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Solving SDGE Models: A New Algorithm for the Sylvester Equation

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  • Ondrej Kamenik

Abstract

This paper presents a new numerical algorithm for solving the Sylvester equation involved in higher-order perturbation methods developed for solving stochastic dynamic general equilibrium models. The new algorithm surpasses other methods used so far (including the very popular doubling algorithm) in terms of computational time, memory consumption, and numerical stability.

Suggested Citation

  • Ondrej Kamenik, 2005. "Solving SDGE Models: A New Algorithm for the Sylvester Equation," Working Papers 2005/10, Czech National Bank.
    • Handle: RePEc:cnb:wpaper:2005/10
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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)

    Citations

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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. repec:bny:wpaper:0028 is not listed on IDEAS
    4. repec:cnb:ocpubv:rb05/2 is not listed on IDEAS
    5. Lan, Hong & Meyer-Gohde, Alexander, 2012. "Existence and uniqueness of perturbation solutions to DSGE models," SFB 649 Discussion Papers 2012-015, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    6. 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.
    7. Lan, Hong & Meyer-Gohde, Alexander, 2011. "Solving DSGE models with a nonlinear moving average," SFB 649 Discussion Papers 2011-087, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    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. Lan, Hong & Meyer-Gohde, Alexander, 2012. "Existence and uniqueness of perturbation solutions to DSGE models," SFB 649 Discussion Papers 2012-015, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    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.

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    More about this item

    Keywords

    Dynamic general equilibrium; doubling algorithm; perturbation approach; recursive algorithm.;
    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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