Rational Expectations Equilibrium in a Sequence of Asset Markets

Abstract

The paper examines a stochastic nature of equilibrium asset prices in a sequence of markets, where agents have diverse pieces of information. As in the recent paper by Radner [1979], it starts in a world with a finite number of signals and introduces some dynamics in a sequential trading mechanism. We show that in an economy with many consumers of differing characteristics in their endowments, preferences and information, a dynamic rational expectations equilibrium in our sequential asset market is generically revealing and has an interesting Martingale property. Incorporating an implicit learning process, we provide a general equilibrium framework for resource allocation under uncertainty where the Martingale property of asset prices by LeRoy [1973] and Lucas [1978] can be examined. The Martingale property of asset prices emerges as an equilibrium condition in the sequential trading mechanism. As in the paper by Harrison and Kreps [1979], it characterizes the condition that no arbitrage gain is possible. We derive this important stochastic property of the asset price in an economy with incomplete markets where there exists a revealing dynamic rational expectations equilibrium. High volatility in the asset price and fluctuations in the value of trade result from the agents' optimizing behavior through a sequential revision of their subjective beliefs over time. But since we cannot aggregate different beliefs and preferences across consumers, it also implies that empirical tests of intertemporal asset pricing based on the model of identical consumers are likely to fail. We provide an alternative testable hypothesis about the intertemporal informational efficiency of the price system.