Journal of Economic Theory  ET2411 journal of economic theory 81, 16 (1998) article no. ET982411

Introduction to Sunspots in Macroeconomics* Jess Benhabib Department of Economics, New York University, 269 Mercer St., 7th Floor, New York, New York 10003 Received February 14, 1998

This introduction provides an overview of the three papers included in this symposium and highlights their contribution to the literature. Journal of Economic Literature Classification Numbers: E00, E3, O40.  1998 Academic Press

Recently there has been renewed interest in sunspot equilibria as a possible explanation of business cycle fluctuations. The impetus for this renewed interest comes from the realization that indeterminacy and sunspots can easily occur in standard real business cycle models or in models of endogenous growth, augmented to include some market imperfections. Typically these imperfections take the form of monopolistic competition or of technologies that exhibit external effects and are modelled in conjunction with some degree of increasing returns. Much of the research in this area has focused on the empirical plausibility of the magnitudes of increasing returns and of the market imperfections required to generate multiple equilibria and sunspots. Some of the early estimates of external effects, markups, and increasing returns by Hall [14, 15], Caballero and Lyons [12], and others, were sufficiently high to comfortably place the economy within range of magnitudes compatible with indeterminate equilibria. Nevertheless a number of empirical researchers refining these earlier findings on disaggregated U.S. data have concluded that returns to scale seem, on average, to be roughly constant, and that market imperfections are small. 1 At the same time more recent theoretical work mildly departing from the simplest one-sector growth models demonstrated that the degree of increasing returns and market imperfections required to generate * Technical support from the C.V. Starr Center for Applied Economics at New York University is gratefully acknowledged. 1 See, for example, Basu and Fernald [2, 3], Burnside, Eichenbaum, and Rebello ([8]) or Burnside [9], among others.

1 0022-053198 25.00 Copyright  1998 by Academic Press All rights of reproduction in any form reserved.

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indeterminate equilibria can be considerably reduced. 2 The papers in this symposium show that the degree of increasing returns or market imperfections needed to generate indeterminacy and sunspot equilibria is small, and falls well within the standard errors of recent empirical estimates: indeed, in the case of the paper by Benhabib and Nishimura, indeterminacy occurs for minimal externalities and under constant marginal returns. Furthermore, the papers in this symposium also show that models with indeterminacy and sunspots can provide a good match to macroeconomic time-series data. Indeterminacy emerges in dynamic models with small market distortions as a type of coordination problem. Roughly speaking, what is needed for indeterminacy is a mechanism such that, starting from some equilibrium, if all agents were to simultaneously increase their investment in an asset, the rate of return on the asset would increase and justify the higher initial investment. One such simple mechanism in one-sector models is increasing returns, typically sustained in a market context via external effects or monopolistic competition. To see how indeterminacy comes about in a model with increasing returns, consider starting from an equilibrium path, but let the agents believe that there is an equilibrium in which the shadow price of investment is higher than its current value and that future returns justify a higher level of investment. If agents act on this belief, the higher current price of investment reduces consumption and induces agents to divert GDP from consumption to investment. If there were no externalities, investment would increase, and the marginal product of capital would begin to decline as additional capital is accumulated. This decline would have to be offset by capital gains in the form of increases in the shadow price of capital in order to validate the belief of agents that higher rates of investment will yield the appropriate return. Trajectories of this sort for investment and prices may be maintained for a number of periods, but the resulting over-accumulation of capital and the exploding prices will violate transversality conditions: an agent will never get to consume enough in the future to justify the sacrifice of a higher rate of investment. In other words, an agent conjecturing such a path of prices and returns would be better off consuming, rather than accumulating additional capital at such a pace. However, in the presence of increasing returns introduced by external effects, or by monopolistic competition that generates aggregate demand externalities, accumulating more of an asset may increase rather than decrease its rate of return. Equilibrium would now require a decline in the 2 See, for example, Harrison [16], and also Weder [18], who build on the two-sector model of Benhabib and Farmer [5] with sector-specific externalities to show that increasing returns need not be economy-wide for indeterminacy to occur: it happens even if only the investment sector exhibits some mild increasing returns.

