On Existence and Uniqueness of Equilibrium in a Class of Noisy Rational Expectations Models

Abstract

I study a general class of noisy rational expectations models that nests the standard Grossman and Stiglitz (1980) and Hellwig (1980) models, but relaxes the usual assumption of joint normality of asset payoffs and supply, and allows for more general signal structures. I provide a constructive proof of existence of equilibrium, characterize the price function, and provide sufficient conditions for uniqueness within the class of equilibria with continuous price functions, which are met by both the Grossman and Stiglitz (1980) model and the Hellwig (1980) model with a continuum of investors. My solution approach does not rely on the typical "conjecture and verify" method, and I exhibit a number of non-normal examples in which asset prices can be characterized explicitly and in closed form. The results presented here open up a broad class of models for applied work. To illustrate the usefulness of generalizing the standard model, I show that in settings with non-normally distributed payoffs, shocks to fundamentals may be amplified purely due to learning effects, price drifts can arise naturally, and the disagreement-return relation depends in a novel way on return skewness.

Keywords: noisy rational expectations, asymmetric information, learning, information aggregation, exponential family

JEL Classification: D82, G14, G12