions,” in: Richard Clarida (ed.), G7 Current Account Imbalances: Sustainability and Adjustment, The University of Chicago Press, forthcoming.
Lettau, Martin and Sydney Ludvigson (2001): “Consumption, Aggregate Wealth and Expected Stock Returns,” Journal of Finance, vol. 56(3), pp. 815-849.
Meese, Richard and Kenneth Rogoff (1983): “Empirical Exchange Rate Models of the Seventies: Do they Fit Out-of-sample?”, Journal of International Economics, vol. 14, pp. 3-24.
Obstfeld, Maurice (2001): “International Economics: Beyond the Mundell-Fleming Model,” IMF Staff Papers, vol 47 (special issue), pp. 1-39.
Obstfeld, Maurice (2004): “External Adjustment,” Review of World Economics, vol. 140(4), pp. 541-568.
Obstfeld, Maurice and Kenneth Rogoff (2000): “The Six Major Puzzles in International Macroeconomics: Is There a Common Cause?“, in: Ben Bernanke and Ken Rogoff, NBER Macroeconomics Annual, MIT Press, Cambridge MA, pp 73-103.
Pavlova, Anna and Roberto Rigobon (2003): “Asset Prices and Exchange Rates,” NBER working paper 9834.
Tille, Cédric (2005): “Financial Integration and the Wealth Effect of Exchange Rate Fluctuations,” Federal Reserve Bank of New York Staff Report 226.
Weil, Philippe (1987): “Overlapping Families of Infinitely-lived Agents,” Journal of Public Economics, vol. 38(2), pp. 183-198, March.

Volume 7, Issue 1, November 2005

Fabrizio Zilibotti on the Equilibrium Dynamics of Policies and Institutions

Fabrizio Zilibotti is Professor of Economics at Institute for International Economic Studies in Stockholm. He is particularly interested in macroeconomics, political economy and the evolution of institutions. Zilibotti’s RePEc/IDEAS entry.

Modern macroeconomics studies the effects of economic policies on economic performance over time. Policies are not exogenous, however. They reflect the aggregation of preferences of those agents who, in a society, are empowered with political rights. Such preferences vary across social groups and over time depending on a number of factors, both economic and non-economic ones. Among these factors, there are past policies: these shape the evolution of macroeconomic outcomes as well as of the asset and income distribution within a society, thereby affecting the future constituency of policies and institutions. The research agenda which I shall describe here focuses on the dynamic interdependence between political and economic equilibrium. I will focus on fiscal policy and labor market regulations.Incorporating politico-economic dynamics in general equilibrium macro models entails some analytical difficulties. The standard logic of competitive models, where agents optimize taking future equilibrium outcomes (e.g., prices) as given, breaks down when political choice is considered, since the current political choice has non-negligible effects on future equilibria, and it would be irrational for agents to ignore them. There are two avenues for tackling this problem. The first is to analyze the set of game-theoretic dynamic equilibria involving reputation and collective punishments. The main problem with this approach is that such set of equilibria is large. Moreover, enforcing punishments requires significant coordination among agents. The alternative approach focuses on Markov Perfect Equilibria (MPE). MPE emphasize lack of commitment entailed in democratic political processes by focusing on equilibria which are limits of finite-horizon equilibria. While restricting attention to MPE reduces the number of equilibria, their characterization is not straightforward. A first generation of papers has resorted to computational analysis (see, e.g., Krusell and Ríos-Rull, 1999). While useful, this approach entails two major limitations. First, the complexity of the analysis makes it difficult to transmit its insights to broad audiences including students and policy-makers, and, second, MPE often involve discontinuous policy functions which are hard to track even through numerical methods.

In a series of recent papers with various coauthors, I have tried to overcome these hurdles, and propose “tractable” dynamic macroeconomic models embedding politico-economic factors. The virtue of small-scale models is their transparent mechanics. This makes it easy to solve problems involving functional equations through guess-and-verify methods, even when equilibria exhibit discontinuous policy functions. The distinctive features of the theory are that (i) policies are decided through period-by-period voting without commitment and (ii) they affect asset accumulation decisions. In this environment, the current political choice affects the future income distribution, and this, in turn, affects the future political equilibrium. This dynamic feedback opens the scope for strategic voting: agents vote taking into consideration how their choice today affects politics tomorrow.

Fiscal Policy and Redistribution

In Hassler, Rodriguez-Mora, Storesletten and Zilibotti (2003), we model an economy where agents are born identical and make a human capital investment. Investments have a stochastic return that makes some agents rich while others remain poor. Since agents are risk-neutral and redistribution has distortionary effects, the welfare state is socially “wasteful”: if agents could commit ex-ante (i.e., before knowing the realization of the return to their investment) to a redistributive policy, they would choose no redistribution. However, such commitments are not feasible in democracies, and ex-post preferences determine the political outcome: the poor demand redistribution and a welfare-state system might be an equilibrium.The theory offers two main insights. First, if a temporary shock triggers sufficient support to initiate redistributive policies, these remain sustained over time, even after the effects of the shock have vanished. This result is due to high current redistribution reducing investments, implying that a larger share of future voters will benefit from redistributive policies. Thus, the welfare state survives beyond the scope for which it had been originally started. This prediction conforms with the evidence that the welfare-state system proved persistent after its first introduction. At the time of the Great Depression, many governments stepped-in with large programs aimed at reactivating the economy and supporting the impoverished generation. However, welfare-state programs would not be abandoned after economic recovery and would, on the contrary, grow in size and scope after World War II.

Second, there exist equilibria where an existing welfare state is irreversibly terminated, even when benefit recipients are initially politically decisive. The breakdown of the welfare state is more likely when pre-tax wage inequality is large, since this strengthens the incentives for private investment and reduces, ceteris paribus, the constituency of the welfare state. Strategic voting motives are key to the existence of this type of equilibria: if agents took future policy as parametric, there could be no welfare state breakdown. This result can cast some light on the dynamics of the Thatcherite revolution in the 1980’s. First, it came about during a period of growing wage inequality, and second its effects proved to be long-lasting. Even after the Tories went out of office in 1997, the constituency for traditional welfare-state policies seems to have faded in the UK. Labour governments by and large continued the economic and social policies inaugurated by Mrs. Thatcher, with limited public pressure for their reversal.

While Hassler, Rodriguez-Mora, Storesletten and Zilibotti (2003) focus on inefficient redistribution, public redistribution may be ex-ante desirable to societies. Hassler, Krusell, Storesletten and Zilibotti (2005a) analyze one such scenario where agents are risk-averse and markets incomplete. The political mechanism is also different: instead of a standard Downsian model, we consider a probabilistic voting mechanism à la Lindbeck and Weibull (1987), where the winning politician maximizes a weighted average of the utility of all groups in society. In this environment, the equilibrium features positive redistribution in the long run. The reason is that by having a higher marginal utility of income, the poor exert a stronger influence on the determination of policies (in the jargoon, there are more “swing voters” among the poor). The transition towards the steady-state may exhibit monotonic dynamics or dampening fluctuations in tax rates, depending on the extent of risk aversion. An interesting result is that oscillating tax rates are not due to political distortions. On the contrary, a benevolent policy-maker with commitment power would choose sharper fluctuations, possibly non-dampening ones, than in the political equilibrium. Political distortions generate an inefficiently persistent fiscal policy. This finding lies in sharp contrast with the predictions of the literature on political business cycles arguing that political economy exacerbates fluctuations (see Alesina, Roubini and Cohen, 1997).

In Hassler, Krusell, Storesletten and Zilibotti (2005b), we extend the analysis of the dynamics of fiscal policy to a Chamley-Judd model of capital taxation, where we show that the absence of commitment can lead to sizeable inefficiencies in both the steady-state levels and the transitional dynamics of taxation. For instance, we show in a “calibrated” example that the steady-state Ramsey tax (with commitment) is 22%, while it is 50% rate in the political equilibrium. Moreover, in the Ramsey economy, taxes are negatively serially autocorrelated, while they are highly persistent in the political equilibrium (with an autoregressive coefficient of 0.4 on a four-year basis).

A large share of government spending is used to finance public goods. In Hassler, Storesletten and Zilibotti (2006), we investigate the political economy of public good provision in a model where governments finance their expenditure via income taxation and taxes are allowed to be age-dependent. Since the tax burden falls more heavily on agents with high labor earnings, the poor want more public good than the rich. The equilibrium is shown to be indeterminate, independent of the initial income and skill distribution among agents. There exists one “sincere” equilibrium with high taxes, where the poor are politically decisive, and a range of “strategic” equilibria with lower taxes, where the rich are politically decisive. In the latter, voters restrain taxation to induce a future majority that will keep taxes low, thereby strengthening the incentive of investors and enlarging the current tax base for the public good. This multiplicity can explain the existence of large cross-country differences in the size and composition of government expenditures. For example, in Scandinavian countries, the average size of government measured by tax revenue is more than half the size of GDP, while it is below one quarter of GDP in the United States and Switzerland. The theory shows that such differences are not necessarily due to variation in exogenous factors or preferences. Another interesting finding is that taxation and public good provision may be inefficiently too low — in contrast with the standard emphasis in the politico-economic literature on factors leading to excess taxation –.

An important aspect of the macro-policy debate is government debt. When debt policy is determined through repeated elections, and agents are less than fully altruistic towards future generations, there is a politico-economic force pushing towards progressive debt accumulation which arises from the lack of political representation of the future generations on which the burden of public debt largely falls. If debt cannot exceed a ceiling (e.g., equal to the maximum PDV of future taxation) governments would find it increasingly hard to finance public good programs. Thus, private affluence can be accompanied by growing “public poverty”: even though productivity and income grow at a sustained rate, public funding of education, health and other public services becomes subject to growing pressure. Indeed, over the last decade, many countries have been under strain to contain their public spending and to face a growing public debt (including both explicit and implicit debt through pension liabilities).

In Song, Storesletten and Zilibotti (2005), we analyze these issues with the aid of a politico-economic model of overlapping generations where the government finances public good provision through labor taxation and by issuing debt. First, we show a negative result: when taxation is not distortionary, public debt grows and converges asymptotically to its maximum level. Thus, both private and public consumption tend to zero in the long run. Then, we introduce distortionary effects of taxation on labor supply (a Laffer curve). Not surprisingly, an endogenous limit on taxation prevents private consumption from falling to zero. A less obvious result is that it can also prevent “public poverty”, namely, it reduces the incentive to accumulate debt. Intuitively, political support for growing public debt is sustained by the belief that future governments will continue public good provision by increasing taxes. However, when agents realize that this is not feasible (or increasingly expensive to achieve), they are induced to support more responsible debt policies today. In other words, endogenous limits to taxation discipline fiscal policy.

This result has implications on the effects of international tax competition. Such competition serves as a commitment device to avoid increasing future taxes above the international level. Consequently, tax competition may actually lead to lower debt and avoid the public poverty trap.

Labor Markets and Child Labor Laws

Dynamic general equilibrium models can also be used to study the introduction or evolution of specific policies and institutions. Some of my recent work analyzes a variety of labor and product market institutions. For instance, Hassler, Rodriguez-Mora, Storesletten and Zilibotti (2005) and Marimon and Zilibotti (1999) analyze the political economy of unemployment insurance to explain the contrasting labor market performance in the US and Western Europe during the last quarter of the XXth Century. Acemoglu, Aghion and Zilibotti (2005) analyze the political economy of industrial policy over the process of development. Doepke and Zilibotti (2005) study the political economy of child labor regulations. I shall now describe in some detail the research discussed in this paper.While child labor is today regarded as a cruel practice that deprives children of rights and opportunities, from a historical perspective, this view of child labor is of a relatively recent origin. In Western countries, until the nineteenth century most children worked, and there was no stigma attached to earning income from children’s work. A change in attitudes towards child labor occurred around the mid-XIXth Century, under the pressure of the union movement. How can this change be explained? According to our theory, the increasing political support for child labor regulation can be explained by economic motives. In particular, we identify two factors behind the increasing support to child labor restrictions. The first is the drive to limit competition: unskilled workers compete with children in the labor market, and therefore stand to gain from higher wages if child labor is restricted. Different from other types of competition, the potential competition comes (at least partly) from inside the unskilled workers’ families. For this reason, workers’ attitudes regarding child labor laws depend not only on the degree to which they compete with children in the labor market, but also on the extent to which their family income relies on child labor. The second motive is parent’s altruism: when the returns to education are sufficiently high, most parents prefer to have small families and educate their children. Then, the support to child labor restriction grows.

To formalize these ideas, we construct a model where altruistic agents age and die stochastically, and decide on fertility, education and family size. A ban on child labor is introduced when supported by a majority of the adult population. First, we derive some analytical results, showing that multiple politico-economic steady states can exist. In one steady state, child labor is legal, unskilled workers have many working children, and there is little support for banning child labor. In the other steady state, child labor is forbidden, families are small, and the ban is supported by a majority of voters. In each case, the existing political regime induces fertility decisions that lock parents into supporting the status quo. The existence of multiple steady states can explain why some developing countries get trapped in equilibria with a high incidence of child labor and weak political support for banning child labor, while other countries at similar stages of development have strict regulations and a low incidence of child labor.

Then, we use a calibrated version of the model to replicate the historical changes which occurred in Britain in the XIXth Century. A prediction of the theory which is in line with the empirical evidence is that the change in workers’ attitudes towards child labor occurs gradually. In the early stages of the transition, the working class does not unanimously back restrictions, since families with many children continue to depend on child labor. However, increasing return to schooling eventually induces newly-formed families to have fewer children and send them to school. Eventually, a majority of the unskilled workers support the banning of child labor. This explanation for the introduction of child labor restrictions is consistent with the observation that child labor regulation were first introduced in Britain (as well as in other Western countries) in the nineteenth century after a period of increasing wage inequality. Moreover, the introduction of child labor restrictions was accompanied by a period of substantial fertility decline and an expansion of education, which is once more consistent with the theory.

This study contributes to the debate on the introduction of child labor laws in developing countries. Even in countries where the majority currently opposes the introduction of child labor regulations, the constituency in favor of these laws may increase over time once the restrictions are in place. Naturally, this requires that other conditions be met. In particular, the cost of schooling must be sufficiently low, so that poor parents actually decide to send their children to school, once the restrictions are in place.


Acemoglu, Daron, Philippe Aghion and Fabrizio Zilibotti (2006): Distance to Frontier, Selection, and Economic Growth, Journal of the European Economic Association, Volume 4, Issue 1, March.
Alesina, Alberto, Nouriel Roubini, and Gerald Cohen (1997): Political Cycles and the Macroeconomy. Cambridge: MIT Press.
Doepke, Matthias and Fabrizio Zilibotti (2005): The Macroeconomics of Child Labor Regulation, American Economic Review, Vol. 95, No. 5, December.
Hassler, John, Kjetil Storesletten and Fabrizio Zilibotti (2006): Democratic Public Good Provision, Journal of Economic Theory, forthoming.
Hassler, John, Per Krusell, Kjetil Storesletten and Fabrizio Zilibotti (2005a): The Dynamics of Government, Journal of Monetary Economics, Vol. 52, No. 7, October.
Hassler, John, Per Krusell, Kjetil Storesletten and Fabrizio Zilibotti (2005b): On the Optimal Timing of Capital Taxes, Mimeo, IIES, Oslo and Princeton.
Krusell, Per and José-Víctor Ríos-Rull (1999): On the Size of U.S. Government: Political Economy in the Neoclassical Growth Model, American Economic Review, Vol. 89, No. 5, December.
Hassler, John, José Vicente Rodriguez-Mora, Kjetil Storesletten and Fabrizio Zilibotti (2005): A Positive Theory of Geographic Mobility and Social Insurance, International Economic Review, Vo. 46, No. 1, March.
Hassler, John, José Vicente Rodriguez-Mora, Kjetil Storesletten and Fabrizio Zilibotti (2003): The Survival of the Welfare State, American Economic Review, Vol. 93, No. 1, March.
Lindbeck, Assar and Jürgen W. Weibull (1987): Balanced-budget redistribution as political equilibrium, Public Choice Vol. 52, No. 3.
Marimon, Ramon and Fabrizio Zilibotti (1999): Unemployment vs. Mismatch of Talents: Reconsidering Unemployment Benefits, Economic Journal, Vol. 109, No. 455, April.
Song, Zheng, Kjetil Storesletten and Fabrizio Zilibotti (2005): Private Affluence and Public Poverty, Mimeo in progress, IIES, Fudan and Oslo.

Volume 6, Issue 2, April 2005

Dirk Krueger and Fabrizio Perri on Risk Sharing across Households, Generations and Countries

Dirk Krueger is Professor of Economics, especially Macroeconomics at Goethe University Frankfurt (Germany). Fabrizio Perri is Associate Professor of Economics at the Stern School of Business, New York University and currently visiting the Research Department at the Federal Reserve Bank of Minneapolis. They have both worked, often in collaboration, on issues of consumption risk sharing, incomplete markets and distributions of income and consumption. Krueger’s RePEc/IDEAS entry. Perri’s RePEc/IDEAS entry.

Risk is pervasive in macroeconomics and the question that our research has focused on most is whether, how and to what extent this risk is shared across households or groups of households. Since the risk that a typical household in the macro economy faces is large the welfare impact of sharing it can be substantial. We now briefly describe our research in this area, carried out jointly and with separate coauthors.

Risk sharing across households

It is a well known fact that the distribution of earnings across households is very dispersed. For us, it is crucial to understand whether these earnings differences across households are completely determined at the beginning of the working life of household members (say by their education, skill or endowments) or whether they are the results of idiosyncratic earnings shocks realized during the working life of the members of the household. Recent research (see for example Storesletten, Telmer and Yaron, 2004) seems to indicate that these types of shocks (which we will call earnings risk) are persistent, large and they can be responsible for as much as 50% of the cross sectional variation in earnings. To get a sense of their magnitude, note that household earnings shocks have the same order of persistence as business cycles shocks, but that their percentage volatility has been estimated to be roughly 20 times as large as the percentage volatility of business cycles shocks! Given the sheer size of household earnings risk it is relevant to understand how and to what extent this risk can be shared across households, or to what extent households are at least self-insured.


One useful benchmark model to assess the extent of risk sharing is the Arrow-Debreu complete markets model. In that model households have access to a full set of state contingent securities for every possible realization of their income so they can fully insure against earnings risk. Several authors have argued (see for example Attanasio and Davis, 1996) that this model overstates the actual risk sharing possibilities available to households, by showing that the complete markets model cannot explain the joint distribution of household earnings and consumption observed in US cross sectional data. Therefore our research on this issue has focused on two popular classes of models that imply only partial risk-sharing or self-insurance of earnings risk.In the first model (which we refer to as the standard incomplete markets model, SIM) households cannot explicitly share risk with one another, but rather can only self-insure by trading a single, uncontingent bond, potentially subject to borrowing constraints. The second model (which we refer to as the debt constraint model, DCM) follows the work of Kehoe and Levine (1993) and has been further developed by Kocherlakota (1996) and Alvarez and Jermann (2000). In this framework a full set of state contingent contracts is available to all agents, but that intertemporal contracts can only be enforced by exclusion from future intertemporal trade. Since exclusion from credit markets is not infinitely costly, in some states of the world agents might find optimal not to repay their debts and suffer the consequences of exclusion from financial markets. This possibility endogenously restricts the extent to which each contingent asset can be traded and thus limits risk sharing. This is an appealing feature as the extent of risk sharing is not exogenously assumed but depends on the fundamentals of the model (i.e. preferences and technology); for some fundamentals the DCM model generates complete risk sharing, while for different fundamentals the model generate only partial or no risk sharing at all.

Our main theoretical contribution has been the analysis of the DCM model with a continuum of agents. In Krueger and Perri (1999) we show how to characterize and compute stationary equilibria of such a model, using the dual approach developed by Atkeson and Lucas (1992) for private information economies. The consumption dynamics mirrors the two main assumptions of this model: a complete set of contingent consumption claims and constraints on allocations that require agents to weakly prefer continuation in the market to reverting to autarky. Since it is agents with currently high income whose constraint is binding, agents with high income growth exhibit strong consumption growth, whereas agents with low income are unconstrained and have their consumption decline at a common rate as implied by a perfect consumption insurance Euler equation (we show in the paper that the equilibrium interest rate lies strictly below the time discount factor, making consumption drift down over time when unconstrained).

The crucial friction in this model is the inability of households to commit to repay their state-contingent debt, leading to endogenously determined borrowing constraints whose size depends on how the consequences of default are determined. In the standard limited commitment model this is specified as having to consume the autarkic allocation from the point of default on. While this is motivated by empirical bankruptcy procedures (and can be relaxed by admitting only temporary exclusion or saving after default, as in Krueger and Perri, 1999), it remains true that the consequence of default is specified essentially exogenous to the model. In Krueger and Uhlig (2005) we endogenize the outside option via competition. The outside option of the agent after default is determined by the best consumption insurance contract a household can obtain from a competing financial intermediary, subject to the constraint that the intermediary has to at least break even with the contract. What we also show in that paper is that, even though the extent of consumption insurance depends on the outside option, the consumption dynamics is essentially the same as in the DCM model.

