Backward and Forward Solutions for Economies with Rational Expectations

Abstract

In models where anticipations of future endogenous variables influence current behavior, there exists an infinity of solutions under the assumption of rational expectations. This problem has been dealt with, in the study of macro-economic models, by the implicit or explicit use of one of three additional requirements: optimality; consistency with alleged economic behavior; or conformity of the endogenous variables to an imposed stationarity condition. These requirements have coincided in existing models, leading to the choice of a unique solution, a forward solution. The purpose of this paper is to review the problem, characterize the solutions, and examine whether these requirements are acceptable. Section I presents a simple model and derives the set of solutions; the model makes no claim to generality, but has the major advantage that the issues are easily understood in this simple case. Section II discusses the requirement of consistency with economic behavior. Section III discusses the requirement of stationarity, and Section IV provides some conclusions.

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