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

49 Pages Posted: 28 Oct 2016 Last revised: 29 Apr 2020

See all articles by Enrique Martínez-García

Enrique Martínez-García

Federal Reserve Bank of Dallas - Research Department

Multiple version iconThere are 2 versions of this paper

Date Written: September, 2016

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.

JEL Classification: C32, C62, C63, E37

Suggested Citation

Martinez-Garcia, Enrique, Finite-Order VAR Representation of Linear Rational Expectations Models: With Some Lessons for Monetary Policy (September, 2016). Globalization and Monetary Policy Institute Working Paper No. 285, Available at SSRN: https://ssrn.com/abstract=2860550 or http://dx.doi.org/10.24149/gwp285r2

Enrique Martinez-Garcia (Contact Author)

Federal Reserve Bank of Dallas - Research Department ( email )

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