Bringing the theory to the data

The workhorse for our empirical analysis is the Consumer Expenditure (CE) Survey which reports data on earnings, hours and detailed consumption expenditures for a fairly large (5000-8000) repeated cross section of US households from 1980 to 2004. One important object we can compute from the data set is within-group income inequality, that is, inequality after controlling for fixed characteristics of the households such as sex, race and education: a statistic of this residual inequality (the variance of logs, say) is the best, if still imperfect, measure of earnings risk we can obtain from the cross sections of the CE.One striking fact that emerges from the CE is that, over the last 25 years, within-group earnings inequality has increased substantially while within-group consumption inequality increased only very modestly. This fact suggests that US households were able to insulate fairly well their consumption profiles from idiosyncratic earnings risk. In Krueger and Perri (2002) we ask whether the two models discussed above are able to explain this fact, in a quantitatively satisfactory way. We first estimate a time-varying process for earnings risk. Following a large previous literature we model earning risk as the sum of two components: a very persistent autoregressive process and a purely transitory shock. We estimate this process on CE data (we are able to identify the two components due to a short panel dimension of the CE) and find that about half of the increase in earnings risk is driven by the persistent component and half by the transitory component. We then feed this process into both models and find that both predict an increase in consumption inequality substantially smaller than the increase in earnings inequality. Comparing models to consumption data we find that the DCM only slightly understates the increase in within-group consumption inequality while the SIM overstates it.

The DCM predicts very little increase in consumption inequality for two reasons: first households have a full set of state-contingent securities available so they can insure well against shocks even if they are persistent. Second the increased earnings risk makes defaulting and living in financial autarky more costly and thus borrowing constraints (which are the only limits to risk sharing) expand as a response. In other words, the increase in earnings risk makes risk sharing more valuable and the DCM predicts that credit/insurance markets will develop in order to provide more of it.

The reason why also the SIM predicts a more modest increase in consumption inequality, compared to the increase in income inequality, is that even with an uncontingent bond agents can effectively self-insure against the temporary earnings shocks so that the increase in earnings risk due to the increase of the variance of temporary shocks does not translate into consumption. This point was also made by Heathcote, Storesletten and Violante (2004).

Another important difference between the two models is the implication for consumer credit. The development of financial markets generated by the DCM implies a sizable increase in consumer credit that matches up well with what we observe in US data. In the SIM model, on the other hand, the increase in risk implies that households want to accumulate more assets for self insurance and make less use of credit lines. Thus along this dimension that model is less consistent with data as it generates a (small) decline in consumer credit.

In Krueger and Perri (2005) we evaluate the two models along a different dimension. We ask directly how household consumption responds to earnings shocks, a feature empirically examined by Dynarski and Gruber (1997) with CE data. Our results mirror the ones derived in Krueger and Perri (2002): relative to the data the DCM understates the consumption response to income shocks while the SIM overpredicts it.

From our work we would draw as final assessment of the two models that the DCM model has the appealing feature that risk sharing is endogenous and responds to changes in fundamentals. It may, however, overstate the true insurance possibilities of households, due to the presence of a full set of state contingent securities. On the other hand, the SIM model probably understates the ability households have to insulate their consumption from income shocks and does not capture the fact that credit and insurance markets may evolve in response to change in fundamentals, such as the stochastic income process households face. We conjecture that a model that combines aspect of both models has the most chances of perfectly capturing the empirical facts we have focused on (note that Blundell, Preston and Pistaferri, 2004 come to similar conclusion by following a different methodology).

Welfare and policy implications

After having explored the positive consequences of an increase in earnings risk for consumption we were ultimately interested in the welfare implications of this increase. And if the welfare costs of this increase are large, is there something economic policy can do to reduce them? The two models discussed above provide very different answers to these questions.In the DCM, in principle the endogenous increase in risk sharing can mitigate the adverse welfare consequences of increased earnings risk. Actually in Krueger and Perri (1999, 2002) we show that there can be situations in which the increase in risk sharing opportunities triggered by the increase in earnings risk is so large that overall consumption risk falls, and welfare rises. In those situations economic policies intended to reduce income volatility (such as unemployment insurance) may have the perverse effect of increasing consumption inequality, because those policies may crowd out the private provision of consumption insurance more than one-to-one. This crowding-out mechanism is similar to the effect at work in Attanasio and Rios-Rull (2001).

On the other hand in the context of the SIM an increase in earnings risk is always welfare reducing as self-insurance can only partially offset it. As a consequence policies that reduce earnings risk are welfare improving. For example, in Conesa and Krueger (2005) we find that in the SIM the optimal income tax code is likely to be progressive because it provides a partial substitute for missing private insurance markets.

Because theory does not give an unambiguous answer to the welfare question, in Krueger and Perri (2004) we use a more empirically guided approach. More concretely, we ask how much would a household in 1973 have been willing to pay to avoid the increase in earnings dispersion that has taken place from 1973 to 2002. In order to do so we first estimate stochastic processes for household consumption and hours worked that are consistent with the evolution of the empirical cross-sectional distributions and with one year consumption mobility matrices from the CE. For consumption we also estimate separate stochastic processes for the between- and within-group component of dispersion, thus capturing both the change in consumption risk and the change in permanent consumption dispersion. Consistently with our previous work we find that the increase in consumption risk has been very modest and thus it has had a very mild welfare impact. On the other hand the increase in between-group dispersion, although not extremely large either, has a much more persistent nature and thus more important welfare consequences. To quantify these we employ a standard lifetime utility framework, together with our estimates of the stochastic processes for the relevant variables. We find that the welfare losses for a substantial fraction of the US population amount to 2 to 3 percent of lifetime consumption and that for some groups (in particular households with low education) the cost can be as large as 6% of lifetime consumption. Heathcote, Storesletten and Violante (2004, 2005) use incomplete markets models to assess the welfare consequences of the recent increase in wage inequality and find numbers comparable to ours. Their approach also captures the interesting effect that, in a model with endogenous labor supply, an increase in wage dispersion raises earnings risk but also raises average earnings, so that the negative welfare impact of higher risk is further mitigated.

Risk sharing across generations

If wages and returns to capital are imperfectly correlated, then there is scope to share aggregate wage and capital income risk across generations. Young households derive most of their income from labor, whereas old households finance old-age consumption mostly via income generated from their assets. If financial markets are incomplete in that households cannot trade a full set of contingent claims on aggregate uncertainty, then a policy such as social security that provides old, asset rich households a claim to labor income, may endow households with welcome risk diversification. In Krueger and Kubler (2002, 2004) we show that even if an economy is dynamically efficient in the sense of Samuelson’s seminal work on the Overlapping Generations model, the introduction of social security may constitute a Pareto-improving reform because it helps to achieve a better allocation of wage/return risk across households. But we also show that for this argument to work quantitatively, shocks to private asset returns have to be as big as return risk to the US stock market, fairly uncorrelated with wage risk and households have to be very risk averse and fairly willing to intertemporally substitute consumption. High risk aversion (a coefficient of relative risk aversion of at least 15) is needed for households to value better risk allocation, while high intertemporal elasticity of substitution is required to keep in check the capital-crowding out effect of social security in general equilibrium. We conclude that, for a realistically calibrated OLG economy the intergenerational risk-sharing effects alone are unlikely to provide a normative argument for the introduction of social security. However, Conesa and Krueger (1999) argue that the positive intragenerational insurance and redistribution effects from the current US social security system may be sufficient to make a transition from the current system to no social security undesirable for a majority of households currently alive.

Risk Sharing across countries

One type of risk that has received a lot of attention in the macroeconomic literature is country specific aggregate risk. Booms and recessions are not perfectly synchronized across nations. Thus international risk sharing could greatly reduce the costs of business cycles.However, some early research (Backus, Kehoe and Kydland, 1992) has shown that, in the context of a standard one-good complete markets international business cycles model (IRBC), complete cross-country risk sharing is not consistent with basic business cycles facts, suggesting that international risk sharing might be limited. In Kehoe and Perri (2002) we analyze whether limited enforcement of international contracts could be responsible for limited risk sharing. We characterize and solve the IRBC model with limited enforcement and find that this imperfection can greatly reduce the amount of international risk sharing in the model. We also find that, although the IRBC model with limited enforcement can account for business cycle facts much better than the complete markets model, discrepancies remain between theory and data.

In some recent work (Heathcote and Perri, 2005) we are exploring this issue in the context of a richer model, namely the IRBC model with two goods and with taste shocks. In that context we find that a high degree of international risk-sharing is consistent with several observations for developed economies, especially in the last 10-15 years. In particular for this period, it is consistent with most international business cycle facts (including the relatively low cross-country correlation of consumption), with the proportion of foreign asset in country portfolios (the international diversification puzzle) and with the low observed correlation of the real exchange rate with relative consumption. This suggests that one of the roles of financial globalization (which has happened in the last 15-20 years) has been to improve international risk sharing among developed countries.

What Next

In our empirical work on inequality a crucial component for the evolution of consumption inequality are service flows from consumer durables. Our empirical results also suggest that these services make up a growing share of consumption of households. This motivates us to explore an extension of the limited commitment model that explicitly incorporates consumer durables and collateralized debt, in the same spirit as Fernandez-Villaverde and Krueger (2002). The asset pricing implications of such a model have already successfully been explored by Lustig and van Nieuwerburgh (2004). We intend to use this model to assess to what extent relaxed collateral constraints and improved risk sharing can affect the dynamics of aggregate expenditures on durables over the business cycle, and more concretely, whether these factors have had role in the decline of US Business cycles volatility that many researchers have documented


Alvarez, Fernando, and Urban Jermann (2000), Efficiency, Equilibrium, and Asset Pricing with Risk of Default, Econometrica, 68, 775-798.
Atkeson, Anthony, and Robert E. Lucas, Jr. (1992), On Efficient Distribution with Private Information, Review of Economic Studies, 59, 427-453.
Attanasio, Orazio, and Stephen Davis (1996), Relative Wage Movements and the Distribution of Consumption, Journal of Political Economy, 104, 1227-1262.
Attanasio, Orazio, and José-Víctor Ríos-Rull (2000), Consumption Smoothing in Island Economies: Can Public Insurance Reduce Welfare?, European Economic Review, 44, 1225-1258.
Backus, David, Patrick Kehoe and Finn Kydland (1992), International Real Business Cycles, Journal of Political Economy, 101, 745-775.
Blundell, Richard, Luigi Pistaferri and Ian Preston (2005), Consumption Inequality and Partial Insurance, mimeo, Stanford University
Conesa, Juan Carlos, and Dirk Krueger (1999), Social Security Reform with Heterogeneous Agents, Review of Economic Dynamics, 2, 757-795.
Conesa, Juan Carlos, and Dirk Krueger (2005), On the Optimal Progressivity of the Income Tax Code, NBER Working Paper 11044.
Dynarski, Susan, and Jonathan Gruber (1997), Can Families Smooth Variable Earnings?, Brookings Papers on Economic Activity, 229-284
Fernández-Villaverde, Jesús, and Dirk Krueger (2002), Consumption and Saving over the Life Cycle: How Important are Consumer Durables?, Proceedings of the 2002 North American Summer Meetings of the Econometric Society: Macroeconomic Theory.
Heathcote, Jonathan, and Fabrizio Perri (2004), The International Diversification Puzzle is not as Bad as You Think, mimeo, New York University
Heathcote, Jonathan, Kjetil Storesletten and Giovanni Violante (2003), The Macroeconomic Implications of Rising Wage Inequality in the US, mimeo, Georgetown University.
Heathcote, Jonathan, Kjetil Storesletten and Giovanni Violante (2005), Insurance and Opportunities: The Welfare Implications of Rising Wage Dispersion, mimeo, Georgetown University.
Kehoe, Timothy, and David Levine (1993), Debt Constrained Asset Markets, Review of Economic Studies, 60, 865-888.
Kehoe, Patrick, and Fabrizio Perri (2002), International Business Cycles with Endogenous Incomplete Markets, Econometrica, 70, 907-928.
Kocherlakota, Narayana (1996), Implications of Efficient Risk Sharing without Commitment, Review of Economic Studies, 63, 595-609.
Krueger, Dirk, and Felix Kubler (2002), Intergenerational Risk Sharing via Social Security when Financial Markets are Incomplete, American Economic Review, 92, 407-410.
Krueger, Dirk, and Felix Kubler (2002), Pareto Improving Social Security Reform when Financial Markets are Incomplete!?, NBER Working Paper 9410.
Krueger, Dirk, and Fabrizio Perri (1999), Risk Sharing: Private Insurance Markets or Redistributive Taxes, Federal Reserve Bank of Minneapolis Staff Report 262.
Krueger, Dirk, and Fabrizio Perri (2002), Does Income Inequality Lead to Consumption Inequality? Evidence and Theory, NBER Working Paper 9292
Krueger, Dirk, and Fabrizio Perri (2004), On the Welfare Consequences of the Increase in Inequality in the United States, in Mark Gertler and Kenneth Rogoff (eds.) NBER Macroeconomics Annual 2003, 83-121, The MIT Press, Cambridge, MA.
Krueger, Dirk, and Fabrizio Perri (2005), Understanding Consumption Smoothing: Evidence from the U.S. Consumer Expenditure Survey Data, forthcoming, Journal of the European Economic Association.
Krueger, Dirk, and Harald Uhlig (2005), Competitive Risk Sharing Contracts with One-Sided Commitment, mimeo, Goethe University Frankfurt.
Lustig, H, and S van Nieuwerburgh (2004), A Theory of Housing Collateral, Consumption Insurance and Risk Premia, mimeo, UCLA.
Storesletten, Kjetil, Chris Telmer and Amir Yaron (2004), Consumption and Risk Sharing over the Life Cycle, Journal of Monetary Economics, 51, 609-633.
Volume 6, Issue 1, November 2004

Stephanie Schmitt-Grohé and Martín Uribe on Policy Evaluation in Macroeconomics

Stephanie Schmitt-Grohé and Martín Uribe are Professors of Economics at Duke University. Their main line of interest lies in monetary macroeconomics, in particular issues of optimal stabilisation policy. Schmitt-Grohé’s RePEc/IDEAS entry. Uribe’s RePEc/IDEAS entry.

Much of our recent research has been devoted to developing and applying tools for the evaluation of macroeconomic stabilization policy. This choice of topic was motivated by an important development in business-cycle theory. By the late 1990s, a frictionless model of the macroeconomy was viewed by many as no longer providing a satisfactory account of aggregate fluctuations. As a response, the new Keynesian paradigm emerged as an alternative framework for understanding business cycles. A key difference between the neoclassical and the new Keynesian paradigms is that in the latter, the presence of various nominal and real distortions provide a meaningful role for stabilization policy, opening the door once again, after decades of dormancy, for policy evaluation.

Developing Tools For Policy Evaluation

An obstacle we encountered early on in executing the research agenda described here was the lack of appropriate tools to evaluate stabilization policies in the context of distorted economies. An important part of our effort was therefore devoted to developing such tools.Most models used in modern macroeconomics are too complex to allow for exact solutions. For this reason, researchers have appealed to numerical approximation techniques. One popular and widely used approximation technique is a first-order perturbation method delivering a linear approximation to the policy function. One reason for the popularity of first-order perturbation techniques is that they do not suffer from the `curse of dimensionality.’ That is, problems with a large number of state variables can be handled without much computational demands. Because models that are successful in accounting for many aspects of observed business cycles are bound to be large (e.g., Smets and Wouters, 2004; and Christiano, Eichenbaum, and Evans, 2003), this advantage of perturbation techniques is of particular importance for policy evaluation. However, an important limitation of first-order approximation techniques is that the solution displays the certainty equivalence property. In particular, the first-order approximation to the unconditional means of endogenous variables coincides with their non-stochastic steady state values. This limitation restricts the range of questions that can be addressed in a meaningful way using first-order perturbation techniques. One such question that is of particular relevance for our research agenda is welfare evaluation in stochastic environments featuring distortions or market failures. For example, Kim and Kim (2003) show that in a simple two-agent economy, a welfare comparison based on an evaluation of the utility function using a linear approximation to the policy function may yield the spurious result that welfare is higher under autarky than under full risk sharing. The problem here is that some second- and higher-order terms of the equilibrium welfare function are omitted while others are included. Consequently, the resulting criterion is inaccurate to order two or higher. The same problem arises under the common practice in macroeconomics of evaluating a second-order approximation to the objective function using a first-order approximation to the decision rules. For in this case, too, some second-order terms of the equilibrium welfare function are ignored while others are not. See Woodford (2003, chapter 6) for a discussion of conditions under which it is correct up to second order to approximate the level of welfare using first-order approximations to the policy function. In general, a correct second-order approximation of the equilibrium welfare function requires a second-order approximation to the policy function.

This is what we set out to accomplish in Schmitt-Grohé and Uribe (2004a). Building on previous work by Collard and Juillard, Sims, and Judd among others, we derive a second-order approximation to the solution of a general class of discrete-time rational expectations models. Specifically, our technique is applicable to nonlinear models whose equilibrium conditions can be written as: Et f(yt+1,yt,xt+1,xt)=0, where the vector xt is predetermined and the vector yt is nonpredetermined.

The main theoretical contribution of Schmitt-Grohé and Uribe (2004a) is to show that for any model belonging to this general class, the coefficients on the terms linear and quadratic in the state vector in a second-order expansion of the decision rule are independent of the volatility of the exogenous shocks. In other words, these coefficients must be the same in the stochastic and the deterministic versions of the model. Thus, up to second order, the presence of uncertainty affects only the constant term of the decision rules. But the fact that only the constant term is affected by the presence of uncertainty is by no means inconsequential. For it implies that up to second order the unconditional mean of endogenous variables can in general be significantly different from their non-stochastic steady state values. Thus, second-order approximation methods can in principle capture important effects of uncertainty on average rate of return differentials across assets with different risk characteristics and on the average level of consumer welfare. An additional advantage of higher-order perturbation methods is that like their first-order counterparts, they do not suffer from the curse of dimensionality. This is because given the first-order approximation to the policy function, finding the coefficients of a second-order approximation simply entails solving a system of linear equations.

The main practical contribution of Schmitt-Grohé and Uribe (2004a) is the development of a set of MATLAB programs that compute the coefficients of the second-order approximation to the solution to the general class of models described above. This computer code is publicly available at the authors’ websites. Our computer code coexists with others that have been developed recently by Chris Sims and Fabrice Collard and Michel Juillard to accomplish the same task. We believe that the availability of this set of independently developed codes, which have been shown to deliver identical results for a number of example economies, helps build confidence across potential users of higher-order perturbation techniques.

Optimal Operational Monetary Policy for the U.S. Economy

After the completion of the second-order approximation toolkit, we felt that we were suitably equipped to undertake a systematic and rigorous evaluation of stabilization policy. A contemporaneous development that highly facilitated our work was the emergence of estimated medium-scale dynamic general equilibrium models of the U.S. economy with the ability to explain the behavior of a relatively large number of macroeconomic variables at business-cycle frequency (e.g., Christiano, Eichenbaum, and Evans, 2003; and Smets and Wouters, 2004).A central characteristic of the studies on optimal monetary policy that existed at the time we initiated our research on policy evaluation, was that they were conducted in the context of highly stylized environments. An important drawback of that approach is that highly simplified models are unlikely to provide a satisfactory account of cyclical movements for but a few macroeconomic variables of interest. For this reason, the usefulness of this strategy to produce policy advise for the real world is necessarily limited.

In a recent working paper (Schmitt-Grohé and Uribe, 2004b), we depart from the literature extant in that we conduct policy evaluation within the context of a rich theoretical framework capable of explaining observed business cycle fluctuations for a wide range of nominal and real variables. Following the lead of Kimball (1995), the model emphasizes the importance of combining nominal and real rigidities in explaining the propagation of macroeconomic shocks. Specifically, the model features four nominal frictions, sticky prices, sticky wages, money in the utility function, and a cash-in-advance constraint on the wage bill of firms, and four sources of real rigidities, investment adjustment costs, variable capacity utilization, habit formation, and imperfect competition in product and factor markets. Aggregate fluctuations are assumed to be driven by supply shocks, which take the form of stochastic variations in total factor productivity, and demand shocks stemming from exogenous innovations to the level of government purchases. Altig et al. (2003) and Christiano, Eichenbaum, and Evans (2003) argue that the model economy for which we seek to design optimal operational monetary policy can indeed explain the observed responses of inflation, real wages, nominal interest rates, money growth, output, investment, consumption, labor productivity, and real profits to productivity and monetary shocks in the postwar United States. In this respect, Schmitt-Grohé and Uribe (2004b) aspires to be a step ahead in the research program of generating monetary policy evaluation that is of relevance for the actual practice of central banking.

In our quest for the optimal monetary policy scheme we restrict attention to what we call operational interest rate rules. By an operational interest-rate rule we mean an interest-rate rule that satisfies three requirements. First, it prescribes that the nominal interest rate is set as a function of a few readily observable macroeconomic variables. In the tradition of Taylor (1993), we focus on rules whereby the nominal interest rate depends on measures of inflation, aggregate activity, and possibly its own lag. Second, the operational rule must induce an equilibrium satisfying the zero lower bound on nominal interest rates. And third, operational rules must render the rational expectations equilibrium unique. This last restriction closes the door to expectations driven aggregate fluctuations.

The object that monetary policy aims to maximize in our study is the expectation of lifetime utility of the representative household conditional on a particular initial state of the economy. Our focus on a conditional welfare measure represents a fundamental departure from most existing normative evaluations of monetary policy, which rank policies based upon unconditional expectations of utility. Exceptions are Kollmann (2003) and Schmitt-Grohé and Uribe (2004c). As Kim et al. (2003) point out, unconditional welfare measures ignore the welfare effects of transitioning from a particular initial state to the stochastic steady state induced by the policy under consideration. Indeed, we document that under plausible initial conditions, conditional welfare measures can result in different rankings of policies than the more commonly used unconditional measure. This finding highlights the fact that transitional dynamics matter for policy evaluation.

