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Solving Linear Rational Expectations Models with Lagged Expectations Quickly and Easily

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Alexander Meyer-Gohde

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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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Publisher Info
Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2007-069.

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Length: 33 pages
Date of creation: Dec 2007
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Handle: RePEc:hum:wpaper:sfb649dp2007-069

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Related research
Keywords: Lagged expectations; linear rational expectations models; block tridiagonal; Generalized Schur Form; QZ decomposition; LAPACK;

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Find related papers by JEL classification:
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. N. Gregory Mankiw & Ricardo Reis, 2002. "Sticky Information Versus Sticky Prices: A Proposal To Replace The New Keynesian Phillips Curve," The Quarterly Journal of Economics, MIT Press, vol. 117(4), pages 1295-1328, November. [Downloadable!] (restricted)
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  2. Trabandt, Mathias, 2007. "Sticky Information vs. Sticky Prices: A Horse Race in a DSGE Framework," Working Paper Series 209, Sveriges Riksbank (Central Bank of Sweden). [Downloadable!]
    Other versions:
  3. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September. [Downloadable!] (restricted)
  4. Peng-fei Wang & Yi Wen, 2006. "Solving linear difference systems with lagged expectations by a method of undetermined coefficients," Working Papers 2006-003, Federal Reserve Bank of St. Louis. [Downloadable!]
  5. King, Robert G & Watson, Mark W, 1998. "The Solution of Singular Linear Difference Systems under Rational Expectations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1015-26, November.
  6. Harald Uhlig, 1998. "A Toolkit for Analysing Nonlinear Dynamic Stochastic Models Easily," QM&RBC Codes 123, Quantitative Macroeconomics & Real Business Cycles. [Downloadable!]
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  7. Bennett T. McCallum, 2003. "Multiple-Solution Indeterminacies in Monetary Policy Analysis," NBER Working Papers 9837, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  8. Andres, Javier & Lopez-Salido, J. David & Nelson, Edward, 2005. "Sticky-price models and the natural rate hypothesis," Journal of Monetary Economics, Elsevier, vol. 52(5), pages 1025-1053, July. [Downloadable!] (restricted)
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  9. Michael T. Kiley, 2006. "A quantitative comparison of sticky-price and sticky-information models of price setting," Finance and Economics Discussion Series 2006-45, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
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  10. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-11, July. [Downloadable!] (restricted)
  11. Burmeister, Edwin, 1980. "On Some Conceptual Issues in Rational Expectations Modeling," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 12(4), pages 800-816, November. [Downloadable!] (restricted)
  12. Oleg Korenok & Norman R. Swanson, 2007. "How Sticky Is Sticky Enough? A Distributional and Impulse Response Analysis of New Keynesian DSGE Models," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(6), pages 1481-1508, 09. [Downloadable!] (restricted)
  13. Anderson, Gary & Moore, George, 1985. "A linear algebraic procedure for solving linear perfect foresight models," Economics Letters, Elsevier, vol. 17(3), pages 247-252. [Downloadable!] (restricted)
  14. Benjamin D. Keen, 2007. "Sticky Price And Sticky Information Price-Setting Models: What Is The Difference?," Economic Inquiry, Western Economic Association International, vol. 45(4), pages 770-786, October. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Herings P. Jean-Jacques & Peeters Ronald & Yang Michael S., 2009. "Piracy on the internet: Accommodate it or fight it? A dynamic approach," Research Memoranda 034, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
  2. Ricardo Reis, 2009. "A Sticky-Information General-Equilibrium Model for Policy Analysis," NBER Working Papers 14732, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  3. 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. [Downloadable!]
  4. Alexander Meyer-Gohde, 2008. "The Natural Rate Hypothesis and Real Determinacy," SFB 649 Discussion Papers SFB649DP2008-054, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  5. Yao, Fang, 2009. "Time-dependent pricing and New Keynesian Phillips curve," Discussion Paper Series 1: Economic Studies 2009,08, Deutsche Bundesbank, Research Centre. [Downloadable!]
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