Empirically feasible solutions and explicit dynamics for rational expectation models

Abstract

Fairly general rational expectation (RE) models are proved to have linear vector autoregressive moving average (VARMA) models as their reduced forms, using Muth's method of undetermined coefficients (MUC). An advantage of using VARMAs is that RE estimation can benefit from well-developed theory of solutions of stochastic difference equations and computer packages for VARMA and state space (SS) models. For example, we report theoretical derivations of explicit dynamics associated with the RE structure for Muth's and Lucas-Sargent-Wallace's models, suggesting generalizations and new solutions. We illustrate an RE structure estimation by using energy prices and Fackler and Krieger's ( J. Bus. Econom. Statist. 4 (1986), 71–80) study of five major macroeconomic variables.