In our welfare evaluations, we depart from the widespread practice in the neo-Keynesian literature on optimal monetary policy of limiting attention to models in which the nonstochastic steady state is undistorted. Most often, this approach involves assuming the existence of a battery of subsidies to production and employment aimed at eliminating the long-run distortions originating from monopolistic competition in factor and product markets. The efficiency of the deterministic steady-state allocation is assumed for purely computational reasons. For it allows the use of first-order approximation techniques to evaluate welfare accurately up to second order, a simplification that was pioneered by Rotemberg and Woodford (1999). This practice has two potential shortcomings. First, the instruments necessary to bring about an undistorted steady state (e.g., labor and output subsidies financed by lump-sum taxation) are empirically uncompelling. Second, it is ex ante not clear whether a policy that is optimal for an economy with an efficient steady state will also be so for an economy where the instruments necessary to engineer the nondistorted steady state are unavailable. For these reasons, we refrain from making the efficient-steady-state assumption and instead work with a model whose steady state is distorted.

Departing from a model whose steady state is Pareto efficient has a number of important ramifications. One is that to obtain a second-order accurate measure of welfare it no longer suffices to approximate the equilibrium of the model up to first order. Instead, we obtain a second-order accurate approximation to welfare by solving the equilibrium of the model up to second order. Specifically, we use the methodology and computer code developed in Schmitt-Grohé and Uribe (2004a).

Our numerical work suggests that in the model economy we study, the optimal operational interest-rate rule takes the form of a real-interest-rate targeting rule. For it features an inflation coefficient close to unity, a mute response to output, no interest-rate smoothing, and is forward looking. The optimal rule satisfies the Taylor principle because the inflation coefficient is greater than unity albeit very close to 1. Optimal operational monetary policy calls for significant inflation volatility. This result stands in contrast to those obtained in the related literature. The main element of the model driving the desirability of inflation volatility is indexation of nominal factor and product prices to 1-period lagged inflation. Under the alternative assumption of indexation to long-run inflation, the conventional result of the optimality of inflation stability reemerges.

Open Questions

There remain many challenging unanswered questions in this research program. One is to investigate the sensitivity of the parameters of the optimal operational policy rule to changes in the sources of uncertainty driving business cycles. This question is of importance in light of the ongoing quest in business-cycle research to identify the salient sources of aggregate fluctuations. One alternative would be to incorporate the rich set of shocks identified in econometric estimations of the model considered here (e.g., Smets and Wouters, 2004).The class of operational rules discussed here is clearly not exhaustive. It would be of interest to investigate whether the inclusion of macroeconomic indicators other than those considered here would improve the policymaker’s ability to stabilize the economy. In particular, the related literature has emphasized the use of measures of the output gap that are different from that used by us. Additionally, it has been argued that in models with nominal wage and price rigidities the optimal policy should target an average of wage and price inflation as opposed to only price inflation, which is the case we analyze.

The optimal policy problem we analyze takes the central bank’s inflation target as exogenously given. A natural extension is to endogenize this variable. However, in our theoretical framework, the optimal inflation target is the one associated with the Friedman rule. This is because the assumption of full indexation to past inflation implies the absence of inefficient price and wage dispersion in the long run. Thus the only remaining nominal frictions are the demand for money by households and firms. These frictions call for driving the opportunity cost of holding money to zero in the long run. In other words, the zero bound on nominal interest rate binds in the non-stochastic steady state. The perturbation technique we employ is ill suited to handle this case. Therefore, analyzing the case of an endogenous inflation target entails either changing the model so that the Friedman rule is no longer optimal in the long-run or adopting alternative numerical techniques for computing welfare accurately up to second-order or higher.

One of our findings is that the initial state of the economy plays a role in determining the parameters defining the optimal interest-rate rule. This finding suggests that the optimal operational rule identified here is time inconsistent. In Schmitt-Grohé and Uribe (2004b), we assume that the government is able to commit to the policy announcements made at time 0. It would be of interest to characterize optimal operational rules in an environment without commitment.

Finally, we limit attention to the special case of passive fiscal policy, taking the form of a balanced-budget rule with lump-sum taxation. It is well known that the set of operational monetary rules depends on the stance of fiscal policy. For instance, the determinacy properties of the rational expectations equilibrium associated with a particular monetary rule can change as fiscal policy is altered. Therefore, it would be of interest to introduce operational fiscal rules as an additional policy instrument.


Altig, David, Lawrence J. Christiano, Martin Eichenbaum, and Jesper Lindé (2003): Technology Shocks and Aggregate Fluctuations manuscript, Northwestern University.
Christiano, Lawrence J., Martin Eichenbaum, and Charles Evans (2003): Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy. Northwestern University.
Kim, Jinill, and Sunghyun Henry Kim (2003): Spurious Welfare Reversals in International Business Cycle Models, Journal of International Economics vol. 60, pages 471-500.
Kim, Jinill, Sunghyun Henry Kim, Ernst Schaumburg, and Christopher Sims (2003): Calculating and Using Second Order Accurate Solutions of Discrete Time Dynamic Equilibrium Models, Finance and Economics Discussion Series 2003-61, Board of Governors of the Federal Reserve System.
Kimball, Miles S. (1995): The Quantitative Analytics of the Basic Neomonetarist Model, Journal of Money, Credit and Banking, vol. 27, pages 1241-1277.
Kollmann, Robert (2003): Welfare Maximizing Fiscal and Monetary Policy Rules mimeo, University of Bonn.
Rotemberg, Julio J., and Michael Woodford (1999): Interest Rate Rules in an Estimated Sticky Price Model, in: John B. Taylor, ed., Monetary policy rules NBER Conference Report series. Chicago and London: University of Chicago Press, pages 57-119.
Schmitt-Grohé, Stephanie and Martín Uribe (2004a): Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function, Journal of Economic Dynamics and Control, vol. 28, pages 755-775.
Schmitt-Grohé, Stephanie, and Martín Uribe (2004b): Optimal Operational Monetary Policy in the Christiano-Eichenbaum-Evans Model of the U.S. Business Cycle, NBER working paper 10724.
Schmitt-Grohé, Stephanie and Martín Uribe (2004c): Optimal Simple And Implementable Monetary and Fiscal Rules, NBER working paper 10253.
Smets, Frank and Raf Wouters (2004): Comparing shocks and frictions in US and Euro area business cycles: a Bayesian DSGE approach, Working paper 61, Nationale Bank van Belgie.
Taylor, John B. (1993): Discretion versus Policy Rules in Practice Carnegie Rochester Conference Series on Public Policy, vol. 39, pages 195-214.
Woodford, Michael (2003): Interest and Prices: Foundations of a Theory of Monetary Policy, Princeton Princeton University Press.
Volume 5, Issue 2, April 2004

Craig Burnside on the Causes and Consequences of Twin Banking-Currency Crises

Craig Burnside is Professor of Economics at the University of Virginia. He is interested in macroeconomics and international macroeconomics, in particular asset pricing, business cycles, and currency and fiscal crises. Burnside’s RePEc/IDEAS entry.

Since 1990 economists have watched the collapse of fixed or managed exchange rate regimes in a diverse set of countries that includes, among others, Sweden, Mexico, Thailand, Korea and Turkey. There is disagreement about the causes of these crises, but there is widespread agreement that these currency crises were somehow linked to banking crises that occurred at roughly the same time in each country. This “twin crises” phenomenon was identified by Kaminsky and Reinhart (1999). They argued that in the 1970s, worldwide, there were 26 balance-of-payments crises and 3 banking crises, but only one instance of these crises being coincident. On the other hand, among the 50 balance-of-payments crises and 23 banking crises that occurred after 1980, 18 were coincident. My recent research, most of which has been joint with Martin Eichenbaum and Sergio Rebelo, investigates the causes and consequences of these crises.

The Asian Crisis of 1997-98

At the end of June 1997 the Asian crisis began with the collapse of Thailand’s fixed exchange rate regime after weeks of market speculation. At the time, we were intrigued. The standard explanation for speculative attacks–that they reflect profligate fiscal policy–had an obvious shortcoming when applied to Thailand: its government was running a budget surplus and had done so for several years. As events unfolded, more exchange rate regimes in Asia collapsed, and in each case, the governments in question had been running surpluses, or at worst small budget deficits.In standard “first generation” currency crisis models, such as those of Krugman (1979), Flood and Garber (1984), Obstfeld (1986), Calvo (1987), Wijnbergen (1991), and Calvo and Végh (1998). Ongoing fiscal deficits lead to sustained reserve losses and to the eventual abandonment of a fixed exchange rate. In these models ongoing deficits and rising debt levels precede the collapse of a fixed exchange rate. Since neither deficits nor rising debt levels were observed prior to the crisis in Asia, this led many observers to argue that standard models were inadequate, and that the crises arose from self-fulfilling expectations on the part of speculators.

We were not so sure. Each of the Asian economies that suffered through a currency crisis also experienced a banking crisis. A consequence of these financial crises was that the governments in Asia bore the cost of bailing out failing banks, either by recapitalizing them, or by closing them and honoring their debts. Thus, in Burnside, Eichenbaum and Rebelo (2001a) we argue that the Asian currency crises were caused by fundamentals, in particular, the large prospective deficits associated with government bailout guarantees to failing banks. The expectation that seigniorage revenues would finance these future deficits led to the collapse of the fixed exchange rate regimes.

Our model has a distinctly first generation flavor in that fiscal deficits ultimately financed by seigniorage revenues play a key role in triggering the crisis. A key insight of our work, however, is that the deficits need not precede the currency crisis. The currency crisis can occur in anticipation of later deficits. Thus, a crisis can appear to be unlikely–in the sense that fiscal policy looks healthy prior to the crisis–yet occur.

Could agents in the Asian economies anticipate the coming deficits? We argued that they could on the following basis: in most of the Asian economies that experienced currency crises the banking sector was in trouble prior to the crisis. In Korea and Thailand, especially, the stock market capitalization of the financial sector had been in sharp decline for over a year. Given the scale of the problem, agents could readily anticipate that governments would step in and bear the cost of cleaning up the mess.

General equilibrium dynamics play an important role in the solution of our model. First, like most currency crisis models, ours is explicitly dynamic: equilibrium prices are determined by solving a system of first order conditions that includes a dynamic Euler equation for money balances. Second, unlike many currency crisis models, ours explicitly requires that the government budget constraint be satisfied: this endogenizes at least some aspects of the money supply path, and ensures that the anticipation of future deficits plays a key role in driving the crisis.

The Post-Crisis Government Budget Constraint

Our prospective deficits model suffers from two important shortcomings:

  1. It predicts that there should be a significant rise in seignorage revenue after a currency crisis.
  2. It predicts that currency crises will be followed by substantial inflation to the same extent that they lead to rapid depreciation of the local currency.

Both of these predictions are at odds with what we have observed after many twin crises. In recent episodes (e.g. Mexico 1994, Korea, Thailand and the Philippines in 1997, Brazil 1999 and Turkey 2001) involving substantial depreciation of the local currency, the increase in seignorage revenues after the crisis was, at best, modest. Furthermore, in many of these episodes the increase in inflation was also modest, or substantially lagged behind the depreciation of the currency.This evidence led us to ask the following questions: If not using seigniorage, how do governments pay for the fiscal costs associated with twin banking-currency crises? What are the implications of different financing methods for post-crises rates of inflation and depreciation? Can first generation models be reconciled with the facts?

In Burnside, Eichenbaum and Rebelo (2003a and 2003b) we address these questions. Our answer to the first question is that after currency crises governments finance themselves with a menu of different types of revenue. The problem with the standard theories is that they assume, for convenience, that governments face a simple choice between making explicit fiscal reforms (such as raising tax rates or making social programs less generous) to defend a fixed exchange rate, or printing money and abandoning a fixed exchange rate. We show that, apart from seigniorage revenue, governments have access to other types of revenue that are depreciation-related. First, as in the fiscal theory of the price level–exposited by Sims (1994), Woodford (1995), Dupor (2000), Cochrane (2001), Daniel (2001a, b) and Corsetti and Mackowiak (2002)–they can deflate the dollar value of outstanding nonindexed debt. Second, governments can benefit from what we call “implicit fiscal reforms.” These reforms arise from changes in relative prices that are outside the government’s direct control. For example, if the government purchases mainly nontraded goods, its expenditure, measured in dollars, will decline if the dollar price of nontraded goods declines as the result of a crisis. While this will also be true for revenue, the government may be a net beneficiary of the crisis depending on the exact structure of its budget. Also, government transfers that are indexed to the CPI decline in dollar value if inflation lags behind depreciation. Our empirical evidence–gleaned from case studies of Mexico, Korea and Turkey–suggests that these additional forms of depreciation related revenue are more important than seigniorage in some crisis episodes.

To answer the second and third questions we use variants of our prospective deficits model in which the government budget constraint is more realistically specified. In Burnside, Eichenbaum and Rebelo (2003a) we use a simple reduced form model featuring a Cagan money demand function, and a government budget constraint that allows for nominal debt and nonindexed government transfers. In Burnside, Eichenbaum and Rebelo (2003b) we develop a general equilibrium model with two goods, and a government budget constraint that allows for (i) nominal debt, (ii) transfers that are indexed to the CPI (not the exchange rate), (iii) government purchases of goods and services, the dollar value of which is affected by changes in relative prices, and (iv) taxes that are proportional to economic activity. Using these models we show that the ways in which governments finance themselves after crises have important consequences for inflation and depreciation outcomes. Furthermore, we show that our extended first generation models can be reconciled with the facts as long as PPP only holds for traded goods at the producer level, and as long as we allow for sticky nontradable goods prices.

Our results can be understood as follows. Suppose the banking crisis imposes a fiscal cost, x dollars, on the government. One way the government could pay for this new burden would be through explicit fiscal reforms. If these explicit fiscal reforms raise x dollars of revenue, the model predicts that a currency crisis will be prevented. On the other hand, if the government raises less than x dollars of revenue through explicit fiscal reform, it must abandon the fixed exchange rate regime.

Suppose that all government debt is denominated in dollars, that all goods in the economy are tradable, and that PPP holds. In this case, the only source of additional revenue to the government is the printing press. To the extent that the government prints money the currency will depreciate and, given PPP, there will be a similar amount of inflation.

On the other hand, suppose that the government has a substantial amount of outstanding debt that is denominated in units of local currency. Then, as the currency depreciates, the dollar value of this debt declines. In this way, the government raises revenue implicitly, and does not need to print as much money. This makes the model more consistent with the facts in two ways: seigniorage becomes less important and post-crisis inflation is also lower. Unfortunately, the model becomes less consistent with the facts in that the model also predicts less depreciation.

Now suppose the government spends more on nontraded goods than it raises in revenue by taxing nontraded goods production (or consumption). In this case, the government’s budget balance–measured in dollars–will improve, the greater is the decline in the dollar price of nontraded goods after a crisis. As long as PPP only holds for traded goods and nontraded goods prices are sticky in response to the currency crisis, the government raises even more implicit revenue. For this reason, less money is printed, and there is even less inflation. However, the model is fully consistent with the facts because there will be substantial depreciation. Why? Money demand must rise, in equilibrium, to match the money supply. When money demand is proportional to the nominal transactions volume–say as in a cash-in-advance model–and some prices are sticky, the prices that are flexible adjust more in equilibrium. In our model, when nontraded goods prices are sticky, the producer price of tradables, which, by PPP, is equivalent to the exchange rate, rises more than it would if nontraded goods prices were flexible.

For simplicity we assume that nontraded goods prices remain fixed for some period of time after the crisis, and then rise in proportion to traded goods prices. In a general equilibrium model with explicit price-setting behavior these dynamics might be different, but we think they would be similar, as long as the path for nontraded goods prices implied by the model was realistic.

All of this suggests that first generation models can be rendered consistent with the observed paths of inflation and depreciation after recent currency crises, but only if we model the government budget constraint carefully.

Government Guarantees to Banking Systems and Self-Fulfilling Speculative Attacks

While much of the research I have just described focuses on models in which crises arise out of bad fundamentals in the banking sector, some of my other recent work has considered the possibility of self-fulfilling speculative attacks on fixed exchange rate regimes. In the models of prospective deficits that I have just described, a currency crisis occurs because the government bails out failing banks, and because the government finances part of the bailout with depreciation-related revenue. These models take the banking crisis as given, and work out the implications of the government’s financing choices for equilibrium prices.In Korea and Thailand, the banks were in trouble prior to the crisis. It is arguable, however, that these banks were exposed to exchange rate risk, and that the crisis caused their balance sheets to deteriorate even further. In other crisis episodes we see otherwise healthy banks which are exposed to exchange rate risk, mainly because they have dollar liabilities but do their lending in local currency. When a currency crisis occurs these banks fail. This leads us to ask two questions:

  1. Why do banks expose themselves to exchange rate risk?
  2. Does the fact that otherwise healthy banks are exposed to exchange rate risk open the door to the possibility of currency crises driven by agents’ self-fulfilling expectations?

In Burnside, Eichenbaum and Rebelo (2001b) we look at the first question using a model of bank behavior in which banks borrow dollars from abroad in order to finance domestic loans denominated in local currency. In the model, the government fixes the exchange rate, but there is an exogenous probability of the fixed exchange rate regime being abandoned in favor of a floating rate regime with a devalued currency. The government also must decide whether or not to issue guarantees to bank creditors. Suppose the government issues no guarantees. Not surprisingly, the model predicts that banks will hedge their exchange rate exposure, say in the forward market. On the other hand, suppose that the government promises to bail out banks that fail in the state of the world in which the exchange rate regime is abandoned. [Mishkin (1996) and Obstfeld (1998) go as far as to argue that a government’s promise to maintain a fixed exchange rate is often seen as an implicit guarantee to banks’ creditors against the effects of a possible devaluation.] In this case, the banks will not only not hedge, but they will attempt to transfer as many profits as possible from the bad state of the world to the good state of the world by selling dollars forward. So government guarantees play a key role in determining banks’ behavior.Again, the dynamic aspect of a bank’s problem plays a key role. Bankers maximize expected payments to their shareholders but face uncertainty about the exchange rate. When there are no government guarantees, banks hedge because they face higher borrowing costs if they are exposed to exchange rate risk. These higher borrowing costs reflect the costs associated with bankruptcy. On the other hand, under government guarantees, a bank’s creditors do not care if it is exposed to risk. Furthermore, banks actually have an incentive to take on risk: they want to leave nothing on the table in the bad state of the world.

In Burnside, Eichenbaum and Rebelo (2003c), we treat the probability of a currency crisis as endogenous. Using a model similar to the one I have just described we show that if the government does not issue guarantees, banks hedge, and self-fulfilling speculative attacks are impossible in equilibrium. On the other hand, if the government does issue guarantees, banks are exposed to exchange rate risk. Suppose, in this situation, agents come to believe that the fixed exchange rate regime will be abandoned. They will speculate against the currency, causing the central bank to float the currency. This will lead to the failure of the banks exposed to exchange rate risk. The government, in turn, will have to bail out the banks. If the government uses depreciation-related revenue to finance the bailout, the speculative attack on the currency is rational.

Finally, in Burnside (2004), I describe how the issuance of government guarantees combined with the methods by which these guarantees are financed affects the probability of a crisis taking place. I show that the greater the amount of revenue that can be raised through implicit fiscal reforms, the lower the probability of a crisis of a given magnitude. The reason is simple: the larger the potential implicit fiscal reforms, the less seignorage is required to finance the budget. Other things equal, the less money is printed the lower are the post-crisis rates of depreciation and inflation.

In sum, this research points to the importance of government policy and the government budget in currency and financial crises. Government guarantees can be seen as an important determinant of a country’s exposure to self-fulfilling twin crises. Whether or not financial crises are self-fulfilling, guarantees impose significant fiscal costs on governments. Absent explicit fiscal reforms, paying for these costs requires that the government abandon a fixed exchange rate regime. The structure of the government’s debt and budget act as important determinants of the outcomes for inflation and depreciation. In our models, these outcomes are determined by solving equilibrium models with forward looking pricing equations.


