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Solving SDGE Models: A New Algorithm for Sylvester Equation

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  • Ondrej Kamenik

Abstract

This paper presents a new numerical algorithm for solving Sylvester equation involved in higher order perturbation method used for solution of stochastic dynamic general equilibrium models. The new algorithm is better than methods used so far (esp. very popular doubling algorithm) in terms of computational time, memory consumption, and numerical stability. Further, the paper applies the algorithm in a simulation of a large macroeconomy model providing a simple welfare analysis of a few monetary rules. The welfare analysis compares household's lifetime expected utility.

Suggested Citation

  • Ondrej Kamenik, 2004. "Solving SDGE Models: A New Algorithm for Sylvester Equation," Computing in Economics and Finance 2004 222, Society for Computational Economics.
    • Handle: RePEc:sce:scecf4:222
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    References listed on IDEAS

    as
    1. Anderson, Evan W. & McGrattan, Ellen R. & Hansen, Lars Peter & Sargent, Thomas J., 1996. "Mechanics of forming and estimating dynamic linear economies," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 4, pages 171-252, Elsevier.
    2. Laxton, Douglas & Pesenti, Paolo, 2003. "Monetary rules for small, open, emerging economies," Journal of Monetary Economics, Elsevier, vol. 50(5), pages 1109-1146, July.
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    Cited by:

    1. Juillard Michel, 2011. "Local approximation of DSGE models around the risky steady state," wp.comunite 0087, Department of Communication, University of Teramo.
    2. 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.
    3. Junior Maih, 2014. "Efficient Perturbation Methods for Solving Regime-Switching DSGE Models," Working Papers No 10/2014, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    4. Hong Lan & Alexander Meyer-Gohde, 2012. "Existence and Uniqueness of Perturbation Solutions to DSGE Models," SFB 649 Discussion Papers SFB649DP2012-015, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Ian Babetskii & Ales Bulir & Fabrizio Coricelli & Jan Filacek & Michal Franta & Roman Horvath & Branislav Saxa & Katerina Smidkova, 2008. "CNB Economic Research Bulletin: Ten Years of Inflation Targeting," Occasional Publications - Edited Volumes, Czech National Bank, edition 1, volume 6, number rb06/1 edited by Ian Babetskii & Katerina Smidkova, January.
    6. Andrew Binning, 2013. "Solving second and third-order approximations to DSGE models: A recursive Sylvester equation solution," Working Paper 2013/18, Norges Bank.
    7. Alena Bicakova & Kamil Dybczak & Ales Krejdl & Jiri Slacalek & Michal Slavik, 2007. "CNB Economic Research Bulletin: Fiscal Policy and its Sustainability," Occasional Publications - Edited Volumes, Czech National Bank, edition 2, volume 5, number rb05/2 edited by Ian Babetskii & Vladimir Bezdek, January.
    8. Martin M. Andreasen, 2010. "How Non-Gaussian Shocks Affect Risk Premia in Non-Linear DSGE Models," CREATES Research Papers 2010-63, Department of Economics and Business Economics, Aarhus University.
    9. 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.

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    More about this item

    Keywords

    sylvester equation; SDGE; perturbation method; welfare analysis;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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