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Solving linear rational expectations models with lagged expectations quickly and easily

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  • Meyer-Gohde, Alexander

Abstract

A solution method is derived in this paper for solving a system of linear rational-expectations equation with lagged expectations (e.g., models incorporating sticky information) using the method of undetermined coefficients for the infinite MA representation. The method applies a combination of a Generalized Schur Decomposition familiar elsewhere in the literature and a simple system of linear equations when lagged expectations are present to the infinite MA representation. Execution is faster, applicability more general, and use more straight-forward than with existing algorithms. Current methods of truncating lagged expectations are shown to not generally be innocuous and the use of such methods are rendered obsolete by the tremendous gains in computational efficiency of the method here which allows for a solution to floating-point accuracy in a fraction of the time required by standard methods. The associated computational application of the method provides impulse responses to anticipated and unanticipated innovations, simulations, and frequency-domain and simulated moments.

Suggested Citation

  • Meyer-Gohde, Alexander, 2007. "Solving linear rational expectations models with lagged expectations quickly and easily," SFB 649 Discussion Papers 2007-069, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2007-069
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    Cited by:

    1. repec:hum:wpaper:sfb649dp2009-030 is not listed on IDEAS
    2. Ricardo Reis, 2009. "A Sticky-information General Equilibrium Model por Policy Analysis," Central Banking, Analysis, and Economic Policies Book Series, in: Klaus Schmidt-Hebbel & Carl E. Walsh & Norman Loayza (Series Editor) & Klaus Schmidt-Hebbel (Series (ed.),Monetary Policy under Uncertainty and Learning, edition 1, volume 13, chapter 8, pages 227-283, Central Bank of Chile.
    3. Yao, Fang, 2009. "Time-dependent pricing and New Keynesian Phillips curve," Discussion Paper Series 1: Economic Studies 2009,08, Deutsche Bundesbank.
    4. Jan-Oliver Menz & Lena Vogel, 2009. "A Detailed Derivation of the Sticky Price and Sticky Information New Keynesian DSGE Model," Macroeconomics and Finance Series 200902, University of Hamburg, Department of Socioeconomics.
    5. Yao, Fang, 2009. "Non-constant hazard function and inflation dynamics," SFB 649 Discussion Papers 2009-030, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    6. Meyer-Gohde, Alexander, 2008. "The natural rate hypothesis and real determinacy," SFB 649 Discussion Papers 2008-054, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    7. repec:hum:wpaper:sfb649dp2008-054 is not listed on IDEAS
    8. Lieb, L.M., 2009. "Taking real rigidities seriously: implications for optimal policy design in a currency union," Research Memorandum 032, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    9. Alali, Walid Y., 2009. "Solution Strategies of Dynamic Stochastic General Equilibrium (DSGE) models," EconStor Preprints 269876, ZBW - Leibniz Information Centre for Economics.
    10. Alali, Walid Y., 2009. "Solution Strategies of Dynamic Stochastic General Equilibrium (DSGE) models," MPRA Paper 116480, University Library of Munich, Germany.

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    More about this item

    Keywords

    Lagged expectations; linear rational expectations models; block tridiagonal; Generalized Schur Form; QZ decomposition; LAPACK;
    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
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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