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

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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.

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  • Enrique Martínez García, 2020. "A Matter of Perspective: Mapping Linear Rational Expectations Models into Finite-Order VAR Form," Globalization Institute Working Papers 389, Federal Reserve Bank of Dallas.
    • Handle: RePEc:fip:feddgw:88096
    DOI: 10.24149/gwp389
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    More about this item

    Keywords

    Linear Rational Expectations Models; Finite-Order Vector Autoregressive 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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