On the structure of Ramsey equilibrium: Cycles,indeterminacy, and sunspots

Summary We consider a one-sector neoclassical capital accumulation model under borrowing constraints with infinitely-lived heterogeneous households. Under the standard assumptions of strictly concave and time-additive utility functionals and a strictly concave production function we show that perfect foresight equilibria can be non-unique, even locally non-unique (indeterminate), and periodic of arbitrary long periodp. Moreover, we prove that there can exist non-trivial rational expectations (sunspot) equilibria when the agent's expectations about future factor prices depend on extrinsic uncertainty.Remarks made by an anonymous referee were extremely helpful in preparing the final draft of this paper.     

On the uniqueness of fully informative rational expectations equilibria

Summary. This paper analyzes two equivalent equilibrium notions under asymmetric information: risk neutral rational expectations equilibria (rn-REE), and common knowledge equilibria. We show that the set of fully informative rn-REE is a singleton, and we provide necessary and sufficient conditions for the existence of partially informative rn-REE. In a companion paper (DeMarzo and Skiadas (1996)) we show that equilibrium prices for the larger class of quasi-complete economies can be characterized as rn-REE. Examples of quasi-complete economies include the type of economies for which demand aggregation in the sense of Gorman is possible (with or without asymmetric information), the setting of the Milgrom and Stokey no-trade theorem, an economy giving rise to the CAPM with asymmetric information but no normality assumptions, the simple exponential-normal model of Grossman (1976), and a case of no aggregate endowment risk. In the common-knowledge context, we provide necessary and sufficient conditions for a common knowledge posterior estimate, given common priors, to coincide with the full communication posterior estimate. Received: May 29, 1997; revised version: July 18, 1997     

Understanding Markov-switching rational expectations models

We develop a set of necessary and sufficient conditions for equilibria to be determinate in a class of forward-looking Markov-switching rational expectations models and we develop an algorithm to check these conditions in practice. We use three examples, based on the new-Keynesian model of monetary policy, to illustrate our technique. Our work connects applied econometric models of Markov-switching with forward looking rational expectations models and allows an applied researcher to construct the likelihood function for models in this class over a parameter space that includes a determinate region and an indeterminate region.     

Inflation and growth in a disequilibrium macroeconomic model

The purpose of this paper is to study the dynamics of temporary equilibria in a disequilibrium growth model. Dynamics rests upon adjustment mechanisms of prices, capital stock, money balances, and labour supply. Wage dynamics is supposed to be influenced by indexation processes, and this question is related to the investment behaviour of firms. We give sufficient conditions for existence, unicity, and asymptotic stability of steady states of this model. We also show that steady states correspond to a long-run Phillips curve, which is vertical when inflationary expectations are fully reflected in wage and price changes.     

A dynamic model of expectations equilibrium

This paper describes a dynamic information adjustment process which achieves (rational) expectations equilibria for stochastic exchange environments. An informational temporary equilibrium is an exchange equilibrium in which agents' expectations are conditioned on their initial information and market data generated in previous informational temporary equilibria. An equilibrium is a temporary equilibrium which reveals no further information. This process leads to an equilibrium even when the data observed by agents is insufficient to permit the existence of an expectations equilibrium.     

Generalized potentials and robust sets of equilibria

This paper introduces generalized potential functions of complete information games and studies the robustness of sets of equilibria to incomplete information. A set of equilibria of a complete information game is robust if every incomplete information game where payoffs are almost always given by the complete information game has an equilibrium which generates behavior close to some equilibrium in the set. This paper provides sufficient conditions for the robustness of sets of equilibria in terms of argmax sets of generalized potential functions. These sufficient conditions unify and generalize existing sufficient conditions. Our generalization of potential games is useful in other game theoretic problems where potential methods have been applied.     

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.     

Are Rational Expectations Equilibria with Private Information Eductively Stable?

The paper derives conditions for eductive stability of rational expectations equilibria in simple linear economic models with private information. Following Guesnerie (1992; 2002), the concept of eductive stability is used. It is shown that even in a private information setting, rational expectations equilibria might be justified as a result of mental process of reasoning of the agents. The paper considers an equilibrium concept, where the agents are unable to condition their forecasts on the actual market price. It is shown that eductive stability in this case requires that a condition is satisfied that is also relevant in the symmetric information case. This condition is compared to the respective stability condition that must hold if agents are able to use the current market price as an additional source of information. It turns out that the conditions for eductive stability that emerge under both equilibrium concepts differ.revised version received September 11, 2003     

The effects of risk preferences in mixed-strategy equilibria of games

We consider the effects of risk preferences in mixed-strategy equilibria of 2×2 games, provided such equilibria exist. We identify sufficient conditions under which the expected payoff in the mixed equilibrium increases or decreases with the degree of risk aversion. We find that (at least moderate degrees of) risk aversion will frequently be beneficial in mixed equilibria.     

Admissible market data structures: A complete characterization

This paper characterizes the market data which, if observed by traders in a stochastic exchange environment, will permit the general existence of (rational) expectations equilibria. It is proved that if a trader observes and conditions his expectations on some nonconstant market data, he must observe at least the equilibrium price and his own equilibrium trade. Any data which do not satisfy this requirement, such as the price alone, or the price and the volume of trade, will fail to permit the existence of an expectations equilibrium for some otherwise well-behaved stochastic environment.     