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shadow price of capital, which, together with investment and consumption, would gradually return to its steady state value. 3 (A more formal and detailed account of the above is given in Benhabib and Farmer [6].) The articles in this symposium provide models of the economy that rely on mechanisms that mimic aspects of increasing returns in order to generate indeterminacy. The article by Wen [20] is based on a widely used model of procyclical variation in capacity utilization which has been shown to amplify the effects of technology shocks. Wen notes, however, that this mechanism also acts like increasing returns, since in reduced form, it amplifies the output effects of increased input usage. The model generates indeterminacy in a one-sector model with much lower and empirically realistic levels of increasing returns because of this amplification property. It also has the merit of unifying the capacity utilization approach to business cycle fluctuations with the approach introducing sunspot equilibria. The paper of Weder [19] combines the two-sector model of Benhabib and Farmer [5] and the model of Gali [17], which is based on variable markups. He introduces a durable consumption sector in addition to the investment and the non-durable consumption sectors. The multisector structure combined with the differing sectoral demand elasticities yields variable average markups that depend on the composition of output. This allows Weder to provide a strong fit to second moments of U.S. data, even under mild increasing returns. The paper by Benhabib and Nishimura [6a] relies on a different amplification mechanism that can only arise in models with more than one sector. In a typical multisector model, the rates of return and marginal products of factors depend not only on stocks of assets, but also on the composition of output across sectors. Increasing the production and the stock of a capital asset, say due to an increase in its price, may well increase its rate of return, mimicking technological increasing returns in a one-sector model. It is therefore possible to have constant aggregate returns in all sectors at the social level and to still obtain indeterminacy with minor or even negligible external effects in some of the sectors. While sunspot equilibria and indeterminacy seem to arise in standard dynamic general equilibrium models for empirically plausible macroeconomic parametrizations, there still remains the question as to whether they can provide a good fit to the data. It is often suggested that sunspot models should do at least as well as the standard real business cycle models 3

Another approch under monopolistic competition is to assume different demand structures for consumption and investment goods, where the average markup becomes countercyclical as the composition of output changes over the cycle. This means that one component of the return to an asset, which is the marginal product divided by the markup, can increase as the asset is accumulated, and therefore mimic increasing returns. For the analysis of such a case see Gali [17].

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because they contain extra degrees of freedom. However, indeterminacy and sunspots cannot be obtained for any arbitrary parametrization of the economy, and they require some market imperfection to create a wedge between the social optimum and the market equilibrium. It is quite possible for the sunspot models of the macroeconomy to perform less well in matching the data because they are necessarily restricted to the parameter range which yields indeterminacy, and which makes sunspot equilibria possible. At the same time, merely substituting sunspot shocks for technology shocks in a model with multiple equilibria may also result in an inferior match to the data. To illustrate this problem, consider a sunspot model of business cycles which suppresses technology shocks. The equilibrium condition for the labor market requires that the wage rate multiplied by the marginal utility of consumption equals the marginal utility of leisure: wU C (C, 1&L)=U 1&L(C, 1&L).

(1)

If utility is concave and separable in consumption and leisure, and the wage rate declines in the quantity of labor, and if we abstract from movements in aggregate capital stock which are not large over the cycle, this equation implies that consumption is countercyclical. One possible solution is to have the wage rate increase in labor, either by adding sufficient increasing returns, or by introducing countercyclical markups to offset the declining marginal product of labor. 4 This approach also yields indeterminacy, but only if the size of the markups or the degree of increasing returns is relatively large (see Benhabib and Farmer [4] or Gali [17].) Indeterminacy can also arise if utility is non-separable and U 1&L, C is sufficiently negative to induce leisure to be an inferior good, implying a labor supply curve that is downward sloping. Not surprisingly, since consumption is procyclical in the data, attempts to estimate an equilibrium model driven by sunspots alone, without technology shocks, can yield an upward sloping labor demand curve, a downward sloping labor supply curve, or both. (See Farmer and Guo [13] and the comments of Aiyagari [1].) It seems therefore that models which generate indeterminacy and sunspot equilibria with modest and empirically plausible market imperfections must still rely on technology shocks to generate sufficiently procyclical consumption. This feature is common to the multisector models both of Benhabib and Nishimura [6a] and of Weder [19] and the one-sector model of Wen [20] based on variable capacity utilization. The combination of variable markups and a multisector structure, however, allows Weder [19] to obtain a very good match to the data, even without technology shocks and with modest increasing returns. 4 In equilibrium the wage rate will be given by the marginal product of labor divided by the markup. If the markup is countercyclical, the wage rate may increase in labor.