Burnside, Craig (2004): Currency Crises and Contingent Liabilities, Journal of International Economics, vol. 62, pages 25-52.
Burnside, Craig, Martin Eichenbaum and Sergio Rebelo (2001a): Prospective Deficits and the Asian Currency Crisis, Journal of Political Economy, vol. 109, pages 1155-1197.
Burnside, Craig, Martin Eichenbaum and Sergio Rebelo (2001b): Hedging and Financial Fragility in Fixed Exchange Rate Regimes, European Economic Review, vol. 45, pages 1151-1193.
Burnside, Craig, Martin Eichenbaum and Sergio Rebelo (2003a): On the Fiscal Implications of Twin Crises, in Michael P. Dooley and Jeffrey A. Frankel, eds. Managing Currency Crises in Emerging Markets. Chicago: University of Chicago Press.
Burnside, Craig, Martin Eichenbaum and Sergio Rebelo (2003b): Government Finance in the Wake of Currency Crises, NBER Working Paper No. 9786.
Burnside, Craig, Martin Eichenbaum and Sergio Rebelo (2003c): Government Guarantees and Self-Fulfilling Speculative Attacks. Forthcoming, Journal of Economic Theory.
Calvo, Guillermo (1987): Balance of Payments Crises in a Cash-in-Advance Economy, Journal of Money Credit and Banking, vol. 19, pages 19-32.
Calvo, Guillermo A. and Carlos A. Végh (1998): Inflation Stabilization and BOP Crises in Developing Countries, in John B. Taylor and Michael Woodford, eds., Handbook of Macroeconomics, Vol. 1C. Amsterdam: North-Holland.
Cochrane, John (2001): Long-term Debt and Optimal Policy in the Fiscal Theory of the Price Level, Econometrica, vol. 69, pages 69-116.
Corsetti, Giancarlo and Bartosz Mackowiak (2002): Nominal Debt and the Dynamics of Currency Crises. Manuscript, Yale University.
Daniel, Betty C. (2001a): The Fiscal Theory of the Price Level in an Open Economy, Journal of Monetary Economics, vol. 48, pages 293-308.
Daniel, Betty C. (2001b): A Fiscal Theory of Currency Crises, International Economic Review, vol. 42, pages 969-988.
Dupor, William (2000): Exchange Rates and the Fiscal Theory of the Price Level, Journal of Monetary Economics, vol. 45, pages 613-630.
Flood, Robert and Peter Garber (1984): Collapsing Exchange Rate Regimes: Some Linear Examples, Journal of International Economics, vol. 17, pages 1-13.
Kaminsky, Graciela and Carmen Reinhart (1999): The Twin Crises: the Causes of Banking and Balance-of-Payments Problems, American Economic Review, vol. 89, pages 473-500.
Krugman, Paul (1979): A Model of Balance of Payments Crises, Journal of Money, Credit and Banking, vol. 11, pages 311-325.
Mishkin, Frederic (1996): Understanding Financial Crises: A Developing Country Perspective, in Michael Bruno and Boris Pleskovic, eds. Annual World Bank Conference on Development Economics. Washington, DC: World Bank.
Obstfeld, Maurice (1998): The Global Capital Market: Benefactor or Menace? Journal of Economic Perspectives, vol. 12, pages 9-30.
Obstfeld, Maurice (1986): Speculative Attack and the External Constraint in a Maximizing Model of the Balance of Payments, Canadian Journal of Economics, vol. 29, pages 1-20.
Sims, Christopher (1994): A Simple Model for the Determination of the Price Level and the Interaction of Monetary and Fiscal Policy. Economic Theory, vol. 4, pages 381-399.
Wijnbergen, Sweder van (1991): Fiscal Deficits, Exchange Rate Crises and Inflation, Review of Economic Studies, vol. 58, pages 81-92.
Woodford, Michael (1995): Price Level Determinacy Without Control of a Monetary Aggregate, Carnegie-Rochester Conference Series on Public Policy, vol. 43, pages 1-46.
Volume 5, Issue 1, November 2003

Kjetil Storesletten on Inequality in Macroeconomics

Kjetil Storesletten is Professor of Economics at the University of Oslo, Norway. He is interested in heterogeneity in macroeconomics, in particular political economy and the impact of aggregate and individual risk on economic allocations. Storesletten’s RePEc/IDEAS entry.

Over the last decade or so, economists have made substantial effort departing from the representative agent framework and exploring the role of heterogeneity in macroeconomics. The central insight is that uninsurable risk and heterogeneity can have substantial impact on aggregate economic outcomes, the impact of government policies, and the mere choice of such policies. In this vein of research I have focused on three broad questions:

  1. How important is risk on the household-level?
  2. What are the implications of this risk for government policy and
  3. How does this heterogeneity shape political conflict and policy outcomes?

Quantifying risk on the household-level

One of the most divisive and politically loaded questions in economics is whether cross-sectional dispersion and changes over time in income and labor earnings are driven by luck — shocks exogenous and unexpected to the household –, or by effort and innate ability — factors endogenous and known to the agents at birth. Individual data exhibit large dispersion in wages and earnings, and the within-cohort earnings-dispersion (measured as variance of logs) is increasing sharply with age. However, as econometricians know less than the agents in their data samples, data on earnings alone do not suffice to address this question. One way to bring theory to bear on this issue is to consider data on consumption. Deaton and Paxson (1994) document that within-cohort consumption dispersion is also linearly increasing over the life-cycle, albeit not as steeply as earnings dispersion. In Storesletten, Telmer and Yaron (2004a), we show that these facts are quantitatively consistent with a standard life-cycle model with incomplete markets, provided that a substantial fraction — roughly half — of the labor-market uncertainty people face must be realized throughout the working years, as opposed to early in life, before entering the labor market. Without shocks during working years, the theory can account for increasing inequality in income, but not consumption. Moreover, the joint behavior of income and consumption inequality implies that idiosyncratic shocks must be highly persistent. These results have strong implications for policies such as unemployment insurance and social security and for theories of savings and portfolio choice.

One alternative explanation of this evidence on earnings and consumption dispersion, one consistent with complete markets, could be that agents’ preferences were not separable between consumption and leisure. The more productive agents would then work harder and be compensated with higher consumption. As wage dispersion increases with age, so would dispersion in both consumption and leisure. That implication is testable: Storesletten, Telmer, and Yaron (2001a) argues that empirical evidence on labor supply makes this story implausible, since the dispersion in labor supply is roughly constant over the life-cycle. This is inconsistent with a standard model of complete risk sharing — there are no “plausible” combinations of attitudes toward risk and substitutability between consumption and leisure simultaneously generating a non-increasing dispersion in hours worked and an increasing dispersion in consumption and labor earnings. I interpret this as further evidence of substantial uninsurable risk at the household level.

While the above studies focus on inequality over the life-cycle, one important reason for the recent awareness of inequality and heterogeneity in economics is the sharp increase in cross-sectional dispersion in wages and earnings over time — the trend in inequality over the 1970-2000 period (see Katz and Autor, 1999, for a survey). Concern for the surge in inequality is, arguably, driven by the presumption that these changes are associated with dire welfare consequences. However, dispersion of hours worked, consumption and wealth (excluding the top 1%) have remained roughly constant through time, while the wage-hour correlation has risen sharply. In Heathcote, Storesletten and Violante (2003), we decompose the rise in wage inequality over time into changes in the variance of permanent, persistent and transitory shocks. With the estimated changes in the wage process as the only primitive, we show that a standard calibrated life-cycle model with incomplete markets can successfully account for all these changes over time in cross-sectional U.S. data.

Now what about short-term fluctuations in cross-sectional inequality? In Storesletten, Telmer, and Yaron (2004b), we explore if household-level earnings risk vary over the business cycle and to what extent this risk is persistent. The answer influences our understanding of economic short-term fluctuations, something I return to below. The main statistical problem is that available panel data-sets have a very limited time dimension. For example, the Panel Study on Income Dynamics starts in 1968. As there are at most 5 business cycles during the available panel years 1968-1993, it is difficult to identify how cross-sectional variation interacts with business cycles. In this work, we overcome this by conditioning on household age and the macroeconomic history during which a household has worked. We combine the individual earnings data with business-cycle regimes identified using aggregate data. Thus, we can use aggregate data going back as far as 1930. The main empirical findings are that idiosyncratic risk is persistent and increases significantly in downturns.

Economic implications of heterogeneity and risk

Now, given the above evidence of risk on the household-level, should we, as macro-economists, care? Below I argue risk and heterogeneity shapes our view on core macro issues such as fiscal policy, asset prices, portfolio choice, and the cost of aggregate short-term fluctuations.

Starting with the latter, in Storesletten, Telmer and Yaron (2001b), we ask whether the welfare costs of business cycles depend on how aggregate shocks interact with idiosyncratic shocks. We find that if eliminating business cycles amounts to eliminating the negative correlation between the variability of idiosyncratic shocks and the overall level of economic activity (which we documented in our 2004b work), then the welfare costs of business cycles are much larger than previous work has suggested. These results support the popular view that distributional effects are an important aspect of understanding the welfare cost of business cycles.

What about asset prices and portfolio choices? While financial advisors often argue that young workers should hold stocks older workers should hold bonds, empirical evidence suggest that in reality people do exactly the opposite (Ameriks and Zeldes, 2001). Could individual earnings risk shed light on this apparent puzzle? A different, but related argument is due to Mankiw (1986) and Constantinides and Duffie (1996). They have suggested that individual labor-income risk could potentially resolve the “equity premium puzzle” — the statement that it is difficult to reconcile the historical return-premium of stocks over bonds with a standard calibrated representative-agent model with time-additive preferences. The key condition is, they argue, that this risk is counter-cyclical — large individual shocks when returns are low (i.e., in recessions) and small when returns are high (i.e., in booms). Such process is precisely what we recovered in our 2004b work I described above. In Storesletten, Telmer and Yaron (2002), we incorporate that individual earnings process into a standard life-cycle model and inquire about portfolio holdings over the life-cycle and its implications for the equity premium. Absent individual risks, our model suggests that young households should hold most of their financial wealth as stocks, whereas old ones should hold mostly bonds, consistent with Jagannathan and Kocherlakota (1996) and the standard financial advisor’s advice. Young households have far more human wealth than financial wealth, and since wages are far less variable than stock returns, human wealth is like a non-traded bond. Getting older means having less non-traded bonds and, therefore, maintaining an overall balanced portfolio requires increasing the bond share. This can be thought of as the intergenerational sharing of aggregate risk: aggregate risk is transferred from the old to the young via stock ownership. Idiosyncratic risk changes all this. It means that human wealth is risky and it deters those who have the most of it, the young, from holding stocks. The net effect is that idiosyncratic risk inhibits the intergenerational sharing of aggregate risk and, thus, drives up the reward to bearing aggregate risk: the equity premium. In this life-cycle model the wealthy middle aged are most suited to handle both aggregate and idiosyncratic shocks. Therefore, they end up holding more of their per-capita share of stocks, consistent with the empirical portfolio profile. Moreover, they demand a premium to these stocks, which drives up the equilibrium equity premium.

Given the above empirical evidence of substantial household-level risk, it is interesting to examine the scope of using government redistribution policies as an (ex-ante) vehicle of insurance. Such an exercise is of particular interest in light of the recent debate on reforming Social Security, the largest U.S. redistribution. Most proposals for reform involve less redistribution, moving from a benefit-defined system towards a contribution-defined system. In Storesletten, Telmer and Yaron (1999) we use a calibrated life-cycle model with incomplete markets to quantify the value of insurance, under the veil of ignorance, implicit in the current U.S. system. We find it to be worth 1.5% of lifetime income, given a risk aversion of 2. This is a large number, compared with other welfare assessments of risk in the quantitative macro literature (cf. Rios-Rull, 1994). However, when trading off the insurance value with the distortions of the pension system on aggregate savings, we find that privatization schemes contained in the proposals might still be welfare improving.

The overall aim of introducing heterogeneity in macroeconomics is, in addition to further our understanding of how the economy works, to provide tools for actual policy analysis. The area where this agenda has had the most influence is, perhaps, the analysis of future fiscal policy in light of the aging of the baby-boom generation (cf. Auerbach and Kotlikoff, 1987). The main insight of this literature has been that most Western economies, including the U.S., should expect large future tax increases or substantial reductions in expenditures. However, this literature has usually abstracted from an important component of demographic change: immigration. Using a calibrated general equilibrium life-cycle model, which explicitly accounts for differences between immigrants and natives, I investigated whether an immigration policy reform alone could resolve the fiscal problems associated with the ageing of the baby boom generation (Storesletten, 2000). Such policies exist and are characterized by increased inflow of working-age high- and medium-skilled immigrants. One particular feasible policy involves admitting 1.6 million middle-aged high-skilled immigrants annually. Moreover, I find that high-skilled immigrants are a huge fiscal gain to the U.S. government, while low-skilled immigrants represent a net loss.

Political economy

So far I have described my research on the economic consequences of heterogeneity taking government policies are exogenous. For example, in Storesletten (2000), I derived the implications of different immigration policies. However, in recognizing the importance of heterogeneity across households, one opens up an important tension in economics: political conflict over government policies implies that the set of politically feasible policies is more restricted than the set of economically feasible ones. There is now a growing literature bringing politico-economic aspects into macroeconomics, describing government policies as endogenous outcomes collectively determined by rational self-interested individuals. While many important politico-economic issues are dynamic in nature, technical limitations have, however, so far prevented a thorough investigation of dynamic political choices in macroeconomics. Put bluntly, the main reason why the theoretical literature is scant on dynamics, is a lack of convenient analytical tools. The study of economic dynamics is perhaps hard, but there is a large body of work on the subject: for a given policy environment, it is textbook material how to analyze an economy’s behavior over time when the economic actors are fully rational. Similarly, pure political theory has worked on dynamic policy determination (although this literature is less well developed). The combination of politics and economics is what poses a difficulty; one needs to model strategic voting interactions, where political agents consider the consequences of their choice on future political outcomes, as well as appeal to dynamic (usually competitive) equilibrium theory to ensure that all economic agents consumers, firms and government maximize their respective objective functions under rational expectations, and resource constraints.

Prior to Hassler, Rodriguez-Mora, Storesletten and Zilibotti (2003a), the only nontrivial dynamic models (that is, that are not repeated static frameworks or purely backward-looking setups) relied essentially on numerical solution (see, e.g., Krusell and Rios-Rull (1999) and the discussions therein). In this work, we provide a tractable framework where voters are influenced both by the state of the economy, the current income distribution and foresee effects of the current policy outcomes on both future income distributions and future voting outcomes, which they care about and therefore take into account when they vote. A key result is that the future constituency for redistributive policies depends positively on current redistribution, since this affects both private investments and the future distribution of voters. The model features multiple equilibria. In some equilibria, positive redistribution persists forever. In others, even a majority of beneficiaries of redistribution vote strategically so as to induce the end of the welfare state next period. Skill-biased technical change makes the survival of the welfare state less likely.

Can this line of research shed light on more applied politico-economic issues such as unemployment and the choice of unemployment benefits? There has emerged a consensus among economists that the high level of unemployment in Europe relative to the U.S. is caused by the generous unemployment benefits and, to a lesser extent, firing restrictions in Europe (cf. Ljungqvist and Sargent, 1998). But why then don’t European countries reform their welfare system in order to bring down unemployment? In Hassler, Rodriguez Mora, Storesletten and Zilibotti (2001), we argue that the cross-country empirical regularities in geographical mobility, unemployment and labor market institutions can be explained in a model with endogenous mobility and rational voting over unemployment insurance (UI). Agents with higher cost of moving, i.e., more attached to their current location, prefer more generous UI. The key assumption is that an agent’s attachment to a location increases the longer she has resided there. UI reduces the incentive for labor mobility and increases therefore the fraction of attached agents and the political support for UI. The main result is that this self-reinforcing mechanism can give rise to multiple steady-states: one “European” steady-state featuring high unemployment, low geographical mobility and high UI, and one “American” steady-state featuring low unemployment, high mobility and UI.


Ameriks, John, and Stephen P. Zeldes (2001): How Do Household Portfolio Shares Vary with Age?, Unpublished manuscript, Columbia University.
Auerbach, Alan J., and Lawrence J. Kotlikoff (1987): Dynamic Fiscal Policy, Cambridge University Press, Cambridge.
Constantinides, George M., and Darrell Duffie, (1996), Asset Pricing with Heterogeneous Consumers, Journal of Political Economy, vol. 104, pages 219-240.
Deaton, Angus, and Christina Paxson, (1994): Intertemporal Choice and Inequality, Journal of Political Economy, vol. 102, pages 437-467.
Hassler, John, José V. Rodríguez Mora, Kjetil Storesletten, and Fabrizio Zilibotti (2001): A Positive Theory of Geographical Mobility and Social Insurance, CEPR Discussion Paper No. 2964.
Hassler, John, Kjetil Storesletten, and Fabrizio Zilibotti (2003): Democratic Public Good Provision, CEPR Discussion Paper No. 4044.
Heathcote, Jonathan, Kjetil Storesletten, and Gianluca Violante (2003): The Macroeconomic Implications of Rising Wage Inequality in the United States, Mimeo, Georgetown University.
Jagannathan, Ravi, and Narayana Kocherlakota (1996): Why Should Older People Invest Less in Stocks than Younger People?, Federal Reserve Bank of Minneapolis Quarterly Review vol. 20, pages 11-23.
Katz, Lawrence F., and David H. Autor (1999): Changes in the Wage Structure and Earnings Inequality, in Orley Ashenfelter and David Card (eds.), Handbook of Labor Economics, volume 3A, pages 1463-1555, North-Holland.
Krusell, Per, and José-Víctor Ríos-Rull (1999): On the Size of the U.S. Government: Political Economy in the Neoclassical Growth Model, American Economic Review, vol. 89, pages 1156-1181.
Ljungqvist, Lars, and Thomas J. Sargent (1998): The European Unemployment Dilemma, Journal of Political Economy, vol. 106, pages 514-550.
Mankiw, Neil G. (1986): The Equity Premium and the Concentration of Aggregate Shocks, Journal of Financial Economics, vol. 17, pages 211-219.
Ríos-Rull, José-Víctor (1994): On the Quantitative Importance of Market Completeness, Journal of Monetary Economics, vol. 34, pages 463-496.
Storesletten, Kjetil (2000): Sustaining Fiscal Policy through Immigration, Journal of Political Economy, vol. 108, pages 300-323.
Storesletten, Kjetil, Chris I. Telmer, and Amir Yaron (1999): The Risk Sharing Implications of Alternative Social Security Arrangements, Carnegie-Rochester Conference Series on Public Policy, vol. 50, pages 213-259.
Storesletten, Kjetil, Chris I. Telmer, and Amir Yaron (2001a): How Important Are Idiosyncratic Shocks? Evidence from Labor Supply, American Economic Review, vol. 91, pages 413-417.
Storesletten, Kjetil, Chris I. Telmer, and Amir Yaron (2001b): The Welfare Cost of Business Cycles Revisited: Finite Lives and Cyclical Variation in Idiosyncratic Risk, European Economic Review, vol 45, pages 1311-1339.
Storesletten, Kjetil, Chris I. Telmer, and Amir Yaron (2002): Asset Pricing with Idiosyncratic Risk and Overlapping Generations, Working paper, Carnegie Mellon University.
Storesletten, Kjetil, Chris I. Telmer, and Amir Yaron (2001b): The Welfare Cost of Business Cycles Revisited: Finite Lives and Cyclical Variation in Idiosyncratic Risk, European Economic Review, vol. 45, pages 1311-1339.
Storesletten, Kjetil, Chris I. Telmer, and Amir Yaron (2004a): Consumption and Risk Sharing over the Life Cycle, Journal of Monetary Economics, forthcoming.
Storesletten, Kjetil, Chris I. Telmer, and Amir Yaron (2004b): Cyclical Dynamics in Idiosyncratic Labor-market Risk, Journal of Political Economy, forthcoming.

Volume 4, Issue 2, April 2003

Tony Smith on Business Cycles and Inequality

Anthony A. Smith, Jr., is Associate Professor of Economics at Carnegie Mellon University. His field of research is frictions and heterogeneity in dynamic macroeconomic models. Smith’s RePEc/IDEAS entry.

How do business cycles affect inequality? What effects do business cycles have on the distributions of income, wealth, consumption, and, especially, welfare across different types of consumers? Are disadvantaged consumers–for example, the poor and the unemployed–more exposed to business cycle risk than the rich and the employed? These kinds of questions lie at the heart of much of the public debate about the costs and benefits of macroeconomic stabilization policy. Rather than focus on the average cost or benefit across the entire population, this debate instead typically centers on the question of who gains and who loses from macroeconomic policy. The distribution of gains and losses across the population also plays an important role in determining which macroeconomic policies (especially fiscal policies) are adopted in a democratic society. Because research on the interaction between inequality, business cycles, and macroeconomic policy is still in its infancy, we do not yet have satisfactory answers to many of the questions posed above. Nonetheless, this text describes a set of partial answers that Per Krusell and I provide in recent research to the question of how business cycles affect different groups in the economy. This text then suggests some avenues for future research.

In Krusell and Smith (2002), which is an extension of our earlier work in Krusell and Smith (1999), Per Krusell and I study the distributional implications of business cycle risk. Building on the work of Huggett (1993) and Aiyagari (1994), we construct a model of economic inequality in an environment featuring incomplete markets and business cycles. We then use this model to study the effects of a hypothetical macroeconomic stabilization policy that eliminates business cycles. The model is a version of the stochastic growth model with a large number of infinitely-lived consumers (dynasties). Consumers are ex ante identical, but there is ex post heterogeneity due to shocks to labor productivity which are only partially insurable. Consumers can accumulate capital (the single asset available) in order to partially smooth consumption over time. At each point in time, consumers may differ in the history of productivities experienced, and hence in accumulated wealth. Consumers also differ in their degree of patience: consumers’ discount factors evolve stochastically. The stochastic evolution of the discount factors within a dynasty captures some elements of an explicit overlapping-generations structure with altruism and less than perfect correlation in genes between parents and children (see also Laitner 1992, 2001). With this interpretation in mind, the stochastic process governing the evolution of the discount factors is calibrated so that the average duration of any particular value of the discount factor is equal to the lifetime of a generation. The purpose of the heterogeneity of the discount factors is to allow the model to replicate the observed heterogeneity in wealth, the key endogenous variable in the model.

A key equilibrium object in this class of models is the law of motion of the distribution of wealth. In principle, computing this object is a formidable task since the distribution of wealth is infinite-dimensional. In earlier work (see Krusell and Smith 1997, 1998), Per Krusell and I show, however, that this class of models, when reasonably parameterized, exhibits “approximate aggregation”: loosely speaking, to predict prices consumers need to forecast only a small set of statistics of the wealth distribution rather than the entire distribution itself. This result makes it possible to use numerical methods to analyze this class of models. More generally, this result opens the possibility of using quantitative dynamic general equilibrium models to study how the business cycle and inequality interact and to study the distributional effects of macroeconomic policies designed to ameliorate the effects of aggregate (macroeconomic) shocks.

