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On the uniqueness of solutions to rational expectations models

Author

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  • Heiberger, Christopher
  • Klarl, Torben
  • Maußner, Alfred

Abstract

Klein (2000) advocates the use of the Schur decomposition of a matrix pencil to solve linear rational expectations models. Meanwhile his algorithm has become a center piece in several computer codes that provide approximate solutions to (non-linear) dynamic stochastic general equilibrium models. A subtlety not resolved by Klein is whether or not a certain Schur decomposition could fail to solve the model while a second one would provide a solution. We show that this cannot happen.

Suggested Citation

  • Heiberger, Christopher & Klarl, Torben & Maußner, Alfred, 2015. "On the uniqueness of solutions to rational expectations models," Economics Letters, Elsevier, vol. 128(C), pages 14-16.
    • Handle: RePEc:eee:ecolet:v:128:y:2015:i:c:p:14-16
    DOI: 10.1016/j.econlet.2014.12.025
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
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    Cited by:

    1. Meyer-Gohde, Alexander, 2023. "Numerical stability analysis of linear DSGE models: Backward errors, forward errors and condition numbers," IMFS Working Paper Series 193, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).
    2. John G. Thistle, 2018. "The Origin and the Resolution of Nonuniqueness in Linear Rational Expectations," Papers 1806.06657, arXiv.org, revised Apr 2019.
    3. 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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    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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