Working Paper

Finite-Order VAR Representation of Linear Rational Expectations Models: With Some Lessons for Monetary Policy

Abstract: This paper considers the characterization via finite-order VARs of the solution of a large class of linear rational expectations (LRE) models. I propose a unified approach that uses a companion Sylvester equation to check the existence and uniqueness of a solution to the canonical (first-order) LRE model in finite-order VAR form and a quadratic matrix equation to characterize it decoupling the backward- and forward-looking aspects of the model. I also investigate the fundamentalness of the shocks recovered. Solving LRE models by this procedure is straightforward to implement, general in its applicability, efficient in the use of computational resources, 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 practical implementation of the methodology. I argue that existing empirical evidence on the transmission mechanism of monetary policy shocks from structural VARs (when the specification is inconsistent with theory due to the identification restrictions, lag specification, etc.) should be taken with a grain of salt as it may not have a proper structural interpretation.

Keywords: Linear Rational Expectations Models; Vector Autoregression Representation; Sylvester Matrix Equation; New Keynesian Model; Monetary Policy Shocks;

JEL Classification: C32; C62; C63; E37;

https://doi.org/10.24149/gwp285r2

Bibliographic Information

Provider: Federal Reserve Bank of Dallas

Part of Series: Globalization Institute Working Papers

Publication Date: 2018-08-01

Number: 285

Pages: 49 pages

Note: Previous versions of this paper circulated under the title, "System Reduction and Finite-Order VAR Solution Methods for Linear Rational Expectations Models."