Per Krusell and I use the model described above to provide a quantitative answer to the following question: If the aggregate shocks driving the business cycle are eliminated, how are different groups of consumers affected? We answer this question in the spirit of the celebrated calculation of Lucas (1987) in which Lucas finds that the welfare costs of business cycles are very small. In particular, we assume that removing business cycles does not change averages across cycles: both booms and recessions are eliminated and replaced by their average in a sense to be made precise below. In addition, we do not spell out an explicit macroeconomic policy that the government could use to eliminate business cycles. In this sense, our calculation, like Lucas’s, can be viewed as an upper bound on the welfare benefits (if any) of macroeconomic stabilization policy, since any actual policy would presumably introduce distortions that offset the positive effects of stabilization. Unlike Lucas, however, we do not simply replace consumption with its average (or trend) but instead replace the aggregate shocks by their averages and then allow consumers to make optimal choices in the new environment without cycles. By studying a general equilibrium environment, we also allow consumers’ new choices in response to the removal of aggregate shocks to have equilibrium effects on wages and interest rates. These general equilibrium effects on prices turn out to be quite important, as I describe below.

Replacing the aggregate technology shock and the unemployment rate (which varies exogenously in the model with cycles) with their averages is conceptually and technically straightforward. It is less obvious, however, how the basic idea of averaging across cycles should affect an individual consumer’s stochastic process for labor productivity. To accomplish the task of removing the aggregate shock from a consumer’s employment process, we adopt what we call the “integration principle”: fix an individual consumer’s “luck” and then average across realizations of the aggregate shock.

The key idea of this principle can be illustrated using a simple static example in which the economy is in either good times or bad times and an individual consumer is either employed or unemployed, where the probability of employment depends in part on whether the economy is in good or bad times. Let z denote the aggregate state, which takes on the value g (for “good”) with probability p and the value b (for “bad”) with probability 1-p, where 0<b<g<1. In good times (z=g), the unemployment rate is low and in bad times (z=b), the unemployment rate is high. Let i be a random variable uniformly distributed on the unit interval representing the consumer’s idiosyncratic “luck”. By assumption, a consumer’s luck is statistically independent of both the aggregate state and any other consumer’s luck (and, in a more general dynamic setting, of the past history of luck). Higher values of i mean worse luck: in particular, in the world with cycles, the consumer is employed if i<g and z=g or if i<b and z=b. Applying a law of large numbers across the continuum of consumers, this stochastic structure implies that the unemployment rate is g in good times and b in bad times.

To apply the integration principle in this example, fix i for each consumer and average over the good and bad realizations of the aggregate state z to obtain an outcome for the consumer’s labor productivity e. Consumers with sufficiently good luck (i<b) are employed in both good and bad times, so they are unaffected by averaging: e=1. Similarly, consumers with sufficiently bad luck (i>g) are unemployed in both good and bad times, so they too are unaffected by averaging: e=0. The fate of consumers in the intermediate range [b,g], however, does depend on the aggregate state. Averaging across realizations of the aggregate state, these consumers are employed with probability p and unemployed with probability 1-p, so e=p. As this example illustrates, averaging across the aggregate state in accordance with the integration principle reduces idiosyncratic risk: in the world with cycles, consumers receive only extreme outcomes (e=1 or e=0) but in the world without cycles, a fraction g-b of consumers receive an intermediate outcome (e=p), thereby reducing the cross-sectional variance of labor productivity.

Loosely speaking, using the integration principle to eliminate the effects of business cycles reduces idiosyncratic risk because some of this risk is correlated with the business cycle: when business cycles are removed, the part of the idiosyncratic risk that is correlated with the business cycle is removed too. In our realistically calibrated economy, we find that the cross-sectional standard deviation of labor productivity decreases by 16%. Thus the integration principle differs from the principle advanced in Atkeson and Phelan (1994) in which the removal of the business cycle simply removes correlation across consumers, leaving their processes for labor productivity unchanged.

I have explained the integration principle in detail because it lies at the heart of the differential effects of eliminating business cycles on different groups of consumers. The basic experiment that Per Krusell and I perform is to “freeze” the economy with cycles at a point in time, remove (via an unspecified and unanticipated macroeconomic policy) the business cycle shocks using the integration principle, and then track the behavior of the economy as it transits deterministically to a steady state. We then compare, using a consumption-equivalent measure as in Lucas (1987), the welfare of different consumers (as of the time of the removal of business cycles) in the worlds with and without cycles.

Our most striking finding is that the welfare effects of eliminating business cycles are U-shaped across different wealth groups, regardless of the state of the macroeconomy when the cycles are eliminated:in a nutshell, the poor and the rich gain while the middle class loses. As could be expected, the poor benefit directly from the reduction in uninsurable risk. The middle class and the rich care less about uninsurable risk because they have sufficient wealth to buffer employment shocks. General equilibrium effects on interest rates and wages, however, have important welfare implications for the middle class and for the rich. In response to the reduction in uninsurable risk, consumers in the aggregate accumulate less capital. As a result, interest rates rise (benefiting the rich for whom asset income is important) and wages fall (hurting the middle class for whom labor income is important). Looking across all consumers, there is a small average gain equivalent to 0.1% of consumption per period; this number is an order of magnitude larger than the costs of business cycles computed by Lucas (1987) in a representative-agent framework. This small gain, however, masks substantial heterogeneity across different types of consumers: the majority of consumers–the middle class–experience small welfare losses from the elimination of cycles, whereas the welfare gains of the poor and the rich are quite large: in the range of 4% for the poorest unemployed consumers and 2% for the richest consumers. These findings suggest that aggregate stabilization policies can substitute for social insurance policies: the poor benefit the most from the elimination of business cycle risk. At the same time, eliminating business cycle risk has significant distributional effects that an analysis based on a representative-agent framework fails to capture.

Another striking finding is that wealth inequality increases dramatically when business cycles are removed: for example, the Gini coefficient for wealth increases from 0.8 to 0.9 and the fraction of consumers with negative net worth increases from 11% to 31%. This spreading out of wealth stems from the heterogeneity in the degree of patience of different consumers. Although consumers’ discount factors are not permanently different, they are very persistent. If discount factors were in fact permanently different, then the distribution of wealth would spread out indefinitely, with the most patient consumers controlling all of the economy’s wealth, were it not for the uninsurable risk that provides an incentive for the least patient consumers to hold assets for precautionary reasons. When idiosyncratic risk is reduced, then, this precautionary motive on the part of the least patient (and hence poorest) consumers is mitigated to some extent, so that the heterogeneity in discount rates can operate more strongly to push the economy apart. Although wealth inequality increases, the integration principle implies that earnings inequality (which is exogenous in this model) decreases. At the same time, income inequality remains more or less unchanged while consumption inequality increases.

These findings also suggest an interesting policy experiment to be undertaken in future research. Rather than provide social insurance to the poor and unemployed indirectly by means of aggregate stabilization policy, instead let poor/unemployed consumers receive subsidies financed by taxing rich consumers. These subsidies are designed to mitigate the effects of the idiosyncratic risk that is felt most strongly by the poor and unemployed. These consumers will thus be made better off, as in the experiment described above. The welfare of the rich is affected in two ways. On the one hand, the taxes they face reduce their welfare. On the other hand, the social insurance funded by these taxes, by redistributing idiosyncratic risk from those who feel it the most strongly (the poor) to those who feel it the least strongly (the rich whose wealth allows them to absorb idiosyncratic shocks), reduces the effective amount of idiosyncratic risk in the economy. This reduction in risk reduces precautionary savings, so that the economy as a whole accumulates less capital and interest rates rise. This increase in interest rates improves the welfare of the rich and might be large enough to offset the welfare-reducing effects of taxation. Finally, as in the experiment described above, this set of policies might hurt the middle class by reducing their wages, but if these welfare losses are small the middle class could be compensated using only a small part of the tax revenue, the bulk of which is directed to the poor. In sum, it seems possible that this combination of fiscal policies–taxing the rich to provide insurance to the poor and to provide a small income subsidy to the middle class–could make everyone better off.

Although some of these findings are provocative, at least some of them are also quite sensitive to the manner in which Per Krusell and I have modeled inequality and, in particular, to the mechanisms that we are using to generate substantial wealth inequality as in U.S. data. Domeij and Heathcote (2002) and Castaneda, Diaz-Gimenez, and Rios-Rull (2002), for example, study models without heterogeneity in discount factors but with exogenous processes for labor productivity that are chosen, in part, to replicate facts about the distribution of wealth. In these models, a reduction in idiosyncratic risk (thanks to the elimination of business cycle risk) would, as in the model of Aiyagari (1994), reduce rather than increase wealth inequality. Other researchers have focused on entrepreneurship (see, for example, Quadrini 2000 and De Nardi and Cagetti 2002) and limited stock market participation (see, for example Guvenen 2002) as key mechanisms driving wealth inequality. Another set of researchers emphasizes the importance of different kinds of uninsurable shocks. Krebs (2002) studies the effects of business cycles in an environment in which consumers face idiosyncratic human capital risk. Storesletten, Telmer, and Yaron (2002a, 2002b) study the effects of business cycles in a life-cycle model with countercyclical variation in idiosyncratic risk. Finally, Angeletos and Calvet (2002) study models with idiosyncratic production rather than endowment risk and argue that in these environments reductions in idiosyncratic risk can increase rather than decrease aggregate savings.

In short, there currently exists a wide variety of research on inequality which emphasizes different kinds of fundamental mechanisms and different kinds of uninsurable shocks. As suggested above, these different environments can generate different answers to the question of how business cycles affect inequality and the distribution of welfare. In order to provide convincing quantitative answers to this question, then, future research will need to confront these various models to both macroeconomics and cross-sectional data in more rigorous ways and to search for deeper common elements linking the different models. Precisely because some of the answers provided by the framework that Per Krusell and I studied are intriguing, it is important to investigate the robustness of these answers to variations in the mechanisms and shocks underlying economic inequality and to seek further empirical evidence that might sort out the quantitative importance of the different approaches.

Another important item on the research agenda is to study the effects on inequality of explicitly specified macroeconomic stabilization policies, such as automatic stabilizers, cyclical unemployment insurance (see, for example, Gomes 2002), and international macro markets along the lines suggested by Shiller (1993, 2003).


Aiyagari, S. Rao (1994). “Uninsured Idiosyncratic Risk and Aggregate Saving“, Quarterly Journal of Economics, 109, 659-684.
Angeletos, George-Marios, and Laurent Calvet (2002). “Idiosyncratic Production Risk, Growth, and the Business Cycles”, manuscript (MIT).
Atkeson, Anthony, and Christopher Phelan (1994). “Reconsidering the Cost of Business Cycles with Incomplete Markets”, NBER Macreconomics Annual, 187-206.
Cagetti, Marco, and Cristina de Nardi (2002)’ “Entrepreneurship, Frictions and Wealth”, Federal Reserve Bank of Minneapolis Working Paper 620.
Castaneda, Ana, Javier Diaz-Gimenez, and Jose-Victor Rios-Rull (2002). “Accounting for the U.S. Earnings and Wealth Inequality”, Journal of Political Economy, forthcoming
Domeij, David, and Jonathan Heathcote (2002). “Factor Taxation with Heterogeneous Agents“, Stockholm School of Economics Working Paper Series in Economics and Finance 372.
Gomes, Joao (2002). “The Right Stimulus: Extended Unemployment Insurance Benefits or Tax Cuts?”, manuscript (Wharton School, University of Pennsylvania).
Guvenen, Fatih (2002). “Reconciling Conflicting Evidence on the Elasticity of Intertemporal Substitution: A Macroeconomic Perspective“, University of Rochester, Center for Economic Research (RCER) Working Paper 491.
Huggett, Mark (1993). “The Risk-Free Rate in Heterogeneous-Agent Incomplete-Insurance Economies”, Journal of Economic Dynamics and Control, 17, 953-969.
Krebs, Tom (2002). “Growth and Welfare Effects of Business Cycles in Economies with Idiosyncratic Human Capital Risk“, Brown University Working Paper 2002-31.
Krusell, Per, and Anthony A. Smith, Jr. (1997). “Income and Wealth Heterogeneity, Portfolio Selectio, and Equilibrium Asset Returns”, Macroeconomic Dynamics, 1, 387-422.
Krusell, Per, and Anthony A. Smith, Jr. (1998). “ Income and Wealth Heterogeneity in the Macroeconomy“, Journal of Political Economy, 106, 867-896.
Krusell, Per, and Anthony A. Smith, Jr. (1999). “On the Welfare Effects of Eliminating Business Cycles“, Review of Economic Dynamics, 2, 245-272.
Krusell, Per, and Anthony A. Smith, Jr. (2002). “Revisiting the Welfare Effects of Eliminating Business Cycles“, manuscript, Carnegie-Mellon University.
Laitner, John P. (1992). “Random Earnings Differences, Lifetime Liquidity Constraints, and Altruistic Intergenerational Transfers”, Journal of Economic Theory, 58, 135-170.
Laitner, John P. (2002). “Wealth Accumulation in the U.S.: Do Inheritances and Bequests Play a Significant Role?”, manuscript (University of Michigan).
Lucas, Jr., Robert E. (1987). Models of Business Cycles, Basil Blackwell, New York.
Quadrini, Vincenzo (2000). “Entrepreneurship, Saving and Social Mobility“, Review of Economic Dynamics, 3, 1-40.
Shiller, Robert (1993). Macro Markets: Creating Institutions for Managing Society’s Largest Economic Risks, Oxford University Press.
Shiller, Robert (2003). The New Financial Order: Risk in the 21st Century, Princeton University Press.
Storesletten, Kjetil, Christopher Telmer, and Amir Yaron (2002a). “Cyclical Dynamics in Idiosyncratic Labor-Market Risk”, Journal of Political Economy, forthcoming
Storesletten, Kjetil, Christopher Telmer, and Amir Yaron (2002b). “The Welfare Costs of Business Cycles Revisited: Finite Lives and Cyclical Variation in Idiosyncratic Risk”, European Economic Review 45, 1311-1339.

Volume 4, Issue 1, November 2002

Robert Shimer on Labor Market Frictions and Business Cycles

Robert Shimer is Associate Professor of Economics at Princeton University. His field of research is search and matching applied to labor markets. Shimer’s RePEc/IDEAS entry.

I would like to use this opportunity to discuss some of my recent research on the business cycle implications of labor market frictions. For reasons that I will discuss more below, I will frame my discussion in terms of the Mortensen-Pissarides matching model (Pissarides 1985, Mortensen and Pissarides 1994, and Pissarides 2000). This model has been used extensively for policy analysis, for example to examine the role that unemployment insurance and mandatory firing costs play in generating highunemployment rates in Europe (Pissarides 1999). With some exceptions (notably Merz 1995 and Andolfatto 1996), however, there has been little exploration of the model’s ability to match a standard set of business cycle facts. In a recent working paper (Shimer 2002a), I argue that the Mortensen-Pissarides model is quantitatively incapable of generating significant employment fluctuations in response to empirically plausible productivity shocks. That is, the model has almost no amplification mechanism. Despite this, the structure of the model allows us to think about other types of shocks that look to be a much more promising explanation for business cycle fluctuations.

The Mortensen-Pissarides Matching Model

I begin by describing the simplest version of the Mortensen-Pissarides matching model. There are two types of agents, workers and firms, both risk-neutral and infinitely-lived with a common discount rate. Workers may be either employed or unemployed. Employed workers earn an endogenous wage w but may not search for another job. Unemployed workers get a fixed payment b and may find a job. Firms have access to a production technology with constant returns to scale in labor. That is, each employed worker yields a fixed revenue p and must be paid the wage w. To hire new workers, firms must create a vacancy at a per-period cost of c. In other words, a firm’s per-period profits are n(p-w) – c v, where n is the number of employees and v is the number of vacancies. Free entry drives the discounted profits from creating a vacancy to zero.

Rather than modelling the search process explicitly, the Mortensen-Pissarides model reduces it to a black-box “matching function”. Let U denote the fraction of workers who are unemployed and V denote the number of vacancies in the economy. Then the number of matches is a function M(U,V), increasing in both arguments. The standard assumption is that this function has constant returns to scale, which implies that each unemployed worker finds a job with probability M(U,V)/U and each vacancy is filled with probability M(U,V)/V, both functions only of the vacancy-unemployment ratio V/U. The vacancy-unemployment ratio, and hence the rate at which unemployed workers find jobs, is in turn determined endogenously by firms’ collective vacancy decisions.

In the simplest version of the Mortensen-Pissarides matching model, the job destruction decision, i.e. the probability with which employed workers become unemployed, is treated as exogenous: all matches end with probability d per period. Mortensen and Pissarides (1994) extend this simple model to endogenize the job destruction decision.

A central feature of this model is that the matched worker and firm are in a bilateral monopoly situation. That is, an employed worker could always leave her job and find another employer; however, because search is time-consuming, workers are impatient, and all jobs are identical, she prefers to work for her current employer. Likewise, a firm could fire an employee and attempt to hire another one, but this will take time and will not yield a better match. There are many wages consistent with the pair agreeing to match, and so the model provides little guidance as to how wages are determined. Pissarides (1985) assumes wages satisfy an axiomatic Nash bargaining solution. A worker’s threat point is unemployment and a firm’s threat point is a vacancy. The two agents split the gains from production in excess of this threat point.

From the perspective of a matched worker and firm, wage bargaining is a zero sum game with distributional but not allocational consequences, and so the Nash bargaining assumption might seem innocuous. But from an aggregate perspective, wage bargaining matters. Firms’ expectations of future wages is crucial to their job creation decisions, which balance the up-front cost of creating a vacancy against the expected profits from employing workers. If firms anticipate having to pay high wages in the future, they will be reluctant to create vacancies today, reducing job creation and raising the unemployment rate.

Although the central role that wage bargaining plays in the determination of employment and unemployment rates in the Mortensen-Pissarides model is sometimes seen as a shortcoming, I will argue below that the bilateral monopoly situation is the reason why we can use the model to think about a different type of shock that looks to be a promising explanation for at least some part of business cycle fluctuations. In a reduced form model, these shocks amount essentially to changes in workers’ bargaining power.

Quantitative Behavior

In Shimer (2002a), I examine a stochastic version of this simple model, with shocks driven by a first-order autoregressive process for productivity, p, and the job destruction rate, d. At any point in time, the state of the economy is described by the current level of productivity, the current job destruction rate, and the current unemployment rate. In principle, the curse of dimensionality should make this problem very difficult to handle computationally. But I show that the equilibrium vacancy-unemployment ratio and wage can be expressed as functions only of the first two state variables, productivity and the job destruction rate. Moreover, both functions are easy to compute numerically — and in some special cases, analytically. After computing the vacancy-unemployment ratio at each productivity level and job destruction rate, I simulate a large number of paths and recover the stochastic properties of unemployment, vacancies, and wages in response to these exogenous shocks.

I choose model parameters to match as many macro/labor facts as possible. Due to its simplicity, the model cannot replicate some standard business cycle facts (Cooley and Prescott 1995). For example, there is no investment or capital in this model; and the risk-neutrality assumption implies the intertemporal elasticity of substitution is infinite. But there are a number of other facts that the model potentially can match. One that is particularly important is the cyclical behavior of vacancies and unemployment. The correlation between the detrended time series for the two variables is strongly negative, -0.88 (Abraham and Katz 1986, Blanchard and Diamond 1989), and they have approximately the same standard deviation of the percent deviation from trend. That is, if unemployment is 17 percent below trend (5 percentage points instead of 6 percentage points), vacancies are approximately 17 percent above trend. This means that the vacancy-unemployment ratio, and hence the ease of finding a job, is strongly procyclical. On the other hand, wages and productivity are much less variable and much less correlated with either vacancies or unemployment.

I next consider the behavior of the model economy in response to a productivity shock. Qualitatively, this raises the profit from a filled job p – w, encouraging firms to create vacancies. A higher vacancy-unemployment ratio decreases the rate at which vacancies are filled, restoring the zero profit condition. It also makes it easier for workers to find jobs, lowering the unemployment rate. Under reasonable parameter restrictions, vacancies and unemployment move in opposite directions, along a downward sloping “Beveridge curve,” consistent with the previously mentioned fact. But quantitatively, almost all of a productivity shock accrues to workers in the form of higher wages, leaving only a muted response of vacancies and unemployment. Equivalently, it takes an unrealistically large productivity shock to generate reasonable movements in vacancies and unemployment. The model offers little amplification of the underlying shocks.

I also consider the economy’s response to a job destruction shock. This has a direct effect on the unemployment rate because the employment-to-unemployment transition rate increases. It also has an indirect effect: a decline in the expected future duration of jobs discourages vacancy creation. This raises average unemployment duration and further increases the unemployment rate. Moreover, the increase in unemployment duration tends to reduce wages slightly, mitigating the decline in profits. In net, I find a large response of the unemployment rate to a job destruction shock but little movement in the vacancy-unemployment ratio or wages. As a result, vacancies and unemployment are counterfactually positively correlated in response to such shocks, while wages are realistically rigid.

If one only wanted to explain a subset of the data, the model behaves quite well. For example, Blanchard and Diamond (1989), Mortensen and Pissarides (1994) and Cole and Rogerson (1999) find that the model can match the behavior of unemployment and vacancies (as well as some other variables), but do not examine the behavior of wages. Essentially, these papers introduce unrealistically large productivity shocks in order to generate fluctuations. On the other hand, Ramey and Watson (1997) and Pries (2002) assume that job finding rates are constant and exogenous or equivalently that the vacancy-unemployment ratio is acyclical. Both models generate large unemployment changes associated with only moderate wage fluctuations. Similarly, in the Lucas and Prescott (1974) search model, workers seek production opportunities available in an exogenously-determined supply. Models in this framework (e.g. Gomes, Greenwood, and Rebelo 2001) therefore cannot explain why the vacancy-unemployment ratio is procyclical, although they are again capable of matching the cyclical behavior of wages. It is only by looking simultaneously at the behavior of unemployment, vacancies, wages, and productivity that the difficulty of matching the business cycle facts emerges. The lesson to take away from this is that it is important to explore models quantitatively along as many dimensions as possible.

