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Solving SDGE Models: A New Algorithm for Sylvester Equation

Author

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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.
    Full references (including those not matched with items on IDEAS)

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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, 2015. "Efficient perturbation methods for solving regime-switching DSGE models," Working Paper 2015/01, Norges Bank.
    4. 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.
    5. repec:cnb:ocpubv:rb05/2 is not listed on IDEAS
    6. Lan, Hong & Meyer-Gohde, Alexander, 2012. "Existence and Uniqueness of Perturbation Solutions in DSGE Models," Dynare Working Papers 14, CEPREMAP.
    7. 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.
    8. 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.
    9. repec:hum:wpaper:sfb649dp2011-087 is not listed on IDEAS
    10. repec:cnb:ocpubv:rb06/1 is not listed on IDEAS
    11. Andrew Binning, 2013. "Solving second and third-order approximations to DSGE models: A recursive Sylvester equation solution," Working Paper 2013/18, Norges Bank.
    12. repec:hum:wpaper:sfb649dp2012-015 is not listed on IDEAS

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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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