Dynamic higher order expectations

Abstract

In models where privately informed agents interact, agents may need to form higher order expectations, i.e. expectations of other agents' expectations. This paper develops a tractable framework for solving and analyzing linear dynamic rational expectations models in which privately informed agents form higher order expectations. The framework is used to demonstrate that the well-known problem of the infinite regress of expectations identified by Townsend (1983) can be approximated to an arbitrary accuracy with a finite dimensional representation under quite general conditions. The paper is constructive and presents a fixed point algorithm for finding an accurate solution and provides weak conditions that ensure that a fixed point exists. To help intuition, Singleton's (1987) asset pricing model with disparately informed traders is used as a vehicle for the paper.