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Solving rational expectations models at first order: what Dynare does

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  • Villemot, Sébastien

Abstract

This paper describes in detail the algorithm implemented in Dynare for computing the first order approximated solution of a nonlinear rational expectations model. The core of the algorithm is a generalized Schur decomposition (also known as the QZ decomposition), as advocated by several authors in the litterature. The contribution of the present paper is to focus on implementation details that make the algorithm more generic and more efficient, especially for large models.

Suggested Citation

  • Villemot, Sébastien, 2011. "Solving rational expectations models at first order: what Dynare does," Dynare Working Papers 2, CEPREMAP.
    • Handle: RePEc:cpm:dynare:002
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    File URL: https://www.dynare.org/wp-repo/dynarewp002.pdf
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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. Collard, Fabrice & Juillard, Michel, 2001. "A Higher-Order Taylor Expansion Approach to Simulation of Stochastic Forward-Looking Models with an Application to a Nonlinear Phillips Curve Model," Computational Economics, Springer;Society for Computational Economics, vol. 17(2-3), pages 125-139, June.
    3. 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.
    4. 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.
    5. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 1-20, October.
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    Cited by:

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    2. Audzei, Volha, 2023. "Learning and cross-country correlations in a multi-country DSGE model," Economic Modelling, Elsevier, vol. 120(C).
    3. Ivashchenko, Sergey & Mutschler, Willi, 2020. "The effect of observables, functional specifications, model features and shocks on identification in linearized DSGE models," Economic Modelling, Elsevier, vol. 88(C), pages 280-292.
    4. Enrique Martínez García & Mark A. Wynne, 2014. "Technical note on \"assessing Bayesian model comparison in small samples\"," Globalization Institute Working Papers 190, Federal Reserve Bank of Dallas.
    5. Boehl, Gregor, 2022. "Efficient solution and computation of models with occasionally binding constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    6. Meyer-Gohde, Alexander & Saecker, Johanna, 2024. "Solving linear DSGE models with Newton methods," Economic Modelling, Elsevier, vol. 133(C).
    7. Lan, Hong & Meyer-Gohde, Alexander, 2014. "Solvability of perturbation solutions in DSGE models," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 366-388.
    8. Böhl, Gregor & Strobel, Felix, 2020. "US business cycle dynamics at the zero lower bound," IMFS Working Paper Series 143, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).
    9. 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).
    10. Enrique Martínez-García & Diego Vilán & Mark A. Wynne, 2012. "Bayesian Estimation of NOEM Models: Identification and Inference in Small Samples," Advances in Econometrics, in: DSGE Models in Macroeconomics: Estimation, Evaluation, and New Developments, pages 137-199, Emerald Group Publishing Limited.
    11. Martínez-García, Enrique, 2021. "Get the lowdown: The international side of the fall in the U.S. natural rate of interest," Economic Modelling, Elsevier, vol. 100(C).
    12. Jarod Coulter & Roberto Duncan & Enrique Martínez-García, 2022. "Flexible Average Inflation Targeting: How Much Is U.S. MonetaryPolicy Changing?," Revista Economía, Fondo Editorial - Pontificia Universidad Católica del Perú, vol. 45(89), pages 102-149.
    13. Kollintzas, Tryphon & Tsoukalas, Konstantinos, 2015. "Bank and Sovereign Risk Interdependence in the Euro Area," CEPR Discussion Papers 10485, C.E.P.R. Discussion Papers.
    14. Meyer-Gohde, Alexander, 2024. "Solving and analyzing DSGE models in the frequency domain," IMFS Working Paper Series 207, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).
    15. Huber, Johannes & Meyer-Gohde, Alexander & Saecker, Johanna, 2023. "Solving linear DSGE models with structure-preserving doubling methods," IMFS Working Paper Series 195, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).
    16. Amedeo Argentiero & Carlo Andrea Bollino, 2015. "Uncovering Unobserved Economy: A General Equilibrium Characterization," Metroeconomica, Wiley Blackwell, vol. 66(2), pages 306-338, May.
    17. David Alan Peel & Pantelis Promponas, 2016. "Forecasting the nominal exchange rate movements in a changing world. The case of the U.S. and the U.K," Working Papers 144439514, Lancaster University Management School, Economics Department.
    18. 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).

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    More about this item

    Keywords

    Dynare; Numerical methods; Perturbation; Rational expectations;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models

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