Volume 4, Issue 2, April 2003

The Research Agenda: Tony Smith on Business Cycles and Inequality

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

EconomicDynamics Interviews Narayana Kocherlakota

EconomicDynamics Newsletter: Your recent research on optimal unemployment insurance and optimal capital taxation shows that small differences in the information structure can have dramatic impacts on the optimal design of these institutions. Does this not make it an impossible task for a policy maker to design a sensible policy?

Narayana Kocherlakota: My new paper on optimal unemployment insurance, and my RESTUD (2001) paper with Harold Cole, both show that the nature of optimal social insurance changes dramatically if people can save secretly. But I don't view this change as being "small". Think about the government's costs of monitoring savings. When savings are observable, these costs are zero. When savings are unobservable, these costs are infinite. In this sense, the change is big.

I think these kinds of results point to two important directions for future research. The first is theoretical: to provide sharp characterizations of optimal social insurance when the government can monitor savings and income, but only by paying auditing costs. The second is empirical: to obtain some kind of measure of how big these costs are.

ED: Would you argue the same would hold with your work on capital taxation? You show that when individual skills are unobservable and evolve stochastically, capital tax rates should be positive. The standard result was that capital tax rates should be zero.

NK: The now standard results on capital tax rates were derived by Chamley and Judd using the Ramsey approach to optimal taxation. This approach assumes that lump-sum taxes are unavailable, and that the government is forced to use distortionary linear taxes. Chamley and Judd show that even though lump sum taxes are unavailable, it is generally optimal for capital tax rates to be zero in the long run.

In my paper with Mikhail Golosov and Aleh Tsyvinski, "Optimal Indirect and Capital Taxation," we abandon the Ramsey approach to optimal taxation. Instead, we consider a large class of model economies that are dynamic extensions of James Mirrlees' original optimal taxation setup. The main ingredients of these models are that skills are privately observable and that they evolve stochastically. We show that if individual capital holdings can be monitored, then it is optimal to tax those holdings.

Note that unemployment is one example of the kind of privately observable skill shocks that we have in mind. People are unemployed either because they can't find a job (formally, their "skills" are low in the given period) or they can find a job (their skills are high) and they choose not to work. If savings are observable, then optimal unemployment insurance requires taxation of individual savings.

Of course, it is impossible to tax capital holdings (or equivalently savings) if individuals can save secretly. In that case, the nature of optimal social insurance against skill shocks changes dramatically. As I suggested in my first answer, I think it would be very fruitful to study intermediate cases in which savings can be monitored at a finite cost.

ED: In an influential JET paper, you argue that "Money is Memory." Does this mean with should add a new role for money in the Economics Principles textbooks?

NK: Actually, I would argue something far stronger: we should eliminate all of the standard explanations (medium of exchange, unit of account, and store of value) from the textbooks. Why do I say this? These "explanations" do not capture why money is necessary to achieve good outcomes in a society. Rather, they are merely descriptions of what money does.

Why is money necessary to achieve good outcomes in a society? Well, imagine a world without money, but with a perfect record of all past transactions. (One way to imagine this is a giant spreadsheet which lists everyone's name, and every event that ever happened to them.) In this world, we can accomplish anything that we could have with money (without adding any additional penalties or punishments that we might typically associate with credit). We do so using elaborate chains of gifts.

For example, suppose I go to the bookstore and ask for a book. The bookseller checks my past transactions. If I've given sufficiently more gifts than I've received in the past, then he gives me a textbook. Why is he willing to do so? Because in the future, when he goes to the grocery store, the grocer is willing to give the bookseller more bananas than if the bookseller had not given me the book. Why is the grocer willing to do so? Because he is rewarded by being able to receive more gifts in the future, etc, etc.

This is the key insight in "Money is Memory": a monetary equilibrium is merely an elaborate chain of gifts. After all, when I give the bookseller a fifty dollar bill in exchange for a book, he receives nothing of intrinsic value. All he receives is a token that indicates to others that he gave up something worth $50 ... that he has made a gift and so has kept up his part in the gift-giving chain that is a monetary economy. Without money, we would need to have the giant spreadsheet - or the gifts would never take place (because the only reason to make the gifts is to let others know that you have!).

