How Equilibrium Prices Reveal Information in Time Series Models with Disparately Informed, Competitive Traders

Abstract

Accommodating asymmetric information in a dynamic asset pricing model is technically challenging due to the problems associated with higher-order expectations. That is, rational investors are forced into a situation where they must forecast the forecasts of other agents (i.e., form higher-order expectations). In a dynamic setting, this problem telescopes into the infinite future and the dimension of the relevant state space approaches infinity. By employing the frequency domain approach of Whiteman (1983) and Kasa (2000), this paper demonstrates how information structures previously believed to lead to disparate expectations in equilibrium (e.g., Singleton (1987)) converge to a symmetric equilibrium. The revealing aspect of the price process lies in the invertibility of the observed state space, which makes it possible for agents to inferthe economically fundamental shocks, thus eliminating the need to forecast the forecasts of others.