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A Note on the Uniqueness of Solutions to Rational Expectations Models

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Abstract

Klein (2000) advocates the use of the Schur decomposition of a matrix pencilo solve linear rational expectations (RE) models. Meanwhile his algorithm hasecome a center piece in several computer codes that provide approximate olutions to (non-linear) dynamic stochastic general equilibrium (DSGE) models. Aubtlety not resolved by Klein is whether or not a certain Schur decompostionould fail to solve the model while a second one would provide a solution. Wehow that this cannot happen.

Suggested Citation

  • Christopher Heiberger & Torben Klarl & Alfred Maussner, 2012. "A Note on the Uniqueness of Solutions to Rational Expectations Models," Discussion Paper Series 319, Universitaet Augsburg, Institute for Economics.
    • Handle: RePEc:aug:augsbe:0319
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    File URL: https://opus.bibliothek.uni-augsburg.de/opus4/files/71099/319.pdf
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    References listed on IDEAS

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    1. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
    2. 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.
    3. Heer, Burkhard & Maußner, Alfred, 2008. "Computation Of Business Cycle Models: A Comparison Of Numerical Methods," Macroeconomic Dynamics, Cambridge University Press, vol. 12(5), pages 641-663, November.
    4. Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. "Solving dynamic general equilibrium models using a second-order approximation to the policy function," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 755-775, January.
    5. Gomme, Paul & Klein, Paul, 2011. "Second-order approximation of dynamic models without the use of tensors," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 604-615, April.
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    Cited by:

    1. John G. Thistle, 2018. "The Origin and the Resolution of Nonuniqueness in Linear Rational Expectations," Papers 1806.06657, arXiv.org, revised Apr 2019.
    2. Meyer-Gohde, Alexander, 2021. "On the accuracy of linear DSGE solution methods and the consequences for log-normal asset pricing," IMFS Working Paper Series 154, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).

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    More about this item

    Keywords

    Linear Rational Expectations Models; Schur Decomposition; DSGE Models;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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