A Matter of Perspective: Mapping Linear Rational Expectations Models into Finite-Order VAR Form

Abstract

This paper considers the characterization of the reduced-form solution of a large class of linear rational expectations models. I show that under certain conditions, if a solution exists and is unique, it can be cast in finite-order VAR form. I also investigate the conditions for the VAR form to be stationary with a well-defined residual variance-covariance matrix in equilibrium, for the shocks to be recoverable, and for local identification of the structural parameters for estimation from the sample likelihood. An application to the workhorse New Keynesian model with accompanying Matlab codes illustrates the practical use of the finite-order VAR representation. In particular, I argue that the identification of monetary policy shocks based on structural VARs can be more closely aligned with theory using the finite-order VAR form of the model solution characterized in this paper.

Keywords: Linear Rational Expectations Models, Finite-Order Vector Autoregressive Representation, Sylvester Matrix Equation, New Keynesian Model, Monetary Policy Shocks

JEL Classification: C32, C62, C63, E37