The existence of rational expectations equilibrium: a retrospective

This paper provides a selective review of theoretical research on the consistency of rational expectations equilibrium and its properties in microeconomic models. The general equilibrium framework is emphasized throughout the paper. After defining rational expectations equilibrium for a pure exchange economy, the paper presents a simple counterexample to illustrate that rational expectations equilibria need not exist. Results are summarized for the generic existence of fully revealing rational expectations equilibria in smooth economies satisfying additional dimensionality assumptions. Then the rational expectations equilibrium existence problem is related to earlier analysis of informationally decentralized allocation mechanisms. Next the efficiency properties of rational expectations equilibrium allocations are examined. Finally, the possibilities for partially revealing rational expectations equilibria are discussed.Equilibrium (Economics) - Mathematical models ; Rational expectations (Economic theory)

Non-implementation of Rational Expectations as a Perfect Bayesian Equilibrium

We show that a rational expectations equilibrium need not be incentive compatible, need not be implementable as a perfect Bayesian equilibrium and may not be fully Pareto optimal, unless the utility functions are state independent. A comparison of rational expectations equilibria with core concepts is also provided.Differential information economy, Rational expectations equilibrium, Implementation, Game trees, Private core

A new perspective to rational expectations: maximin rational expectations equilibrium

We introduce a new notion of rational expectations equilibrium (REE) called maximin rational expectations equilibrium (MREE), which is based on the maximin expected utility (MEU) formulation. In particular, agents maximize maximin expected utility conditioned on their own private information and the information that the equilibrium prices generate. Maximin equilibrium allocations need not to be measurable with respect to the private information of each individual and with respect to the information that the equilibrium prices generate, as it is in the case of the Bayesian REE. We prove that a maximin REE exists universally (and not generically as in Radner (1979) and Allen (1981)), it is effcient and incentive compatible. These results are false for the Bayesian REE

Rational expectations in urban economics

Canonical analysis of the classical general equilibrium model demonstrates the existence of an open and dense subset of standard economies that possess fully-revealing rational expectations equilibria. This paper shows that the analogous result is not true in urban economies. An open subset of economies where none of the rational expectations equilibria fully reveal private information is found. There are two important pieces. First, there can be information about a location known by a consumer who does not live in that location in equilibrium, and thus the equilibrium rent does not reflect this information. Second, if a consumer’s utility depends only on information about their (endogenous) location of residence, perturbations of utility naturally do not incorporate information about other locations conditional on their location of residence. Existence of a rational expectations equilibrium is proved. Space can prevent housing prices from transmitting information from informed to uninformed households, resulting in an inefficient outcome.Urban Economics; General Equilibrium; Private Information; Rational Expectations

Rational expectations in urban economics

Canonical analysis of the classical general equilibrium model demonstrates the existence of an open and dense subset of standard economies that possess fully-revealing rational expectations equilibria. This paper shows that the analogous result is not true in urban economies. An open subset of economies where none of the rational expectations equilibria fully reveal private information is found. There are two important pieces. First, there can be information about a location known by a consumer who does not live in that location in equilibrium, and thus the equilibrium rent does not reflect this information. Second, if a consumer’s utility depends only on information about their (endogenous) location of residence, perturbations of utility naturally do not incorporate information about other locations conditional on their location of residence. Existence of a rational expectations equilibrium is proved. Space can prevent housing prices from transmitting information from informed to uninformed households, resulting in an inefficient outcome.Urban Economics; General Equilibrium; Private Information; Rational Expectations

The rationality of expectations formation and excess volatility

I establish, in simple deterministic overlapping generations economies, that if each agent holds rationally formed expectations in the sense that any other expectations justifying his choices imply a smaller likelihood for the history he observes with limited memory, then there are rationally formed expectations equilibria exhibiting an excess volatility that no rational expectations equilibrium can match. Given that the limited records or finite memory case may arguably be the relevant one from a positive viewpoint, this result suggests that the possibility of excess volatility as an equilibrium phenomenon has been downplayed by the use of the rational expectations hypothesis.Expectations, rationality, volatility.

Exogenous expectations on endogenous uncertainty: recursive equilibrium and survival

This paper analyses general equilibrium models with finite heterogeneous agents having exogenous expectations on endogenous uncertainty. It is shown that there exists a recursive equilibrium with the state space consisting of the past aggregate portfolio distribution and the current state of the nature and that it implements the sequential equilibrium. We establish conditions under which the recursive equilibrium is continuous. Moreover, we use the continuous recursive relation of the aggregate variables to prove that if the economy has two types of agents, the one who commits persistent mistakes on the expectation rules of the future endogenous variables is driven out of the market by the others with correct anticipations of the variables, that is, the rational expectations agents.

Learning, adaptive expectations, and technology shocks

This study explores the macroeconomic implications of adaptive expectations in a standard real business cycle model. When rational expectations are replaced by adaptive expectations, we show that the self-confirming equilibrium is the same as the steady-state rational expectations equilibrium for all admissible parameters but that dynamics around the steady state are substantially different between the two equilibria. The differences are driven mainly by the dampened wealth effect and the strengthened intertemporal substitution effect, not by the escapes emphasized by Williams (2003). As a result, adaptive expectations can be an important source of frictions that amplify and propagate technology shocks and seem promising for generating plausible labor market dynamics.Equilibrium (Economics)

Learning, adaptive expectations, and technology shocks

This study explores the macroeconomic implications of adaptive expectations in a standard real business cycle model. When rational expectations are replaced by adaptive expectations, we show that the self-confirming equilibrium is the same as the steady state rational expectations equilibrium for all admissible parameters, but that dynamics around the steady state are substantially different between the two equilibria. The differences are driven mainly by the dampened wealth effect and the strengthened intertemporal substitution effect, not by the escapes emphasized by Williams (2003). As a result, adaptive expectations can be an important source of frictions that amplify and propagate technology shocks and seem promising for generating plausible labor market dynamics.Macroeconomics