Finite-Order VAR Representation of Linear Rational Expectations Models: In a Nutshell

Abstract

This note summarizes the salient derivations of Martínez-García (2018). Specifically, it shows that the solution to a large class of linear rational expectations (LRE) models can be represented in finite-order VAR form. Martínez-García (2018) proposes a unified approach that uses a companion quadratic matrix equation to decouple the backward- and forward-looking parts of the canonical form of the LRE model and a Sylvester equation to pin down the solution and simplify its characterization so it can be expressed as a finite-order VAR.

Keywords: Linear Rational Expectations Models, Vector Autoregression Representation, Sylvester Matrix Equation, Quadratic Matrix Equation

JEL Classification: C32, C62, C63