Rational Expectations Models with Higher Order Beliefs

Abstract

This paper develops a general method of solving rational expectations models with higher order beliefs. Higher order beliefs are crucial in an environment with dispersed information and strategic complementarity, and the equilibrium policy depends on infinite higher order beliefs. It is generally believed that solving this type of equilibrium policy requires an infinite number of state variables  (Townsend, 1983). This paper proves that the equilibrium policy rule can always be represented by a finite number of state variables if the signals observed by agents follow an ARMA process, in which case we obtain a general solution formula. We also prove that when the signals contain endogenous variables, a finite-state-variable representation of the equilibrium may not exist. The key innovation in our method is to use the factorization identity and Wiener filter to solve signal extraction problems conditional on infinite signals. This method can be used in a wide range of applications. 

About the presenter's visit

Naoki Takayama will be visiting the School of Economics on 3-10 March 2020.  While here he will be using room 608 Colin Clark Building.  If you would like to meet with him please contact Dr Satoshi Tanaka who will be his host while at The University of Queensland.  Dr Tanaka can be contacted on s.tanaka@uq.edu.au.