Alternative Wage Setting Assumptions

Wage flexibility, particularly wage flexibility in new jobs, is central to these results. Suppose there was a productivity increase, but firms did not expect wages in new jobs to change. This would amplify the effect on firm entry, since firms would enjoy all of the productivity increase in the form of higher profits. Conversely, if firms anticipated declining wages without an associated change in productivity, this would also lead to an increase in entry and a decline in the unemployment rate. Moreover, quantitatively both of these effects are likely to be big. For example, firms’ economic profits are at least an order of magnitude smaller than their wage bill, so a one percent decline in wages leads to at least a ten percent increase in profits and an associated spurt in job creation. (On the other hand, rigidity of wages in old jobs, perhaps due to implicit or explicit wage contracts, has no effect on job creation.)

An assertion that that rigid real wages amplify productivity shocks and that wage shocks are an important source of business cycle fluctuations is unsatisfactory. From a theoretical perspective, one would like to know why real wages are rigid in response to productivity shocks and yet sometimes change in the absence of such shocks. From a normative perspective, it is impossible to analyze a change in labor market policies in the absence of a policy-invariant model of wages. The important next step is therefore to develop alternative models of wage determination from first principles, which do not have a strong link between wage and productivity movements.

One feature of the labor market that may be important in this regard is asymmetric information. A firm knows more about its productivity than does an employee, while a worker knows more about her outside opportunities than does her employer. For a worker to signal that she has a good outside opportunity is costly. She must leave the firm. Likewise, for a firm to credibly signal that it has low productivity is costly. It must typically lay off some workers or sharply reduce the hours of existing employees. The wage also plays an important role, conveying information to the worker about the firm’s productivity — it is at least willing to pay her wage — and to the firm about the worker’s outside opportunities — she is at least willing to work at that wage.

In Shimer (2002b), I develop a simple model with one-sided asymmetric information. A worker does not know how productive her job is. She is able to make take-it-or-leave-it wage demands, but is reluctant to ask for too high a wage because, if the firm refuses her demand, she is laid off. There are two important determinants of wages in this model. First, workers examine the hazard rate of the productivity distribution. If the hazard rate is large, asking for a higher wage is risky, i.e. it results in a substantial increase in the layoff probability. Second, workers consider how long it will take to get another job offer. If job offers are scarce, workers will be reluctant to risk demanding a high wage. This also feeds back into firm behavior. If firms anticipate that workers will demand high wages, they will create few jobs, making job offers scarcer and suppressing wage demands. In parametric examples, I find that an increase in mean productivity raises wages and reduces unemployment, much as in a model with symmetric information. An increase in the variance of productivity lowers wages and has an ambiguous effect on unemployment, an effect that is absent from models with symmetric information. If recessions are periods of low mean productivity and high variance, as Storesletten, Telmer, and Yaron (2001) suggest, we would observe little variation in wages and significant declines in employment.

The wage setting regime, i.e. workers making take-it-or-leave-it wage demands, is important for these results. Since there is no reason to believe that this is an accurate characterization of wage setting in reality, relaxing this assumption is desirable. Of course, any other wage-setting assumption faces the same criticism. An alternative possibility is to focus on Pareto optimal incentive-compatible mechanisms in an economy with two-sided asymmetric information. Here the tools developed in the endogenous incomplete markets literature (e.g. Spear and Srivastava 1987, Thomas and Worrall 1990, Atkeson and Lucas, 1992) are likely to prove useful. It is an open question whether such a model predicts significant employment fluctuations in response to modest exogenous shocks.


Abraham, Katharine, and Lawrence Katz (1986): “Cyclical Unemployment: Sectoral Shifts or Aggregate Disturbances?,” Journal of Political Economy, 94, 507-522.
Andolfatto, David (1996): “Business Cycles and Labor-Market Search,” American Economic Review, 86, 112-132.
Atkeson, Andrew and Robert Lucas (1992): “On Efficient Distribution with Private Information,” Review of Economic Studies, 59, 427-453.
Blanchard, Olivier, and Peter Diamond (1989): “The Beveridge Curve,” Brookings Papers on Economic Activity, 1, 1-60.
Cole, Harold, and Richard Rogerson (1999): “Can the Mortensen-Pissarides Matching Model Match the Business-Cycle Facts?,” International Economic Review, 40, 933-959.
Cooley, Thomas, and Edward Prescott (1995): “Economic Growth and Business Cycles,” in Frontiers of Business Cycle Research, ed. by Thomas Cooley. Princeton University Press, New Jersey.
Gomes, Joao, Jeremy Greenwood, and Sergio Rebelo (2001): “Equilibrium Unemployment,” Journal of Monetary Economics, 48, 109?152.
Lucas, Robert and Edward Prescott (1974): “Equilibrium Search and Unemployment,” Journal of Economic Theory, 7, 188-209.
Merz, Monika (1995): “Search in the Labor Market and the Real Business Cycle,” Journal of Monetary Economics, 36, 269?300.
Mortensen, Dale, and Christopher Pissarides (1994): “Job Creation and Job Destruction in the Theory of Unemployment,” Review of Economic Studies, 61, 397-415.
Pissarides, Christopher (1985): “Short-Run Equilibrium Dynamics of Unemployment, Vacancies, and Real Wages,” American Economic Review, 75, 676-690.
Pissarides, Christopher (1999): “Policy influences on unemployment: The European experience,” Scottish Journal of Political Economy, 46, 389-418.
Pissarides, Christopher (2000): “Equilibrium Unemployment Theory”. MIT Press, Cambridge, MA, second edition.
Pries, Michael (2002): “Persistence of Employment Fluctuations: A Model of Recurring Job Loss,” forthcoming Review of Economic Studies.
Ramey, Gary, and Joel Watson (1997): “Contractual Fragility, Job Destruction, and Business Cycles,” Quarterly Journal of Economics, 112, 873-911.
Shimer, Robert (2002a): “The Cyclical Behavior of Equilibrium Unemployment, Vacancies, and Wages: Evidence and Theory,” Mimeo.
Shimer, Robert (2002b): “Wage Setting with Asymmetric Information,” Mimeo.
Spear, Stephen and Sanjay Srivastava (1987): “On Repeated Moral Hazard with Discounting,” Review of Economic Studies, 54, 599-617.
Storesletten, Kjetil, Chris Telmer, and Amir Yaron (2001) “Asset Pricing with Idiosyncratic Risk and Overlapping Generations,” Mimeo.
Thomas, Jonathan and Tim Worrall (1990): “Income Fluctuation and Asymmetric Information: An Example of a Repeated Principal-Agent Problem,” Journal of Economic Theory, 51, 367-390.

Volume 3, Issue 2, April 2002

Peter Howitt on Schumpeterian Growth Theory

Peter Howitt is the Charles Pitts Robinson and John Palmer Barstow Professor and Professor of Economics, Brown University. He has published extensively on growth theory and monetary theory. Here he reports on his latest research on growth theory. Peter Howitt’s RePEc/IDEAS entry.

Over the past 15 years, much of my time has been spent developing a new generation of endogenous growth theory, together with Philippe Aghion. Our original contribution was Aghion and Howitt (1992). We have since generalized the simple model of that paper considerably and applied it to a variety of different questions. Most of what we have done is contained in our recent book (Aghion and Howitt, 1998a). Our theory is based on Schumpeter’s concept of “creative destruction.” It portrays a free enterprise economy that is constantly being disturbed by technological innovations from which some people gain and others lose, an economy in which competition is a Darwinian struggle whose survivors are those that succeed in creating, adopting and improving new technologies.Schumpeterian theory differs fundamentally from the earlier AK versions of endogenous growth theory, in which technological progress was portrayed as just another form of capital accumulation. In AK theory, the mainspring of growth was the private process of thrift, an essentially private process involving no interpersonal conflicts. Schumpeterian theory recognizes that, on the contrary, technological change is a social process, and that ever since the start of the Industrial Revolution, people’s skills, capital equipment and technological knowledge have been rendered obsolete and destroyed by the same inventions that have created fortunes for others. Our new theory treats innovation as a separate activity from saving, and it is explicit about who gains from it, who loses, how the gains and losses depend on social arrangements, and how such arrangements affect society’s willingness and ability to progress. The rest of this essay discusses some of the insights that the theory provides into four different issues: competition, patent policy, cross-country income differences and technological revolutions.

Competition and Economic Growth

The earliest Schumpeterian growth models predicted that competition should reduce growth, through a well-known appropriability effect; that is, by reducing the prospective monopoly rents that spur innovation. The available evidence seems however to contradict this prediction. This evidence has sent us back to the drawing board, and the result of this rethinking has been a more sophisticated version of Schumpeterian theory containing a variety of channels through which competition might in fact spur economic growth. The simplest of these involves barriers to entry. To the extent that these barriers raise the cost to outside firms of introducing new technologies, they reduce the incentive to perform R&D, thus reducing the long-run growth rate.Consider next the role of agency costs that allow managers to operate businesses in their own interests rather than maximizing the owners’ profits. Aghion et al (1999) have shown that when these costs are severe, competition can act as a stimulus to growth. In their model, each firm is controlled by a manager who is interested primarily in minimizing effort, but who wants the firm to remain solvent in order to continue enjoying the non-monetary benefits of control. Since innovation takes effort, the manager will innovate only as often as needed to remain solvent. To the extent that an increase in competition reduces the firm’s flow of profits it reduces the scope for managerial slack, and forces managers to innovate more often.

We explore another channel in Aghion et al (2001), which takes into account not just the absolute level of profits obtained by a successful innovator but the incremental profits; that is, the difference between the profits of a firm that innovates and one that does not. In the basic first-generation Schumpeterian model such a distinction did not arise because in equilibrium all important innovations were made by outside firms, owing to the replacement effect first analyzed by Arrow. In this paper we assume there are decreasing returns to R&D at the firm level, as the evidence suggests there are; this means that incumbent firms will engage in at least some R&D despite the Arrow effect. We show that although an increase in the intensity of competition will tend to reduce the absolute level of profits realized by a successful innovator, it will tend to reduce the profits of an unsuccessful innovator by even more. Therefore competition can have a positive overall effect on the rate of innovation because firms will try to innovate in order to escape competition. Thus we have a variety of theoretical reasons for doubting that the commonly accepted tradeoff between static efficiency and growth exists. Ongoing econometric investigations that we are undertaking with Bloom, Blundell and Griffith (Aghion et al., 2002) provide strong support for a non-linear relationship in which competition has a positive effect up to a certain point, beyond which it retards growth, as in the framework of Aghion et al (2001).

Patent Policy

Schumpeterian growth theory has shown that the case for stronger protection is not as clear cut as it might seem. For example, the above-mentioned analysis of Aghion et al (2001) shows that stronger patent protection can in some cases reduce the overall pace of technological change, through a “composition effect.” We consider a world with a large number of industries, each of which has two incumbent firms, each with its own technology that is improved from time to time by random innovations. Innovation takes place at the greatest rate in those industries where the two firms are technologically neck-and-neck, because this is where the incentive to escape competition is the greatest. If patent laws were weakened, the incentive to innovate of a firm with any given lead would indeed be blunted, but the steady-state distribution of lead sizes would also be changed; specifically, more firms would be forced to engage in neck-and-neck competition because of a rival’s successful imitation. As a result, a little bit of imitation almost always has the overall effect of raising the economy’s long-run rate of technological progress and therefore of raising the long-run growth rate.Grossman and Helpman (1991) used Schumpeterian growth theory to show that strengthening international patent protection in the South can even weaken the incentive to perform R&D in the North. This happens through a rise in Northern wages; as few products get imitated, more of them remain in production in the North, and this raises the demand for labor in the North, leading to an increase in wages and hence drawing labor out of R&D and into manufacturing. The overall result is thus a decrease in the rate of growth not just in the South but also in the North.

Cross-country income differences

Cross-country comparisons of per-capita GDP have constituted the testing ground of growth theories in recent years. No theories have fared well in these tests. The AK model implies that differences in per-capita GDP among countries should be widening over time. But Evans (1996) has shown that this prediction is clearly refuted by postwar OECD data. Similar refutations of early endogenous growth theories have come from the growth regressions showing conditional beta-convergence.Some have argued that these results support neoclassical theory; that what accounts for differences in income between rich and poor nations is differences in capital accumulation, not differences in technological progress. However, the neoclassical model founders on the fact that convergence appears limited to a select group of rich countries. That is, the data tend to support a theory of “club convergence.”

One model that fits all this evidence is the multi-country Schumpeterian model of Howitt (2000). In this model, each time a firm in one sector of one country innovates by inventing a new intermediate product, the productivity of that intermediate product is determined by a world-wide technology frontier that grows as a result of innovations throughout the world. As long as a country maintains enough incentives that some domestic innovation takes place, it will join the convergence club, and its growth rate will ultimately converge to that of all the other members.

The mechanism through which convergence occurs in this model is technology transfer. That is, the growth rate of productivity equals the product of the frequency and size of innovations. A country that spends little on R&D may temporarily grow slower than the rest of the convergence club, but in the long run the technology currently in use in almost all its industries will be very far from the world frontier. Thus each innovation when it occurs will represent a relatively large improvement over the technology already in place in that industry. In other words, a low frequency of innovations will ultimately generate such a large size of innovations that the product of frequency and size converges to the common world growth rate. In this same model, countries in which conditions are so unfavorable to R&D as to shut down domestic innovation entirely will not grow at all, because R&D is a necessary channel of technology transfer. These countries will stagnate, falling further and further behind the others. Thus the world distribution of per-capita GDP will show the emerging “twin peaks” that Quah claims to have found in the data.

Whether this multi-country Schumpeterian theory bears up under further empirical investigation remains to be seen. Some initial empirical support for the theory is provided by the results of Coe and Helpman (1995) and Coe, Helpman and Hoffmaister (1997), who show that the international R&D spillovers on which the theory is based are indeed substantial. Also, Feyrer (2001) has shown that the emergence of twin peaks in the world income distribution is largely accounted for by emerging twin peaks in productivity, as would be the case in this model.

General Purpose Technology

The destructive side of creative destruction is not just a microeconomic phenomenon. Indeed the whole economy can suffer, at least during a transitional period, as a result of widespread technological change. This is especially true when that technological change involves the introduction of a new “General Purpose Technology” (GPT); that is, a new technology that is used throughout the economy, has a profound effect on the way economic life is organized, and gives rise to a wave of complementary innovations associated with its increasing use. In the long run our standard of living has been greatly enhanced by the succession of GPTs that have been introduced since the first Industrial Revolution. However, the period during which a new GPT is being introduced can be a period of wrenching adjustment, not just at the level of the individual firm but for the economy as a whole.There are many aspects to this adjustment cost. Helpman and Trajtenberg (1998) emphasize the lost output that occurs because the GPT does not arrive ready to use but requires the invention of a set of complementary components. During the period when the components are being developed, the new GPT will not yet be in use. Meanwhile the labor that is drawn into developing new components will be drawn out of producing final output. The result will be a fall in the overall level of output.

Others have pointed out a variety of additional channels through which the cost of adjusting to a new GPT can show up at the macroeconomic level. Greenwood and Yorukoglu (1997) argue that real resources are used up in learning to use the new GPT. Aghion and Howitt (1998b) point out that the process of reallocating labor from sectors using older technologies to those using the new GPT may involve a rise in unemployment, for the same reason that any large reallocation of labor often entails unemployment in a less than frictionless economic system. Howitt (1998) calibrates to U.S. data a Schumpeterian model with capital-embodied technological change, and shows numerically that the introduction of a new GPT that raises the productivity of R&D by 50% until overall productivity has doubled will reduce the level of per-capita GDP below the path it would otherwise have followed, for a period of about two decades, through induced obsolescence of human and physical capital. Thus it seems that Schumpeterian growth theory may have something to say about the productivity slowdown that occurred between the mid 1970s and the mid 1990s. The results of Howitt (1998) exemplify an important general aspect of the dynamics of Schumpeterian growth models. In the short run, as in the neoclassical model of Solow and Swan, the growth rate in output per person can be decomposed into two components, one depending on the rate of capital deepening (the increase in capital per efficiency unit of labor), and the other depending on the rate of technological progress. Technological progress is the only component that matters in the long run, because the amount of capital per efficiency unit of labor will stop growing as it approaches its long-run equilibrium value. But capital deepening is quantitatively the component that dominates the economy’s transitional dynamics, often for long periods of time, and it very often goes in the opposite direction to technological progress. The presence of such long lags makes the theory difficult to estimate and test using time-series data, but Zachariadis (2001) has shown how to overcome these difficulties using cross-sectional evidence.


Aghion, Philippe, Nicholas Bloom, Richard Blundell, Rachel Griffith and Peter Howitt 2002. “Competition and Innovation: An Inverted U Relationship,” unpublished.
Aghion, Philippe, Mathias Dewatripont, and Patrick Rey 1999. “Competition, Financial Discipline and Growth.” Review of Economic Studies. Vol. 66, pages 825-52.
Aghion, Philippe, Christopher Harris, Peter Howitt, and John Vickers 2001. “Competition, Imitation and Growth with Step-by-Step Innovation.” Review of Economic Studies. Vol. 68, pages 467-92.
Aghion, Philippe, and Peter Howitt 1992. “A Model of Growth through Creative Destruction.” Econometrica. Vol. 60, pages 323-51.
Aghion, Philippe, and Peter Howitt 1998a. Endogenous Growth Theory. Cambridge, MA: MIT Press.
Aghion, Philippe, and Peter Howitt 1998b. “On the Macroeconomic Effects of Major Technological Change.” In General Purpose Technologies and Economic Growth, edited by Elhanan Helpman, 121-44. Cambridge, MA: MIT Press.
Coe, David T., and Elhanan Helpman 1995. “International R&D Spillovers.” European Economic Review. Vol 39, pages 859-87.
Coe, David T., Elhanan Helpman, and Alexander W. Hoffmaister 1997. “North-South R&D Spillovers.” Economic Journal. Vol. 107, pages 134-49.
Evans, Paul 1996. “Using Cross-Country Variances to Evaluate Growth Theories.” Journal of Economic Dynamics and Control. Vol. 20, pages 1027-49.
Feyrer, James 2001. “Convergence by Parts.” Unpublished, Brown University.
Greenwood, Jeremy, and Mehmet Yorukoglu 1997. “1974.” Carnegie-Rochester Conference Series on Public Policy. Vol. 46, pages 49-95.
Grossman, Gene M., and Elhanan Helpman 1991. “Quality Ladders and Product Cycles.” Quarterly Journal of Economics. Vol. 106, pages 557-86.
Helpman, Elhanan, and Manuel Trajtenberg 1998. “A Time to Sow and a Time to Reap: Growth Based on General Purpose Technologies.” In General Purpose Technologies and Economic Growth, edited by Elhanan Helpman. Cambridge, MA: MIT Press.
Howitt, Peter 1998. “Measurement, Obsolescence, and General Purpose Technologies.” In General Purpose Technologies and Economic Growth, edited by Elhanan Helpman, 219-51. Cambridge, MA: MIT Press.
Howitt, Peter 2000. “Endogenous Growth and Cross-Country Income Differences.” American Economic Review. Vol. 90, pages 829-46.
Zachariadis, Marios 2001. “R&D, Innovation and Technological Progress: A Test of the Schumpeterian Framework without Scale Effects.” Unpublished, Louisiana State University.
Volume 3, Issue 1, November 2001

José-Víctor Ríos-Rull on the Determinants of Inequality

José-Víctor Ríos-Rull is Professor of Economics at the University of Pennsylvania. His main interests lie in distributional issues in macroeconomics, public economics and demographic economics. Ríos-Rull’s RePEc/IDEAS entry.

I want to take advantage of this opportunity that the EconomicDynamics Newsletter provides me to discuss some questions that interest me, and some tools that we are developing in addressing those questions.A good part of my research has dealt with the determinants of inequality. A large dose of the effort in public policy is aimed to redistribute resources among persons, and this can only be done effectively if we understand what is it that makes people different in the first place. In this respect, we (Castañeda, Díaz-Gimenez and Ríos-Rull (2000)) have estimated a model with temporary (but autocorrelated) shocks to earnings capabilities that generates a distribution of labor earnings and wealth as well as a set of macromagnitudes and a tax system that is similar to that of the U.S. In this model all agents share the same preferences and they differ in age, wealth and in the realization of the earnings shock. The model essentially estimates the properties of a stochastic process for earnings opportunities. This process has built in some life cycle features and some potential for intergenerational transmission of earnings. Our findings state that most of the differences in earnings potential are already there at the beginning of adulthood. Specifically, our estimates decompose the population into four types according to the realization of the shock. In the beginning of adulthood, the differences in the present value of earnings among these four types are large. If the majority of the population is normalized to one, the other three groups show present values for earnings that are 1.63, 4.66 and a whopping 74.93 (this latter group is very small in size) times bigger. Moreover, these characteristics persist over generations. Households at retirement have expected values for their progenie of 1.00, 2.47, 27.92 and 46.56 respectively.

With very different methods, Keane and Wolpin (1997) points to the fact that differences in the fate of people are determined very early in life. Essentially they find that, utility-wise, cross sectional differences are accounted for mostly (90%) by features already present in agents by age 16 rather than in the actual shocks that the agents receive after age 16. Knowles (2001) argues that the explicit consideration of fertility choice and its associated implication of a negative relation between fertility and parental education, changes the implications of models where agents smooth consumption by holding assets when facing uninsurable shocks. In particular, wealth dispersion is greatly increased.