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The papers in this symposium may yield some improvements in matching the data over the standard one-sector real business cycle model, for example by being able to generate impulse-response functions that more closely resemble those obtained from actual data. On the other hand, many of the improvements in matching the time-series properties of the data are not necessarily due to the presence of indeterminacy or of sunspot equilibria. The standard real business cycle model incorporating variable capacity utilization, or expanded to allow for more than one sector, but which nevertheless has a unique equilibrium, can provide an equally good fit to the data. 5 Further empirical research may focus on estimating dynamic macroeconomic models which allow for sunspot equilibria and let the data decide the importance of expectation-driven fluctuations. The crucial aspect of models with indeterminacy, however, is not only that they can provide a reasonable match to the data but that they give rise to a continuum of equilibria which can be Pareto-ranked. In such a context the government may be able to pursue policies to guide the selection of equilibria, or to influence the choice of the sunspot which coordinates the economic behavior of agents. 6 Since policy can play a role that affects welfare in these models, it becomes particularly important to determine whether they have a relevance to reality.

REFERENCES 1. S. R. Aiyagari, ``The econometrics of indeterminacy: An applied study'': A comment, Carnegie Rochester Conf. Ser. Public Policy 43 (1995), 273284. 2. S. Basu and J. G. Fernald, Are apparent productive spillovers a figment of specification error? J. Monet. Econ. 36 (1995), 165188. 3. S. Basu and J. G. Fernald, Returns to scale in U.S. production: Estimates and implications, J. Polit. Econ. 105 (1997), 249. 4. J. Benhabib and R. E. Farmer, Indeterminacy and growth, J. Econ. Theory 63 (1994), 1941. 5. J. Benhabib and R. E. Farmer, Indeterminacy and sector specific externalities, J. Monet. Econ. 37 (1996), 397419. 6. J. Benhabib and R. E. Farmer, Indeterminacy and sunspots in macroeconomics, in ``Handbook of Macroeconomics'' (John Taylor and Michael Woodford, Eds.), to appear.

5 See for example Christiano and Eichenbaum [11] for a variable capacity utilization model or Benhabib, Perli, and Sakellaris [7] for a multisector model. For a brief discussion of these points as well as some of the empirical issues arising in multisector models see the discussion in Section 4 of Benhabib and Nishimura in this issue. 6 Once the economy exhibits indeterminacy, how the agents come to coordinate on a particular equilibrium or a particular sunspot, and whether this coordination remains stable over over time, remain open questions. However, if indeterminacy is an empirically relevant phenomenon, we cannot escape the fact that we must face and investigate the equilibrium selection problem.

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6a. J. Benhabib and K. Nishimura, Indeterminacy and sunspots with constant returns, J. Econ. Theory 81 (1998), 5896. 7. J. Benhabib, R. Perli, and P. Sakellaris, ``Persistence of Business Cycles in Multisector RBC Models,'' C. V. Starr Working Paper 97-19, New York University, 1997. 8. C. M. Burnside, M. Eichenbaum, and S. Rebelo, Capacity utilization and returns to scale, NBER Macroecon. Ann. 10 (1995), 67110. 9. C. M. Burnside, Production function regressions, returns to scale, and externalities, J. Monet. Econ. 37 (1996), 177201. 10. C. M. Burnside and M. Eichenbaum, Factor hoarding and the propagation of business cycle shocks, Amer. Econ. Rev. 86 (1996), 11541174. 11. L. Christiano and M. Eichenbaum, Current real-business-cycle theories and aggregate labor-market fluctuations, Amer. Econ. Rev. 82 (1992), 430450. 12. R. Caballero and R. K. Lyons, External effects in U.S. cyclical productivity, J. Monet. Econ. 29 (1992), 209226. 13. R. E. Farmer and J.-T. Guo, Real business cycles and the animal spirits hypothesis, J. Econ. Theory 63 (1994), 4273. 14. R. E. Hall, The relation between price and marginal cost in U.S. industry, J. Polit. Econ. 96 (1988), 921948. 15. R. E. Hall, Invariance properties of Solow's productivity residual, in ``Growth, Productivity, Unemployment'' (P. Diamond, Ed.), 71112, MIT Press, Cambridge, MA, 1990. 16. S. H. Harrison, ``Production Externalities and Indeterminacy in a Two-Sector Model: Theory and Evidence,'' Working Paper, Northwestern University, 1996. 17. J. Gali, Monopolistic competition, business cycles, and the composition of aggregate demand, J. Econ. Theory 63 (1994), 7396. 18. M. Weder, ``Animal Spirits, Technology Shocks and the Business Cycle,'' Humbolt University Working Paper, 1996. 19. M. Weder, Fickle consumers, durable goods and business cycles, J. Econ. Theory 81 (1998), 3757. 20. Y. Wen, Capacity utilization under increasing returns to scale, J. Econ. Theory 81 (1998), 1736.

















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