A Complete Characterization of ARMA Solutions to Linear Rational Expectations Models

Abstract

Linear rational expectations models with expectations of future endogenous variables have multiple equilibria. For a scalar model with k forward expectational lags and l backward lags, this paper characterizes the complete set of ARMA solutions. It is shown that the maximum degree solutions are ARMA ( k + l , k ), that the solutions of maximum degree are obtained directly from the characteristic polynomial but have arbitrary MA parameters, and that all lower degree ARMA solutions are obtained by deleting common factors in the AR and MA lag polynomials. The results are applied to several macroeconomic examples.