Robustness of sunspot equilibria

Summary. A sunspot equilibrium (SSE) is based on some extrinsic randomizing device (RD). We analyze the robustness of SSE. (1) We say that an SSE allocation is robust to refinements if it is also an SSE allocation based on any refinement of its RD. (2) We introduce two core concepts for analyzing the robustness of SSE in the face of cooperative-coalition formation. In the first, the blocking allocations are based on the RD that defines the SSE. In the second (stronger) core concept, coalitions select their own RDs. For the convex economy with restricted market participation, SSE allocations are robust under each of the definitions and the cores converge on replication of the economy to the set of SSE allocations. For the economy with an indivisible good, SSE allocations are not always robust. We provide examples of each of the following: (i) an SSE allocation that is not robust to refinement, (ii) an SSE allocation that is in neither core, (iii) an SSE allocation that is in the first core, but not in the second, and (iv) a core that does not converge upon replication to the set of SSE allocations. Received: July 31, 1995; revised version August 30, 1996     

Manipulation of endowments and sunspot equilibria

We study the connection between occurrence of manipulation via reallocating endowments by coalitions and sunspot equilibria. The uncertainty about which coalition will form introduces extrinsic uncertainty into the economy. Under certain conditions, manipulation of endowments by coalitions can occur if and only if sunspots matter. We would like to thank Bill Ethier, Atsushi Kajii, Cuong Le Van, Karl Shell, Koji Shimomura, Nicholas Yannelis, an anonymous referee, as well as seminar participants at the Second Asian General Equilibrium Theory Workshop, 2005, Tokyo; Workshop on Uncertainty and Information, IMS, NUS, 2005; Kobe Institute of Economic Research; Public Economic Theory 2005 Conference, Marseille; and the South and South East Asia Econometric Society Meetings, 2006, Chennai for helpful discussions and comments.     

On the plausibility of sunspot equilibria

This paper presents a one-sector business cycle model with variable capacity utilization and externalities that stem from aggregate economic activity. It uses a new formulation of the endogenous capital utilization rate in which utilization costs appear in the form of variable maintenance expenses. Indeterminacy arises at approximate constant returns to scale. This result challenges the viewpoint that indeterminacy is empirically implausible. Sunspot driven model fluctuations duplicate a number of stylized facts of the business cycle. Plausible parameter space contains regions in which stationary sunspot equilibria are stable under learning.     

Indivisibilities,lotteries, and sunspot equilibria

Summary We analyze economies with indivisible commodities. There are two reasons for doing so. First, we extend and provide some new insights into sunspot equilibrium theory. Finite competitive economies with perfect markets and convex consumption sets do not allow sunspot equilibria; these same economies with nonconvex consumption sets do, and they have several properties that can never arise in convex environments. Second, we provide a reinterpretation of the employment lotteries used in contract theory and in macroeconomic models with indivisible labor. We show how socially optimal employment lotteries can be decentralized as competitive equilibria without lotteries once sunspots are introduced.We thank Kenneth Arrow, Aditya Goenka, Ed Green, Jeremy Greenwood, Walter Heller, Steve Matthews, Herve Moulin, Roger Meyerson, Jim Peck, Patrick Kehoe, Ramon Marimon, Ed Prescott, Richard Rogerson, Nancy Stokey and Raghu Sundaram for their comments. We also thank participants in seminars at Northwestern, Yale, USC, Cornell, Barcelona, Madrid, Santander, and the Canadian Economics Association annual meetings in Victoria. We are grateful to the National Science Foundation (through grants SES-8606944 and SES-8821225), the Center for Analytic Economics, the Thorne Fund, and the University of Pennsylvania Research Foundation for research support. The views expressed here are those of the authors, and not necessarily those of the Federal Reserve System or the Federal Reserve Bank of Minneapolis.     

The genesis of expectations and of sunspot equilibria

The existence—under certain conditions—of sunspot equilibria in overlapping generations models is a well-known theoretical result, but a lot of research has still to be made to understand whether and how such equilibria may occur as a consequence of a dynamic process. In this paper, we explore a model with individuals having simple utility functions and discover situations in which the dynamic processes of expectations and observed prices do not converge in spite of the existence of static equilibria. In other words, unfounded beliefs do still have a permanent influence on the real economy but induce erratic evolutions.     

Rationalizable expectations and sunspot equilibria in an overlapping-generations economy

There are two theories for the treatment of market uncertainty: rationalizable expectations and sunspot equilibria. This paper shows how the game-theoretic solution concept of rationalizable expectations can be applied to an overlapping-generations exchange economy. Some general properties of these equilibria are discussed. It is shown that rationalizable-expectations equilibria are the predictions yielded by considering sunspot equilibria in which probability beliefs may differ across individuals. This result allows for a new interpretation of sunspot equilibria and helps to understand their relevance.     

Learning of cycles and sunspot equilibria by Genetic Algorithms

We analyze the learning behaviour of a Simple Genetic Algorithm in an overlapping generations model with one consumption good and fiat money. It is shown by simulations, that in cases where periodic equilibria exist the equilibrium of period two is learned by a Genetic Algorithm and not the monetary steady state. We further show that proper coding leads to convergence of the GA towards the sunspot equilibrium. If individuals who believe in the impact of sunspots are brought together with individuals who ignore the sunspots, the sunspot believes will in most cases drive the other individuals out of the population.     

