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Solving Linear Rational Expectations Models with Lagged Expectations Quickly and Easily

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  • Alexander Meyer-Gohde

Abstract

A solution method is derived in this paper for solving a system of linear rationalexpectations 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 straightforward 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.

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  • Alexander Meyer-Gohde, 2007. "Solving Linear Rational Expectations Models with Lagged Expectations Quickly and Easily," SFB 649 Discussion Papers SFB649DP2007-069, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2007-069
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    Cited by:

    1. 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, Hamburg University, Department Wirtschaft und Politik.
    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. Fabio Verona & Maik Wolters, 2014. "Sticky Information Models in Dynare," Computational Economics, Springer;Society for Computational Economics, vol. 43(3), pages 357-370, March.
    4. Meyer-Gohde, Alexander & Neuhoff, Daniel, 2015. "Solving and estimating linearized DSGE models with VARMA shock processes and filtered data," Economics Letters, Elsevier, vol. 133(C), pages 89-91.
    5. Alexander Meyer-Gohde, 2008. "The Natural Rate Hypothesis and Real Determinacy," SFB 649 Discussion Papers SFB649DP2008-054, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. Mehmet Fatih, Ekinci, 2010. "Inattentive Consumers and Exchange Rate Volatility," MPRA Paper 26472, University Library of Munich, Germany, revised 31 Oct 2010.
    7. Ekinci, Mehmet Fatih, 2017. "Inattentive consumers and international business cycles," Journal of International Money and Finance, Elsevier, vol. 72(C), pages 1-27.
    8. Lena Dräger, 2011. "Endogenous Persistence with Recursive Inattentiveness," Macroeconomics and Finance Series 201103, Hamburg University, Department Wirtschaft und Politik.
    9. Hess Chung & Edward Herbst & Michael T. Kiley, 2015. "Effective Monetary Policy Strategies in New Keynesian Models: A Reexamination," NBER Macroeconomics Annual, University of Chicago Press, vol. 29(1), pages 289-344.
    10. Carrillo, Julio A., 2012. "How well does sticky information explain the dynamics of inflation, output, and real wages?," Journal of Economic Dynamics and Control, Elsevier, vol. 36(6), pages 830-850.
    11. Alexander Meyer-Gohde, 2011. "Sticky Information and Determinacy," SFB 649 Discussion Papers SFB649DP2011-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    12. Yao, Fang, 2009. "Time-dependent pricing and New Keynesian Phillips curve," Discussion Paper Series 1: Economic Studies 2009,08, Deutsche Bundesbank.
    13. Lieb Lenard, 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).
    14. Lan, Hong & Meyer-Gohde, Alexander, 2013. "Solving DSGE models with a nonlinear moving average," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2643-2667.
    15. Fang Yao, 2009. "Non-constant Hazard Function and Inflation Dynamics," SFB 649 Discussion Papers SFB649DP2009-030, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    16. Lena Dräger, 2010. "Why don't people pay attention? Endogenous Sticky Information in a DSGE Model," Macroeconomics and Finance Series 201002, Hamburg University, Department Wirtschaft und Politik.
    17. Lena Draeger, 2010. "Why Don't People Pay Attention?," KOF Working papers 10-260, KOF Swiss Economic Institute, ETH Zurich.
    18. Alexander Meyer-Gohde & Daniel Neuhoff, 2015. "Generalized Exogenous Processes in DSGE: A Bayesian Approach," SFB 649 Discussion Papers SFB649DP2015-014, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

    More about this item

    Keywords

    Lagged expectations; linear rational expectations models; block tridiagonal; Generalized Schur Form; QZ decomposition; LAPACK;

    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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