This is the role of the intrinsically useless object termed money: to credibly record some aspects of past transactions and to make that record accessible to others. It is for this reason that I write that money is always and everywhere a mnemonic phenomenon.

References

Society for Economic Dynamics: Letter from the President

This is a reminder to register for our Annual Meeting to be held June 26-28 in Paris, France. This year we had a record number of submissions for the conference program. In spite of an increase in the number of sessions, we still had to turn down many worthy submissions. The program organizers, Lee Ohanian and Franck Portier have put together a stunning program including Plenary addresses by Jeremy Greenwood of the University of Rochester, George Mailath of the University of Pennsylvania, and Jean Tirole of Institut d'Economie Industrielle, Toulouse.

The local organizers are Jean-Olivier Hairault and Hubert Kempf of EUREQua Universite de Paris I, and Francois Langot, CEPREMAP and GAINS Universite du Maine. They have planned a terrific Social Program that includes a cocktail party at the Hotel de Ville de Paris on Friday June 27th. And a conference dinner at the famous Musée des Arts forains on Saturday June 28th. To register for the conference online visit:

https://www.southwest.net/secure/corporateplanners/sed2003/

I look forward to seeing you in Paris.

Sincerely,

Thomas F. Cooley, President Society for Economic Dynamics

Society for Economic Dynamics: 2003 Meetings

More than 600 papers have been submitted to the program committee, chaired by Lee Ohanian and Frank Portier and more than 300 have been selected and will be presented during the meeting. Plenary sessions will be presented by Jeremy Greenwood (University of Rochester), George Mailath (University of Pennsylvania), Jean Tirole (Institut d'Économie Industrielle, Toulouse).

Social events during the meeting include a cocktail party at the Paris City Hall, and a conference dinner at the Musée des Arts forains (museum for antique fairs) which should be quite entertaining. It will of course be followed by a life show by the Contractions.

Details on the meeting are available at http://minneapolisfed.org/research/events/sed/. You can also go to the local website for the meeting at http://eurequa.univ-paris1.fr/sedweb/sedweb/accueil.htm.

You should plan to attend the meeting, even if you do not present a paper. The program will be stunning and a must for any dedicated researcher, interested in what is going on in economic dynamics. There is a discount for those who register before May 15. To register and book for accommodation, please contact Corporate Planners unlimited at the following web address: https://www.southwest.net/secure/corporateplanners/sed2003/

Do not delay the booking for your accommodation. Paris is a crowded tourist spot at this period of the year, and hotels could be fully booked early on.

Review: De la Croix and Michel's A Theory of Economic Growth

Just published by Cambridge University Press, this book covers most of everything you would ever want to know about growth and fiscal policy in overlapping generations models. For those interested in growth theory, it is an important complement to the existing textbooks that focus more on the Solow growth model and its infinite-lived derivatives. For those interested in overlapping generations models per se, it complements the book by McCandless and Wallace that focuses on monetary equilibria.

The book has six main parts. The first studies equilibria in the basic overlapping generations model and its main extensions, the second considers their optimality and the properties of optimal paths. Chapter 3 is devoted to fiscal issues: transfers, pensions, public spending and second-bests. Chapter 4 introduces public debt. The last chapter deals with other extensions, such as altruism, education, inter-generational externalities and full Arrow-Debreu markets. Finally, a technical appendix shows various tools and functions some students may need.

Note that the book focuses entirely on theory. The theory is not motivated by some analysis of the data, an aspect that other growth textbooks have clearly emphasized. The predictions of the theory are not compared to some stylized facts or tested in some other ways. In that sense, "A Theory of Economy Growth" should really be understood as a manual on the inner workings of overlapping generation models, a toolbox that a researcher can keep handy, or as a guide on how to prove properties of models related to the ones presented. Many will come to appreciate this book for its analytic depth and its attempt to provide a systematic and precise presentation of overlapping generations.

"A Theory of Economic Growth" has been published by Cambridge University Press in October 2002.

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