Sufficient conditions for the existence of sunspot equilibria

This paper reports on conditions on agents' preferences and endowments sufficient to guarantee the existence of sunspot equilibria in a simple overlapping generations model of pure exchange. Sunspot equilibria are those in which uncertainty extrinsic to the economy operates through expectations to yield a fulfilled expectations competitive equilibrium in which the extrinsic randomness has real effects on prices and allocations. The paper also provides necessary and sufficient conditions for these equilibria to have agents trading in a fixed stock of valued fiat money. The condition derived can be interpreted as requiring that intertemporal income effects appropriately dominate substitution effects.     

Existence of adaptively stable sunspot equilibria near an indeterminate steady state

We examine the nonlinear model x_t=E_tF(x_t+1). Markov stationary sunspot equilibria (SSEs) exist near an indeterminate steady state, , provided . Despite the importance of indeterminacy in macroeconomics, earlier results have not provided conditions for the existence of adaptively stable SSEs near an indeterminate steady state. We show that there exist Markov SSEs near x? that are E-stable, and therefore locally stable under adaptive learning, if .     

Real indeterminacy of equilibria in a sunspot economy with inside money

Summary In a two-period sunspot economy with inside money andS possible realizations of the sunspot, we prove that, genetically in the space of utility functions, there areS — 1 degrees of real indeterminacy. This result generalizes the previously known result for sunspot models that, generically in endowments, there is at least one degree of real indeterminacy. The proof involves showing that generically the equilibrium allocation is different across states for some household. This property allows us to perturb the utility function in a simple way and to apply standard transversality arguments to prove our main theorem.We would like to thank David Cass, Atsushi Kajii, Michael Mandler and Paolo Siconolfi for helpful discussions.     

Firm dynamics and markup variations: Implications for sunspot equilibria and endogenous economic fluctuations

This paper analyzes how the interaction between firms’ entry-and-exit decisions and variations in competition gives rise to self-fulfilling, expectation-driven fluctuations in aggregate economic activity and in measured total factor productivity (TFP). The analysis is based on a dynamic general equilibrium model in which net business formation is endogenously procyclical and leads to endogenous countercyclical variations in markups. This interaction leads to indeterminacy in which economic fluctuations occur as a result of self-fulfilling shifts in the beliefs of rational forward looking agents. When calibrated with empirically plausible parameter values and driven solely by self-fulfilling shocks to expectations, the model can quantitatively account for the main empirical regularities characterizing postwar U.S. business cycles and for 65% of the fluctuations in measured TFP.     

The structure of the set of sunspot equilibria in economies with incomplete financial markets

Summary This paper considers the set of equilibria of two-period, sunspot economies withS purely extrinsic states of nature in the second period andI assets with linearly independent nominal payoffs. The span of the payoff matrix contains the vector [1, ... , 1] (i.e., inside money). The set of economies is described in terms of (sunspot-invariant) utility functions. IfS>I> 0, there is an open, dense set of economies such that, given a vector of no arbitrage asset prices, the set of equilibrium allocations contains a smooth manifold of dimensionS—I. Such a manifold contains at least one nonsunspot equilibrium (and at most a finite number of such equilibria).The paper was written while I was a visitor at C.O.R.E., Universitè Catholique de Louvain, with the financial support of a S.P.E.S. fellowship. I would like to thank D. Cass, H. Polemarchakis and P. Siconolfi for their helpful comments.     

Testing theories with learnable and predictive representations

We study the problem of testing an expert whose theory has a learnable and predictive parametric representation, as do standard processes used in statistics. We design a test in which the expert is required to submit a date T by which he will have learned enough to deliver a sharp, testable prediction about future frequencies. We show that this test passes an expert who knows the data-generating process and cannot be manipulated by a uninformed one. Such a test is not possible if the theory is unrestricted.     

The set of sunspot equilibria in economies with incomplete financial markets: variable asset prices

Summary. I consider the set of equilibria of two-period economies with S extrinsic states of nature in the second period and I assets with linearly independent nominal payoffs. Asset prices are variable. If the number of agents is greater than (S-I), the payoff matrix is in general position and S 2I, the set of equilibrium allocations generically (in utility function space) contains a smooth manifold of dimension (S-1). Moreover, the map from states o f nature to equilibrium allocations (restricted to this manifold) is one-to-one at each equilibrium. Received: February 23, 1998; revised version: June 1, 2000     

转型期企业技术行为短视的解释

长期以来,中国企业缺乏技术创新的动力,特别是以技术换市场战略的效果不佳,根源于中国经济转型期宏观环境和微观机制方面的诸多因素导致了企业技术行为的短视。加快中国技术创新,必须让技术创新成为企业技术发展中的自觉行为,而从宏观环境和微观机制方面消除导致企业技术行为短视的根源是关键。     

Correlated equilibrium and sunspot equilibrium

Summary We show by an example that the sunspot equilibria of a competitive economy are not equivalent to the correlated equilibria if sunspots generate transfers between (extrinsic) states of nature (through a contingent commodities market). Nevertheless, we prove that the sunspot equilibrium allocations of a standard overlapping generations economy coincide with the (strategic form) correlated equilibrium allocations of a natural market game mimicking the economy.     

Ergodic chaos, learning and sunspot equilibrium

Summary. In this paper we construct sunspot equilibria that arise from chaotic deterministic dynamics. These equilibria are stationary and have absolutely continuous stationary measures. We prove that they can be learned by a simple rule based on the histograms of past state variables. This work gives a theoretical justification for complex deterministic models that might compete with stochastic models to explain real data. Also we prove the stochastic stability of the indeterminate equilibrium.     

Nash equilibria equal competitive equilibria

With strictly monotone preferences and a continuum of traders, there is a game in which the set of Nash equilibria is exactly the same as the set of competitive equilibria.