Rational expectations in microeconomic models: An overview

This paper is an expository introduction to several topics of current research in the general equilibrium theory of rational expectations. More specifically, we discuss the existence of exact and approximate rational expectations equilibria, the implementation of equilibria, the behavior of learning and smoothing processes by which traders construct expectations from repeated observations of the market, and the lagged use of the information revealed by prices in an intertemporal sequence of markets. The purpose of this discussion is to introduce papers on these topics appearing in the Journal of Economic Theory Symposium on Rational Expectations in Microeconomic Models.     

Asymptotic stability of stationary temporary equilibria and changes in expectations

Recent results on sequences of temporary equilibria have given conditions for local asymptotic stability of stationary temporary equilibria. Simultaneously these conditions entail that stability is preserved under sufficiently small perturbations in the expectations of the agents. The present paper gives an evaluation of how large these perturbations can in fact be without the stability being destroyed. It also discusses the way this evaluation depends on the characteristics of the economy.     

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.     

Monetary policy and heterogeneous expectations

This paper studies the implications for monetary policy of heterogeneous expectations in a New Keynesian model. The assumption of rational expectations is replaced with parsimonious forecasting models where agents select between predictors that are underparameterized. In a Misspecification Equilibrium agents only select the best-performing statistical models. We demonstrate that, even when monetary policy rules satisfy the Taylor principle by adjusting nominal interest rates more than one for one with inflation, there may exist equilibria with Intrinsic Heterogeneity. Under certain conditions, there may exist multiple misspecification equilibria. We show that these findings have important implications for business cycle dynamics and for the design of monetary policy.     

Determinacy of competitive equilibria in economies with many commodities

This paper provides a framework for establishing the determinacy of equilibria in general equilibrium models with infinitely many commodities and a finite number of consumers and producers. This paper defines a notion of regular economy for such models and gives sufficient conditions on the excess savings equations characterizing equilibria under which regular economies have a finite number of equilibria, each of which is locally stable with respect to perturbations in exogenous parameters, and under which regular economies are generic. This paper also defines two notions of concavity, called uniform concavity and weighted uniform concavity, which generalize standard finite-dimensional notions of differential concavity to an infinite-dimensional setting by prohibiting goods from becoming perfect substitutes asymptotically. For the case of economies in which there are countably many commodities, such as discrete time models or markets with countably many assets, results in this paper show that equilibria are generically determinate as long as utility functions and production sets are uniformly concave or weighted uniformly concave. Received: November 7, 1996; revised version: March 13, 1998     

Rationalizability, Strong Rationality, and Expectational Stability

We examine the connection between two stability concepts of rational expectations equilibria: expectational stability, based on the convergence of iterations of expectations, and strong rationality, based on uniqueness of the rationalizable solutions of an associated game with restrictions on beliefs. To compare the concepts we embed a standard expectations model in a game-theoretic framework. It is shown that the two stability concepts coincide when agents are homogeneous. For the general case of heterogeneous agents we show that expectational stability is a necessary condition for strong rationality and we provide a sufficient condition for the latter. Journal of Economic Literature Classification Numbers: C72, C62.     

Monetary Neutrality and Optimality with Symmetric Partial Information

The neutrality and optimality of countercyclical monetary policy are examined in a representative economy featuring competitive equilibria in multiple markets and rational expectations based on a form of private information about current stochastic innovations in the economy. A necessary and sufficient condition for the neutrality of monetary policy is stated in terms of restrictions on the parameters of the linear rule describing prospective monetary feedback. Optimal monetary policy is fully characterized in terms of an alternative set of parameter restrictions. Optimal monetary feedback completely stabilizes deviations in commodity output by eliminating the influence of those current innovations about which agents cannot directly observe from the rational expectations of agents. [311]     

Expectations equilibrium and informational efficiency for stochastic environments

This paper studies the existence of expectations equilibria for message processes on stochastic exchange environments. A message process which permits the general existence of expectations equilibria is termed admissible. The main results are: (1) Every admissible process satisfies a weakened version of the Hurwicz “privacy” condition. (2) The competitive process is admissible, and has a message space of locally minimal size among admissible nonwasteful processes. (3) The only admissible condensations of the competitive process are constant functions.     

Incomplete Markets, Allocative Efficiency, and the Information Revealed by Prices

We compare rational expectations equilibria with different degrees of information revelation through prices. These equilibria arise in a two-period exchange economy with finitely many states and signals, multiple commodities and incomplete financial markets for nominal assets. We show that there are always equilibria where information is redundant in the sense of being of no value to the uninformed traders. We give conditions under which for a generic set of economies, parametrized by endowments and utilities, there exist open sets of equilibria for which allocative and informational efficiency are independent, with implications for monetary policy. Journal of Economic Literature Classification Numbers: D52, D60, D82, E52.     

Industrialization and Expectations in a Small Open Economy

The degree of industrialization in a country can be measured by the diversity of intermediate goods produced in the country. I construct a small-country model in which this diversity is determined endogenously in the process of industrialization. My model shows that the character istics of equilibria depend on the substitutability among intermediate goods; particularly when the substitutability is large, there may be multiple equilibria. When such equilibria exist, optimistic expectations lead to a high degree of industrialization but pessimistic expectations yield a low degree of industrialization.
JEL Classification Numbers: O14, F43, F12