
MultiBelief RationalExpectations Equilibria: Indeterminacy, Complexity and Sustained Deflation
Abstract
In this paper, we extend the concept of rationalexpectations equilibrium, from a traditional singlebelief framework to a multibelief one. In the traditional framework of single belief, agents are supposed to know the equilibrium price “correctly.” We relax this requirement in the framework of multiple beliefs. While agents do not have to know the equilibrium price exactly, they must be correct in that it must be always contained in the support of each probability distribution they think possible. We call this equilibrium concept a multibelief rationalexpectations equilibrium. We then show that such an equilibrium exists, that indeterminacy and complexity of equilibria can happen even when the degree of risk aversion is moderate and, in particular, that a decreasing price sequence can be an equilibrium. The last property is highlighted in a linearutility example where any decreasing price sequence is a multibelief rationalexpectations equilibrium while only possible singlebelief rationalexpectations equilibrium price sequences are those which are constant over time.
Introduction
This paper considers a pureendowment nonstochastic overlappinggenerations economy. In this framework, we extend the concept of rationalexpectations equilibrium, or in other words perfectforesight equilibrium in our setting, in which generations in the model are supposed to know the equilibrium price “correctly.” Thus, there is no surprise in this rationalexpectations equilibrium. We relax this requirement to the one that while generations do not know the equilibrium price exactly, they have a set of purelysubjective probability distributions of possible prices. In addition, they must not be surprised by the realization of the equlibrium price. That is, generations’ multibelief expectations must be “correct” in that the equilibrium price is always contained in the support of each probability distribution they think possible. We call this equilibrium concept multibelief rationalexpectations equilibrium. Furthermore, the realization of the price which clears the market never disappoints generations’ expectations since they assign a positive (but possibly less than unity) probability to the occurrence of that price. Thus, their expectations are “realized.” Importantly, the generations’ beliefs are endogenously determined as a part of multibelief rationalexpectations equilibrium. This is similar to sequential equilibrium in an extensiveform game where the probability distribution at each information set is endogenously determined (although while a unique distribution is determined in a sequential equilibrium, a set of distributions is determined in ours). Obviously, singlebelief rationalexpectations equilibrium where generations’ expectations are singleton sets is ordinary rationalexpectations equilibrium.