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).

References

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