These findings point out something quite important that most differences in economic performance do not occur in the strict realm of the labor market. On the contrary, they have occurred by the time people enter the labor market.

Inspired by these findings, part of my research is now devoted to the understanding of how the family shapes the economic performance of individuals and of their progenie. This requires the construction of models that explicitly take into account that households and individuals are very different entities (going against the old tradition in economics that treats households as the basic economic unit). These models owe a lot to the work of Gary Becker who brought the family to the realm of economics.

These structures have still to be embedded in models of the macroeconomy that display aggregate characteristics that can be mapped back to aggregate data in order to discipline the research. The discipline comes partly due to the quantitative restrictions imposed by macroeconomic aggregates, and partly from the general equilibrium restrictions that the model imposes (things like the number of males of type x married to females of type y, is equal to the number of type y females married to type x males). The key paper in bringing the family to macroeconomics is Aiyagari, Greenwood and Guner (2000).

The basic structure of aggregate models with families

Let me summarily describe how these models operate. Agents differ typically in age, sex, and other economically relevant characteristics such as education or skill. Agents, upon becoming adults, bump into each other and choose whether to form a household, and/or, in the case of females choose whether to try to have a child. Their decisions depend on who they bump into, their general characteristics (age, marital status, education, skills) and perhaps something that is not shared by others, a personal assessment, love in one word. The decisions depend not only on who they bump, but also on what else is out there, this is on what agents expect to happen in the future. Forming a household provides some advantages beyond the pure joy of being together: there are increasing returns to consumption, opportunities to share income risks, and to take advantage of division of labor between home and market activities, as well as the possibility of jointly raise children over whom they have altruist feelings. Besides the decisions of the agents regarding family formation, there are typically some form of consumption/savings decision either in the form of financial assets or in the form of educational investment in the children.

Other questions that are currently addressed

There are some recent social changes that we are addressing that require models with explicit household formation. They include the actual decrease in married couples that has occurred in the U.S. in the last 25 years and that can be accounted for by the increase of both absolute and relative female wages (Regalia and Ríos-Rull 2001). A similar issue that is currently under study is the formidable increase in female (and not so much male) college attendance that has occurred in the last 25 years. To understand it we have to start understanding why it was that men used to go more to college than women. This is not so clear. In recent work (Ríos-Rull and Sanchez 2001) we found that it is not because of parental preference or of cheaper costs of attendance for males, rather it seems that by attending college males acquire a lot more than just higher wages, they became better parents (in the sense that they are more able to educate their children). A student of mine, Nishiyama (2002) tackles some properties of the wealth distribution and of precautionary savings using models where parents and children coexist and where the parents altruistic feelings generate both bequests and inter-vivos transfers. In this way he can measure to what extend parents have altruistic feelings over their children (note that the two workhorses in macroeconomics the infinitely lived dynastic model and the overlapping generations model assume either that parents care about their children as much as they care about themselves or not at all). He finds that parents care about their children about half as about themselves. In another work (Cubeddu and Ríos-Rull 1998) we explore how divorce operates in pretty much the same way as an uninsurable earnings shock, and a very large one at that. Another student of mine, (Bethencourt 2002) is exploring the changes in living arrangements between adult households and there elderly mothers.

Other questions that I would like to address

The interrelation of quantitatively theoretical economic models (models with explicit utility maximization and with the equilibrium requirement of compatibility between agents decisions that can be explicitly solved and compared with data) with demographics is likely to go forward and be used to address more issues. Central among them is, I think, the issue of differential mortality. Life expectancy differs a lot among groups of people, for example, women live more than men (a feature that could perhaps be imputed to better engineering). But more interesting to economists is that married men, and educated men live longer that their single and uneducated counterparts. To understand why is very important: imagine it is that education or income is it that allows people to access better care, or at least to be informed about healthier life styles, then perhaps well intentioned governments may want to subsidize education or health care or even redistribute income in order to increase life expectancy. If, however, the characteristics that makes people be educated and have high income also make them live longer (such as a higher valuation of the future) then the ability of governments to affect life expectancy is much more limited and redistributive policies and policies that subsidize education and health care lose a lot of their appeal.

New technical challenges that have appeared

Models of the family present numerous challenges that have to be addressed. I will now discuss some of those challenges.First and foremost, the household does not have preferences, the individuals do. Somehow, we have to aggregate from the individuals to the household in order to attain an operational decision rule. One way to do this is to formulate the problem in a such a way that both adult household members agree over the allocations of resources. This is not always easy since they may have different time horizons or because the household may break up. Another way to deal with this is to find the allocation that solves a weighted average of the utilities or even (better) to assume a bargaining process between the household members that yield a specific allocations.

Second, the use of models with families brings to the forefront of quantitative economic theory a set of functional forms and parameters that are new and that cannot be clearly related to other work that we do. Things like the human capital acquisition and evolution, the characteristics of affection between people, the mapping between intent and success of having children and so on and so forth. The old way of mapping models to data in macroeconomics by mere parameter picking shows its shortcomings very clearly now. Therefore, calibrating models with families can only be done as part of an explicit estimation process (something that is also behind other work in macroeconomics, although perhaps not so clearly). An obvious way of calibrating these models is then by specifying a list of statistics that the model has to match, and choosing the parameters that do that in the best possible way. This process is also known as exactly identified method of moments, and it is certainly not the only way to do it, but it has the very nice implication of cleanly separating what the model is restricted to do and what the model can tell us. Using a more general version of GMM estimators has the disadvantage that there is a lack of clear separation between what the model can be used for and what is imposed in the model.

Third, related to the previous point, there is now a new set of statistics that can be used as calibration targets, or more generally, to compare model and data. Of course, we still use the same aggregate statistics that allow us to relate to the whole economy and that impose a tremendous amount of discipline such as consumption to output ratio, wealth to output ratio and others. Understanding inequality implies understanding the cross-sectional distribution of wages, hours worked, consumption, education and wealth. But now, these statistics can be looked at in a new light. The data for those variables is collected sometimes at household level and sometimes at person level. Models that explicitly incorporate families allow us to look simultaneously at the joint distribution of all those statistics. This is particularly important because hours and wages of spouses are now part of the information set of the same household.

The role of new computational tools

In the discussion of the last few paragraphs, I have emphasized the calibration process as a formal process of restricting the model by imposing that some of its statistics have certain desired values (typically their data counterparts). Implementing this is only possible if we are able to compute the equilibrium of the models that we use and its statistics very cheaply. Until very recently, computing the equilibrium of a simple economy was a feat. Now the complications arise from two different angles: we want to compute equilibria of complicated economies (economies with many agents that differ in various dimensions) and we want to compute equilibria many times so we can choose the right parameterizations.We all know that there have been enormous improvements in hardware and some in software to do the required calculations. Recently, the power of supercomputers has started to trickle down to the average economist in the form of parallel processing via cheap Beowulf clusters. Here at Penn we just have acquired two of these clusters with a total of 15 processors that we expect will allow us to improve our ability to deal with increasingly more sophisticated models and more stringent estimation procedures. Ellen McGrattan in the Minneapolis Fed was the first one to have one of these machines, and her generous support to help others learn has made their use a lot easier. Parallel processing is particularly appropriate for problems that are intensive in things like value function iteration (and other iterative methods to solve dynamic programming problems), that is, problems where calculations need not be simultaneous. This is exactly the type of problem that is pervasive in quantitative economic theory.


Aiyagari, S. R., Greenwood, J., and Guner, N. 2000. “On the State of the Union,” Journal of Political Economy, 108, 213-44.
Bethencourt, C. 2002.
Castañeda, A. & Díaz-Gimenez, J. & Ríos-Rull, J.-V. 2000. “Accounting for Earnings and Wealth Inequality“. University of Pennsylvania, mimeo.
Cubeddu, L., and Ríos-Rull, J.-V. 1997. “Marital risk and capital accumulation“, Federal Reserve Bank of Minneapolis Staff Report 235.
Keane, M. P., and Wolpin, K. I. 1997. “The Career Decisions of Young Men“, Journal of Political Economy, 105, 473-522.
Knowles, J. 1999. “Can Parental Decisions Explain U.S. Income Ineqality?“, University of Pennsylvania, mimeo.
Nishiyama, S. 2002. “Bequests, Inter Vivos Transfers, and Wealth Distribution,” Review of Economic Dynamics, vol. 5(4), pages 892-931
Regalia, F., and Ríos-Rull, J.-V. 2001. “What Accounts for the Increase in the Number of Single Households?“, University of Pennsylvania, mimeo.
Ríos-Rull, J.-V., and Sanchez-Marcos, V. 2002. “College Attainment of Women,” Review of Economic Dynamics, vol. 5(4), pages 965-998.
Volume 2, Issue 2, April 2001

Dynamic Models of Crime and Punishment, by Antonio Merlo

Antonio Merlo is the Lawrence R. Klein Associate Professor of Economics at the University of Pennsylvania and is Director of the Penn Institute for Economic Research. His field is political economy, in particular bargaining, political stability, and crime. Merlo’s RePEc/IDEAS entry.

An important phenomenon of the last decade has been the sharp and steady decline in crime. In the United States, the crime rate per 100 inhabitants was equal to 5.95 in 1980 and dropped to 5.09 in 1996. While this general trend has been observed for most categories of crime, the most noticeable decline has been observed for property crimes (that is, burglary, larceny, robbery, and motor vehicle theft), which account for over 90% of all crimes. The property crime rate per 100 inhabitants in the United States went down 17% from 5.60 in 1980 to 4.65 in 1996.What accounts for this decline? Both the popular press and the academic literature have been searching for answers to this important question (See for example the article “Crime in America: Defeating the bad guys” in The Economist of October 3, 1998 and the collection of articles in the 1998 Summer issue of the Journal of Criminal Law and Criminology). Several main factors have been identified as possible explanations for this phenomenon. The first is related to demographics. It is well documented that most crimes are committed by youths. Their fraction in the population has being declining in the 1990s. For instance, the fraction of people between the ages of 15 and 25 was 20.5% in 1980 and went down to 15.1% in 1996.

Another key factor is related to law enforcement. Expenditures on police protection have increased from 0.6% of GDP in 1980 to 0.7% of GDP in 1996. Also, many initiatives to change the “style of policing” have been implemented in many U.S. cities. As a result, the clearance rate (i.e., the fraction of crimes cleared by arrest) has been increasing. For example, in 1980 the clearance rate for property crimes was equal to 16.8. In 1996, it increased to 18.5. At the same time, the “severity” of punishment has remained pretty much constant. For example, the expected punishment for property crimes (measured by the average length of prison sentences multiplied by the fraction of offenders sentenced to prison) was equal to 12.5 and 12.3 months in 1980 and 1995, respectively.

There are also other important phenomena that have been taking place in the 1990s that must be taken into consideration when trying to account for what is happening to crime. In particular, changes in the structure of earnings, employment opportunities, and the skill composition of the work force are likely to be intimately related to changes in the level of criminal activity. The following observations all seem to point to a reduction in crime. Real earnings have been increasing. Average real earnings increased by approximately 10% between 1980 and 1996. At the same time, aggregate unemployment has been decreasing and so has the fraction of unskilled individuals in the labor force. For example, the fraction of individuals in the labor force with less than a high school degree has declined substantially between 1980 and 1996.

Other observations, however, point in the direction of an increase in crime. Income inequality has been increasing. By virtually any measure, the distribution of real earnings has become substantially more unequal over the past twenty years. In addition, youth unemployment has been increasing. For example, the unemployment rate for people between the ages of 15 and 19 was equal to 17.1 in 1980 and rose to 17.8 in 1996.

These observations raise important questions. First, are these factors sufficient to explain the observed decline in property crime evidenced between 1980 and 1996? Second, what is the quantitative effect of each one of these factors on property crime? Third, what is the relation between individual economic opportunities, public policies, and property crime? Providing answers to these questions is one of the main goals of my research agenda, conducted in collaboration with Ayse Imrohoroglu (University of Southern California) and Peter Rupert (Federal Reserve Bank of Cleveland). The emphasis on property crime is justified by the fact that unlike violent crimes, property crimes are typically motivated by the prospect of direct pecuniary gain. Economic considerations are therefore most likely to guide individual decisions of engaging in this type of criminal activities.

The main ideas presented here come from a working paper, “What Accounts for the Decline in Crime?” (Imrohoroglu, Merlo, and Rupert (2001)). Some of the ideas are also drawn from an article recently published in the International Economic Review entitled “On the Political Economy of Income Redistribution and Crime” (Imrohoroglu, Merlo, and Rupert (2000)).

To guide our quantitative investigation of the major determinants of observed patterns of property crime, we specify a dynamic equilibrium model with heterogeneous agents. The agents in our model differ ex ante with respect to their income earning abilities. In each period of their finite life, agents receive a stochastic employment opportunity. After knowing their employment status, they decide how much to save and whether to engage in criminal activities in that period. Criminal activities amount to stealing from other agents in the economy. If agents choose to commit a crime, they may be apprehended and punished.

There is a long tradition of economic models of crime initiated by Becker (1968), see for example Harris (1970), Stigler (1970), Ehrlich (1973), and Polinsky and Shavell (1984). Our model shares many of the features of existing models and embeds Becker’s paradigm in a dynamic equilibrium framework. The dynamic nature of our model allows us to investigate individual decisions to engage in criminal activities over the life cycle. The equilibrium aspect of our model allows us to investigate the response of the aggregate crime rate to a variety of factors. We calibrate our model using U.S. data for 1980 so as to reproduce the observed property crime rate. We then use 1996 data to evaluate the effect of changes in demographics, police activities, the distribution of wages, employment opportunities, and the skill composition of the work force on crime.

Our main findings can be summarized as follows. First, the model is capable of reproducing the drop in crime between 1980 and 1996. In particular, the combined effect of the changes in unemployment rates, earnings profiles, age distribution of the population, shares by human capital type, and the ability of the police to capture criminals that have occurred between 1980 and 1996 can account for about 90% of the observed decline in property crime.

Second, the most important factors that account for the observed decline in property crime are (in order of importance): the higher apprehension probability, the stronger economy, and the aging of the population. In particular, the higher apprehension probability alone would have amounted to a 43% decrease in the crime rate, the higher income to a 20% decrease, and the smaller fraction of youth in the population to a 11% decrease.

Third, the effect of unemployment on crime is negligible. This finding is mostly due to the following two factors. First, even though the overall unemployment rate is lower in 1996 as opposed to 1980, youth unemployment rates were actually higher in 1996. Second, the overwhelming majority of criminals in our economy are employed.

Fourth, the increased inequality prevented an even larger decline in property crime. In fact, holding everything else constant, the increase in income inequality between 1980 and 1996 would have caused a 59% increase in property crime. This result is due to the fact that when income inequality increases relatively more people find it profitable to engage in criminal activities.

These results indicate that the two most important determinants of the crime rate are the apprehension probability and income inequality. The higher apprehension probability lowers the crime rate by 43% and the higher income inequality increases the crime rate by 59%. The relative magnitude of these opposing effects plays a very important role in the resulting crime rate.

The satisfactory performance of the model in accounting for the drop in crime observed between 1980 and 1996 raises an obvious question. Can the model successfully account for the behavior of the time series of property crime rates over a longer time period? Over the past quarter century the property crime rate in the United States has displayed some interesting patterns. In fact, the decline during the 1990s is only one of the interesting features of this time series. Property crime peaked in 1980, fell sharply during the first half of the 1980s, rose again during the second half of the 1980s (although not back to its 1980 level), and is currently at its lowest level in a quarter of a century. Can our analysis also account for these patterns?

The experiments we perform to answer this question can be described as follows. Take the calibrated model (which generates a crime rate equal to the one observed in 1980), and input data relative to unemployment rates, earnings profiles, age distribution of the population, shares by human capital type, the ability of the police to capture criminals, and the length of the prison term for a different year. For 1975, 1985, 1990 and 1996, compute the steady-state equilibrium of the model and compare the crime rate generated by the model to the one in the data.

The results we obtain indicate that the factors identified in our analysis as the main determinants of aggregate property crime rates can account for the behavior of the time series of property crime rates between 1975 and 1996. In particular, not only can our analysis qualitatively account for the increase in property crime rates in the 1970s, the drop observed in the first half of the 1980s, the subsequent rise in the later part of the decade and the sharp decline in the 1990s, but it can also reproduce the quantitative changes in the time series.

So far, we have focused attention on the aggregate predictions of the model. The model, however, can also generate implications with respect to individual behavior and, in particular, the composition of the criminal population. Focusing attention on the properties of the benchmark economy calibrated to 1980, our model predicts that about 79% of the people engaging in criminal activities are employed. This implies that approximately 5% (16%) of the employed (unemployed) population engages in criminal activities. This (perhaps surprising) implication of the model is consistent with the data. According to the Bureau of Justice Statistics, in 1979, 71% of all state prisoners were employed prior to their conviction. Studies by Grogger (1998) and Witte and Tauchen (1994) that use other data sets provide further evidence in support of this finding.

Next, we turn our attention to the composition of the criminal population by age and educational attainment. Our model predicts that about 76% of the people who commit property crimes are 18 years of age or younger. According to the Federal Bureau of Investigation, in 1980, 47.7% of all people arrested for property offenses were 18 years of age or younger. While the figure in the data is much lower than the one generated by the model, juvenile property offenders are often released without being formally arrested and charged of a crime. Nevertheless, we believe the model may overstate the amount of juvenile delinquency. Furthermore, the model predicted fraction of criminals without a high school diploma is equal to 46.1%. In 1979, 52.7% of the correctional population in state prisons did not have a high school diploma. Hence, the model seems to be capable of reproducing certain dimensions of the socio-demographic composition of the criminal population fairly well.

Our model also has implications on the amount of recidivism present in the economy. In our benchmark economy, 40% of all criminals had a prior conviction. This percentage is lower than the one in the data. According to the Bureau of Justice Statistics, in 1979, 61% of those admitted to state prisons were recidivists.

Hence, a possible limitation of our model is that it may overstate the amount of juvenile delinquency and understate the amount of recidivism present in the economy. In our model described above, if agents choose to commit a crime they may be apprehended and punished. The extent of punishment amounts to a prison term. However, in reality, convicted criminals may also be “stigmatized.” That is, after a conviction, individuals may face lower wages than if they had not been convicted. This additional component of punishment is not legislated but occurs as a societal outcome that stigmatizes the ex-prisoner. This stigma may force the individual onto an earnings path that is lower than their pre-conviction path.

Several empirical studies have analyzed the effect of this type of stigma. Waldfogel (1994) shows the decline in earnings to be roughly 10% and quite persistent, taking eight years to get halfway back to pre-conviction levels. Allgood, Mustard and Warren (1999) find a decline of 12% and that effect did not disappear for the six years following release. Grogger (1995) and Kling (1999), on the other hand, find only a small decline that is quite temporary. Grogger (1995) finds a drop of only 4% lasting just six quarters. Kling (1999) finds an even smaller effect when looking at street criminals, but a larger effect when considering white-collar crime.

We model “stigma” as a permanent 2% reduction in wages following an incarceration. Compared to our benchmark economy without stigma, the presence of stigma induces a lower amount of juvenile delinquency (59.9 versus 76.1) and a higher amount of recidivism (75.0 versus 40.0) in the economy. These two effects are obviously related. Holding the aggregate crime rate constant, in an economy with relatively more recidivism relatively more crimes are committed by older people (the recidivists). The intuition for why stigma is associated with higher recidivism and lower juvenile delinquency is rather subtle and interesting. By essentially increasing the “severity” of punishment, stigma discourages the involvement in criminal activities. The more persistent the effect of stigma, the more severe is the relative increase in punishment for a young individual relative to an older individual. Hence, ceteris paribus, the presence of stigma discourages juvenile delinquency relatively more. In addition, stigma has a direct effect on recidivism. By reducing post-conviction wages, stigma reduces the opportunity cost of engaging in criminal activities for individuals with a criminal record. This effect generates recidivism.

Recall that in 1980, 47.7% of all people arrested for property offenses were 18 years of age or younger. Moreover, the recidivism rate among state prisoners in 1979 was equal to 61%. Thus, introducing stigma into the analysis improves the overall ability of the model to match salient features of the data.

To conclude, the results presented suggest that our analysis has identified some key factors to help further our understanding of the complex phenomenon of crime. At the same time, however, they clearly display the limitations of our current analysis and help us identify future avenues of research. In particular, a richer model is needed to confront the micro evidence on participation rates in criminal activities by different age and population groups identified by a variety of demographic characteristics. Preliminary attempts to incorporate learning and group-specific, history-dependent apprehension probabilities in our model produced encouraging results. For example, incorporating into the model learning-by-doing in criminal activities (i.e., the more an individual engages in criminal activities the higher his returns from these activities), not only produces results that are similar to the ones induced by stigma (i.e., lower juvenile delinquency and higher recidivism than in the baseline model), but can also account for heterogeneity in participation rates by population groups. The increased flexibility, however, comes with the difficult challenge of collecting the necessary data to calibrate the additional components of the model.


