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Conditions for Unique Solutions in Stochastic Macroeconomic Models with Rational Expectations

This paper examines conditions for the uniqueness of an equilibrium price distribution in stochastic macroeconomic models with rational expectations. A model is developed in which many price distributions, each with a finite variance, satisfy the equilibrium requirements of rationality. Hence, the condition that the variance of the equilibrium price distribution be finite, or equivalently, that the conditionally expected price path be stable, does not guarantee uniqueness. In such cases it is shown that an arbitrary random quantity which is widely publicized can become a leading indicator of prices and, consequently, influence the behavior of actual prices. However, by extending the finite variance (stability) condition to a minimum variance condition, these nonuniqueness problems can be avoided. Such stability or minimum variance conditions suggest a kind of collective rationality which, although not unreasonable, has not yet been fully analyzed in rational expectations models.