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Perturbation methods for Markov-switching DSGE models

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  • Foerster, Andrew

    ()
    (Federal Reserve Bank of Atlanta)

  • Rubio-Ramírez, Juan

    ()
    (Duke University)

  • Waggoner, Daniel F.

    ()
    (Federal Reserve Bank of Atlanta)

  • Zha, Tao

    ()

Abstract

This paper develops a general perturbation methodology for constructing high-order approximations to the solutions of Markov-switching DSGE models. We introduce an important and practical idea of partitioning the Markov-switching parameter space so that a steady state is well defined. With this definition, we show that the problem of finding an approximation of any order can be reduced to solving a system of quadratic equations. We propose using the theory of Grobner bases in searching all the solutions to the quadratic system. This approach allows us to obtain all the approximations and ascertain how many of them are stable. Our methodology is applied to three models to illustrate its feasibility and practicality.

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Bibliographic Info

Paper provided by Federal Reserve Bank of Atlanta in its series Working Paper with number 2013-01.

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Length: 84 pages
Date of creation: 01 Mar 2013
Date of revision:
Handle: RePEc:fip:fedawp:2013-01

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Keywords: Markov-switching parameters; partition; higher order approximations; no certainty equivalence; quadratic system; Grobner bases;

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  16. Ralph S.J. Koijen & Jules H. van Binsbergen & Juan F. Rubio-Ramírez & Jesus Fernandez-Villaverde, 2008. "Likelihood Estimation of DSGE Models with Epstein-Zin Preferences," 2008 Meeting Papers 1099, Society for Economic Dynamics.
  17. Farmer, Roger E.A. & Waggoner, Daniel F. & Zha, Tao, 2009. "Understanding Markov-switching rational expectations models," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1849-1867, September.
  18. Francesco Bianchi, 2009. "Regime Switches, Agents’ Beliefs, and Post-World War II U.S. Macroeconomic Dynamics," 2009 Meeting Papers 198, Society for Economic Dynamics.
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Cited by:
  1. Andrew Foerster, 2013. "Monetary Policy Regime Switches and Macroeconomic Dynamics," 2013 Meeting Papers 906, Society for Economic Dynamics.
  2. Blagov , Boris & Funke, Michael, 2013. "The regime-dependent evolution of credibility: A fresh look at Hong Kong’s linked exchange rate system," BOFIT Discussion Papers 24/2013, Bank of Finland, Institute for Economies in Transition.

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