Allgood, S., Mustard, D.B. and Warren, R.S. 1999. “The Impact of Youth Criminal Behaviour on Adult Earnings.” Manuscript, University of Georgia.
Becker, G. S. 1968. “Crime and Punishment: An Economic Approach.” Journal of Political Economy, 78, 169-217.
Ehrlich, I. 1973. “Participation in Illegitimate Activities: A Theioretical and Empirical Investigation.” Journal of Political Economy, 81, 521-565.
Grogger, J. 1995. “The Effects of Arrests on the Employment and Earnings of Young Men.” Quarterly Journal of Economics, 110, 51-71.
Grogger, J. 1998. “Market Wages and Youth Crime.” Journal of Labor Economics, 16, 756-791.
Harris, J. R. 1970. “On the Economics of Law and Order.” Journal of Political Economy, 78, 165-174.
Imrohoroglu, A, Merlo, A. and Rupert, P. 2000. “On the Political Economy of Income Redistribution and Crime.” International Economic Review, 41, 1-25.
Imrohoroglu, A, Merlo, A. and Rupert, P. 2001. “What Accounts for the Decline in Crime?.” Penn Institute for Economic Research working Paper 01-012.
Kling, J. R. 1999 “The Effect of Prison Sentence Length on the Subsequent Employment and Earnings of Criminal Defendants.” Discussion Paper 208, Woodrow Wilson School, Princeton University.
Polinsky, A. M. and Shavell, S. 1984. “The Optimal Use of Fines and Punishment.” Journal of Public Economics, 24, 89-99.
Stigler, G. J. 1970. “The Optimum Enforcement of Laws.” Journal of Political Economy, 78, 526-536.
Waldfogel, J. 1994. “Does Conviction Have a Persistent Effect on Income and Employment?” International Review of Law and Economics, 14, 103-119.
Witte, A.D. amd Tauchen, H. 1994. “Work and Crime: An Exploration Using Panel Data.” Public Finance, 49, 155-167.
Volume 2, Issue 1, November 2000

Payment Systems and Private Money, by Stephen Williamson

Stephen Williamson is Chester A. Phillips Professor of Financial Economics at the Department of Economics, University of Iowa. He has published extensively on monetary economics, in particular financial intermediation and payment systems. Williamson’s RePEc/IDEAS entry.


Studying payments systems involves both the familiar (at least to students of monetary economics and banking) and the unfamiliar. Familiar issues include the role of the banking system in providing means of payment, the substitution between money and credit, and the role of monetary exchange in economic activity. For these issues, it is often possible to address the relevant questions with off-the-shelf monetary and banking theory. However, some unfamiliar issues, for example involving the analysis of arrangements for clearing and settlement, are difficult to address without investing some time in constructing new models, and this is part of what makes the study of payments systems and private money interesting.

Payments systems activity involves transactions using fiat objects (e.g., government-supplied currency), circulating physical objects (e.g. private bank notes), checks, debit cards, credit cards, and interbank electronic payments (through Fedwire and the CHIPS system in the U.S.). Payments systems and private money are worthy of study for several reasons. First, there has been rapid recent growth in alternatives to cash for transactions. Second, in the U.S. the restrictions prohibiting the issue of private money have been lifted. Third, given the recent advances in information technology, payments arrangements which were formerly not feasible now are. Fourth, with the advent of many efficient alternatives to outside money in making transactions, and a higher volume of payments carried out under the auspices of the central bank (for example, through Fedwire in the U.S.), there are important issues to address concerning how monetary policy should be conducted and how the payments system should be regulated. Some key questions we might like to address are the following:

  • What are the efficiency properties of a private money system?
  • Are there useful lessons from historical experience with private money systems (U.S. pre-Civil War, Canada pre-1935)?
  • How should payments systems be designed with respect to clearing and settlement arrangements? What are the potential risk-sharing and incentive issues?
  • Does monetary policy work differently in a private money system? Do we need a central bank?

In modeling payments system arrangements, two key frictions are needed. First, there must be spatial separation, so that it not be too easy for agents to get together to coordinate exchange. Second, some form of monetary exchange must be required to overcome spatial and information frictions; it must be difficult for agents to engage in barter exchange. In this short review of my recent work with Ted Temzelides, I will describe three models of private money and payments systems, and ask what these models have to say about the relevant issues. These ideas come from two working papers, which are Temzelides and Williamson (2000a, 2000b).

A Model of Private Money and Settlement

This is a random matching model, which is most closely related to Williamson (1999), which in turn used some of the structure from existing monetary random matching models with endogenous prices, principally Shi (1995) and Trejos and Wright (1995). Other related literature is Cavalcanti, Erosa, and Temzelides (1999), Cavalcanti and Wallace (1999), Champ, Smith, and Williamson (1996), and Smith and Weber (1999).

In the model, there is random matching where “local” agents are met with higher frequency than “non-locals,” and there are simple banking arrangements which permit the issue of circulating private monies (bank notes) and clearing arrangements across locations. In the paper, Temzelides and Williamson (2000b), we consider two cases. First, we suppose that there is full information, in which case the matching friction will determine discounts on non-local bank notes. Second, we consider an environment with private information concerning the assets backing a particular bank note, in which case matching frictions and informational frictions will determine the discounts on bank notes.

When there is no clearing of bank notes and full information, non-local notes either do not circulate locally, or they circulate at a discount. The discount arises because the value of holding a local note is higher than the value of holding a non-local note. The difference in values is due to the fact that non-local notes cannot be redeemed locally. Given that non-local notes are discounted, the redemption value of a local note may be sufficiently high that a local agent is not willing to exchange the note with a non-local agent at the going price.

When there is full information and a clearing arrangement for bank notes among banks, then essentially all bank notes are universally redeemable. This implies that non-local bank notes always circulate locally, and they will not trade at a discount. Welfare is higher, and there is more production and exchange. Thus, it is clear that note-clearing arrangements are a good thing when there is full information.

Now, private information about the quality of non-local bank notes changes the story considerably. Here, there are potentially good bank notes and bad ones, and there may be equilibria where only good notes circulate, where only bad ones do, or where both good and bad bank notes circulate. If the private information friction is not too severe, then we will obtain the same results as with full information, in that clearing arrangements are socially beneficial. However, with a sufficient private information friction, welfare-dominated equilibria may exist, i.e. there can be a coordination failure. Also, the clearing arrangement may increase the quantity of low-quality money in circulation relative to high-quality money, and clearing may not eliminate discounts.

These results have important implications for our interpretation of historical monetary regimes where private money was issued. For example, in the pre-Civil War United States, clearing arrangements for bank notes were unusual. Essentially the only successful clearing arrangement was the Suffolk system in New England. On the other hand, in Canada before 1935, all chartered banks issued notes in a system which appeared to have worked efficiently, with a nationwide clearing arrangement and all notes trading at par. The difference between the U.S. system and the Canadian one can be explained by the fact that private information frictions were much more severe in the U.S. than in Canada. The U.S. had many unit banks, while Canada had only a few banks with nationwide branching.

Payments and Settlement in a Deterministic Environment

This model comes from Temzelides and Williamson (2000a). The objective here is to construct a model where there is a role for monetary exchange and where a centralized payments arrangement can substitute for exchange using fiat money. This model has some advantages over monetary search models in that it relies on competitive equilibrium as an equilibrium concept, and is simple enough that results can be obtained when money is divisible. This is a spatial model sharing some elements with the turnpike model studied by Townsend (1980). Related papers in the payments system literature are Freeman (1996a, 1996b, 1998), Kahn and Roberds (1998), Fujiki, Green and Yamazaki (1997), and Lacker (1997).

In the model, there is a countable infinity of locations, with a producer/shopper household at each location. Each period, the producer stays at home and produces while the shopper goes to the next location to obtain goods. There is essentially a double-coincidence-of-wants problem. A given household does not produce every third period, and households are arranged in space such that each household will follow a three-cycle, where they consume in one period but do not produce, produce and consume in the next period, produce and do not consume in the following period, etc. In each period, two thirds of the population will be consuming and two thirds will produce. There are two key elements in the model: Barter is not possible, and privately-issued IOUs will not circulate.

The approach in this paper is to consider successively sophisticated payments arrangements, and to determine the general equilibrium implications of these arrangements. The first arrangement is one where there is no using fiat currency. Effectively, there are endogenous cash-in-advance constraints, whereby households acquire cash when they produce and spend it two periods hence. In an equilibrium with a fixed fiat money stock there will be price dispersion, and a competitive equilibrium will be suboptimal, for the usual reasons. That is, households economize too much on money balances and consumption will be too low.

Now, a second arrangement is one with a centralized clearinghouse. Here, households carry out exchange using IOUs, and these IOUs are settled on net through the clearinghouse at the end of each period. Settlement takes place using outside money. It is important to note that it is important that there be net settlement; with gross settlement the equilibrium allocation is identical to what it was with the previous arrangement. Here, there may be multiple equilibria, which can be ranked in terms of welfare, but each of these equilibria dominates the first arrangement in welfare terms. Thus, a centralized payments system improves welfare, and the velocity of money also increases. The equilibrium allocation is not Pareto optimal, however.

A Pareto optimal allocation can be achieved under a third arrangement, which we can interpret as banking with interbank lending. Here, there is not only within-period credit through the clearinghouse, but borrowing and lending across periods. In this case, in spite of the fact that goods cannot be transported across locations, an efficient allocation is achieved without outside money. Imposing settlement in this environment, where there is no risk, implies that the allocation will be inefficient.

A Random Matching Model with Private Information

This model, from Temzelides and Williamson (2000a), uses a dynamic contracting approach, following Green (1987), Atkeson and Lucas (1992), Phelan (1995), Wang (1995), Williamson (1998), and Aiyagari and Williamson (1999), to study efficient risk-sharing and incentives under a payments system arrangement. This model shares some of the structure of the previous model in that there is random matching and periods when some agents cannot produce, or do not wish to consume, but here these states occur randomly. Each random match takes place between a household who receives a preference shock and a productivity shock, and another household whose preferences and technology are constant for all time. The optimal allocation is solved for, and we interpret the solution in terms of how an optimal payments arrangement should work. The conclusions we arrive at are the following:

  • “Credit” is key to making incentives work in the payments system. Participants who receive a bad shock (can’t produce) can generally still consume in the present, but their future liabilities to the system are higher than they would be otherwise.
  • It is important for incentive reasons that credit and risk-sharing be internalized in the payments system.
  • There are endogenous credit constraints.
  • Idiosyncratic shocks are propagated through the chain of transactions.


These three models have something to say about the functioning of private money systems and the role of payments systems in the economy. Perhaps where they fall short is that they do not address the issue of systemic risk in the payments system. Some policymakers are concerned that too much credit is extended in U.S. payments systems (Fedwire, for example), and that this leaves the system open to the possibility that the failure of a large participant to settle a transaction could lead to a chain of failures, with the Fed (in the case of Fedwire) left to bail everyone out. To evaluate whether systemic risk is in fact a legitimate concern, we need more sophisticated models of risk sharing and moral hazard in the context of centralized payments systems.


Aiyagari, S. R. and Williamson, S. 1999. “Credit in a Random Matching Model with Private Information,” Review of Economic Dynamics 2, 36-64.
Atkeson, A. and Lucas, R. 1992. “On Efficient Distribution with Private Information,” Review of Economic Studies 59, 427-453.
Cavalcanti, R., Erosa, A., and Temzelides, T. 1999. “Private Money and Reserve Management in a Random Matching Model,” Journal of Political Economy 107, 929-945.
Cavalcanti, R. and Wallace, N. 1999. “Inside and Outside Money as Alternative Media of Exchange,” Journal of Money, Credit, and Banking 31, 443-457.
Champ, B., Smith, B. and Williamson, S. 1996. “Currency Elasticity and Banking Panics: Theory and Evidence,” Canadian Journal of Economics 29, 828-864.
Freeman, S. 1996a. “Clearinghouse Banks and Banknote Over-Issue,” Journal of Monetary Economics 38, 101-115.
Freeman, S. 1996b. “The Payments System, Liquidity, and Rediscounting,” American Economic Review 86, 1126-1138.
Freeman, S. 1998. “Rediscounting Under Aggregate Risk,” forthcoming, Journal of Monetary Economics.
Fujiki, H., Green, E., and Yamazaki, A. 1997. “Sharing the Risk of Settlement Failure,” working paper, Federal Reserve Bank of Minneapolis.
Green, E. 1987. “Lending and the Smoothing of Uninsurable Income,” in E. Prescott and N. Wallace, eds. Contractual Arrangements for Intertemporal Trade, University of Minnesota Press, Minneapolis, MN.
Kahn, C. and Roberds, W. 1998. “Real-Time Gross Settlement and the Costs of Immediacy,” working paper, University of Illinois and Federal Reserve Bank of Atlanta.
Lacker, J. 1997. “Clearing, Settlement, and Monetary Policy,” Journal of Monetary Economics 40, 347-382.
Shi, S. 1995. “Money and Prices: A Model of Search and Bargaining,” Journal of Economic Theory 67, 467-498.
Smith, B. and Weber, W. 1998. “Private Money Creation and the Suffolk Banking System,” Journal of Money, Credit and Banking 31, 624-659.
Temzelides, T. and Williamson, S. 2000a. “Payments System Design in Deterministic and Private Information Environments,” working paper, University of Iowa.
Temzelides, T. and Williamson, S. 2000b. “Private Money, Settlement, and Discounts,” working paper, University of Iowa.
Townsend, R. 1980. “Models of Money with Spatially Separated Agents,” in Kareken, J. and Wallace, N., eds. Models of Monetary Economies, Federal Reserve Bank of Minneapolis, Minneapolis, MN.
Trejos, A. and Wright, R. 1995. “Search, Bargaining, Money, and Prices,” Journal of Political Economy 103, 118-141.
Wang, C. 1995. “Dynamic Insurance with Private Information and Balanced Budgets,” Review of Economic Studies 62, 577-595.
Williamson, S. 1998. “Payments Systems with Random Matching and Private Information,” Journal of Money, Credit and Banking 30, 551-569.
Williamson, S. 1999. “Private Money,” Journal of Money, Credit, and Banking 31, 469-491.

Volume 1, Issue 2, April 2000

Search Theory beyond the Matching Function, by Shouyong Shi

Shouyong Shi is Associate Professor at the Department of Economics at Queen’s University (Kingston, Canada). He has published extensively on search models, especially applied to monetary economics. His interests also include capital accumulation, specialization, and financial intermediation. Shi’s RePEc/IDEAS entry.

The predominant theory for analyzing a frictional market is the search theory developed by Diamond (1982), Mortensen (1982) and Pissarides (1990). This theory has two distinctive elements. One is an exogenous matching function that captures a time-consuming matching process and generates unemployment in equilibrium. The other is an ex post (after-match) wage determination scheme, often the Nash bargaining formula, which splits the match surplus between the two sides of the match. This theory has been used to organize a wide range of facts related to unemployment, both over the business cycles and along the growth trend, and to make policy recommendations. In contrast to other unemployment models (e.g., efficiency-wage models), the search theory can be easily integrated into an intertemporal framework.Yet the exogenous matching function and the exogenous surplus-sharing rule remain unsatisfactory. First, these exogenous features critically affect the model’s predictions on efficiency (see Hosios (1990)) and on the effects of labor market policies (Shi and Wen (1999)). Second, and more fundamentally, they eliminate any role for wages to direct matches ex ante (before matches occur) and deprive agents of the ability to actively influence their matches. In my current research I develop search models that do not rely on these exogenous elements and apply them to analyze wage inequality.

A simple way to allow agents to actively organize their matches is to replace the matching function by a two-stage, wage-posting game, where firms simultaneously post wages first and then workers apply to jobs after observing the wages. Such a price/wage-posting model, developed by Peters (1991) and Montgomery (1991), preserves the time-consuming feature of the search theory by assuming that a worker can only apply to a small fraction of the job openings in each period. In contrast to the standard search model, wages are determined before, not after, matches occur and so wages “direct” workers’ search. The matching process and the surplus division are both endogenous outcomes of agents’ actions. Each firm can deliberately change the posted wage to affect the number of applicants it receives. Firms and workers maximize the expected gains from a match, making a trade-off between the matching probability and the ex post gains from a match.

I further develop this model and use it to examine the following issues.

1. “Pricing with Frictions”. In this paper with Kenneth Burdett and Randall Wright, we first show that the price-posting equilibrium in a market with finite numbers of sellers and buyers converges to the equilibrium with infinitely many buyers and sellers. Since the latter is considerably easier to characterize, this result greatly simplifies the price/wage-posting game in large markets.

Then we allow firms to differ in capacity. The main finding is that the equilibrium price and the endogenous matching function both depend on not only the number of buyers and the number of goods for sale in the market, but also on how those goods are distributed across sellers. This result suggests that the standard matching function adopted in the literature is mis-specified. That is, the number of new matches should depend on whether there are many firms, each with a few vacancies, or a few firms, each with many vacancies.

2. “Product Market and the Size-Wage Differential”. In this paper I examine whether the wage-posting model can be useful for explaining the size-wage differential, i.e., the fact that employers with more workers pay higher wages than smaller employers do to workers with the same observable skills. This size-wage differential is a significant fraction of the overall wage inequality but has not been well explained by traditional theories.

For this task, I integrate the product market and the labor market into a price/wage-posting framework. In the product market the price-posting game generates the outcome that buyers pay a higher price to a larger seller than to a smaller seller for the higher service probability the larger seller provides. Thus, a large firm obtains a higher expected revenue per worker than a small firm. To capture this revenue differential, a large firm posts a higher wage to fill the vacancy than a small firm does. High and low wages generate the same expected wage to a searching worker because a high wage attracts more applicants and hence is more difficult to obtain. Thus, large firms not only pay a higher wage than small firms but also have higher expected profit, although the workers are identical and the firms are identical (except for size).

An increase in the product demand changes the distribution of employment across firms with different sizes and has ambiguous effects on the size-wage differential. In particular, trade liberalization increases wage inequality when the product demand is initially low but decreases wage inequality when the product demand is already high.

3. “Unskilled Workers in an Economy with Skill-Biased Technology”. In this paper I extend the wage-posting model to incorporate skill differences and skill-biased technology. The purpose is to check whether search frictions are important for explaining the following facts in the US data: In the 1970s, the skill premium fell but the within-group wage differential rose; in 1980s, the skill premium and the within-group wage differential both rose.

In this model workers are either skilled or unskilled, while firms use either a high technology or a low technology. The high technology is biased toward skilled workers. High-tech firms prefer skilled workers to unskilled workers and pay a skill premium, but they also post wages for unskilled workers in case they do not receive any skilled applicants. There is a wage differential among unskilled workers, i.e., unskilled workers in high-tech firms are paid more than those in low-tech firms. This within-group wage differential arises not from match-specific productivity or the complementarity between skilled and unskilled workers, but rather from the trade-off between a wage and the matching probability. A high-tech firm’s high wage comes with a low matching probability for an unskilled worker while a low-tech firm’s low wage comes with a high matching probability.

In this framework an increase in the skill-biased productivity increases the skill premium and the wage differential among unskilled workers simultaneously. In contrast, an increase in the general productivity of all workers increases the skill premium but reduces the wage differential among unskilled workers. These results indicate that search frictions can be important for accounting for both the skill premium and the within-group wage differential.

4. “Frictional Assignment”. In this paper I examine the assignment problem in a frictional market, i.e., the two-sided matching problem in a market where agents on each side are heterogeneous. In a frictionless market, Becker (1973) has shown that the market assignment is efficient and positively assortative (i.e., it matches high attributes on one side with high attributes on the other side of the market). Neither feature holds in a frictional matching market modeled in the standard search theory. I re-examine these issues with a wage-posting framework and focus on the assignment between skills and machines.

Two results emerge. First, the efficient assignment in this frictional world may not be positively assortative even when skills and machine qualities are complementary with each other in production. This is because skills and machines are not fully utilized and so, by matching high skills with low-quality machines and high-quality machines with low skills, efficiency may be improved if such a matching scheme increases the utilization of both high skills and high-quality machines. Second, the efficient assignment can be decentralized as follows. Each firm chooses three things before matches occur: a machine quality, a desired skill to be matched with, and a wage for the skill. After observing these choices, workers apply to the firms. The ex ante competition between firms and the endogenous division of the match surplus encourage the right number of firms to enter the market to target each skill and induce them to select the efficient machine quality for each skill.

The price/wage-posting framework is tractable and useful for modeling large, frictional labor markets. It allows search theory to go beyond exogenous matching functions and exogenous surplus-splitting rules, to make predictions and policy recommendations that are not vulnerable to these exogenous elements, and to explain some well-known facts about inequality. More fundamentally, the framework reinstates prices the ex ante role of allocating resources.


Becker, Gary S., 1973, “A theory of marriage: part I,” Journal of Political Economy 81, 813-846.
Burdett, Kenneth, Shouyong Shi and Randall Wright, 1998, “Pricing with Frictions”, Federal Reserve Bank of Philadelphia Working Paper 98-9.
Diamond, Peter, 1982, “Wage determination and efficiency in search equilibrium,” Review of Economic Studies 49, 217-227.
Hosios, Arthur, 1990, “On the efficiency of matching and related models of search unemployment,” Review of Economic Studies 57, 279-298.
Montgomery, James D., 1991, “Equilibrium wage dispersion and interindustry wage differentials,” Quarterly Journal of Economics 106, 163-179.
Mortensen, Dale T., 1982, “The matching process as a non-cooperative/bargaining game,” in J.J. McCall (ed.) The Economics of Information and Uncertainty, Chicago: University of Chicago Press.
Peters, Michael, 1991, “Ex ante price offers in matching games: non-steady states,” Econometrica 59, 1425-1454.
Pissarides, Christopher A., 1990, Equilibrium Unemployment Theory, Oxford: Blackwell.
Shi, Shouyong, 1997, “Product Market and the Size-Wage Differential“, mimeo.
Shi, Shouyong, 1998, “Unskilled Workers in an Economy with Skill-Biased Technology”, CREFE working paper 73.
Shi, Shouyong, 1998 “Frictional Assignment”, CREFE working paper 74.
Shi, Shouyong and Quan Wen, 1999, “Labor market search and the dynamic effects of taxes and subsidies,” Journal of Monetary Economics 43, 457-495