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

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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.

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  • Enrique Martínez García, 2016. "Finite-Order VAR Representation of Linear Rational Expectations Models: With Some Lessons for Monetary Policy," Globalization Institute Working Papers 285, Federal Reserve Bank of Dallas.
    • Handle: RePEc:fip:feddgw:285
    DOI: 10.24149/gwp285r2
    Note: Previous versions of this paper circulated under the title, "System Reduction and Finite-Order VAR Solution Methods for Linear Rational Expectations Models."
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    More about this item

    Keywords

    Linear Rational Expectations Models; Vector Autoregression Representation; Sylvester Matrix Equation; New Keynesian Model; Monetary Policy Shocks;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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