System Reduction and Finite-Order VAR Solution Methods for Linear Rational Expectations Models

Abstract

This paper considers the solution of a large class of linear rational expectations (LRE) models and its characterization via finite-order VARs. The solution of the canonical LRE model can be cast in state-space form and solved for by the method of undetermined coefficients. In this paper I propose an approach that simplifies the systematic characterization of the solution into finite-order VAR form and checks existence and uniqueness based on the solution of a companion Sylvester equation. Solving LRE models with a finite-order VAR representation via the Sylvester equation is straightforward to implement, efficient, and can be handled easily with standard matrix algebra. An application to the workhorse New Keynesian model with accompanying Matlab codes is provided to illustrate the implementation of the procedure in practice.