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Perturbation Methods for Markov-Switching DSGE Models

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  • Andrew Foerster
  • Juan Rubio-Ramirez
  • Dan Waggoner
  • Ta Zha

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 de?ned. With this de?nition, we show that the problem of ?nding an approximation of any order can be reduced to solving a system of quadratic equations. We propose using the theory of Gröbner 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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Paper provided by FEDEA in its series Working Papers with number 2013-22.

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Date of creation: Dec 2013
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Handle: RePEc:fda:fdaddt:2013-22

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  3. Eric M. Leeper & Tao Zha, 2003. "Modest policy interventions," Working Paper 2003-24, Federal Reserve Bank of Atlanta.
  4. Roger E. A. Farmer & Daniel F. Waggoner & Tao Zha, 2010. "Minimal State Variable Solutions to Markov-switching Rational Expectations Models," Emory Economics 1003, Department of Economics, Emory University (Atlanta).
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  7. Francesco Bianchi, 2012. "Regime Switches, Agents’ Beliefs, and Post-World War II U.S. Macroeconomic Dynamics," Working Papers 12-04, Duke University, Department of Economics.
  8. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
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  13. Christopher A. Sims & Tao Zha, 2006. "Were There Regime Switches in U.S. Monetary Policy?," American Economic Review, American Economic Association, vol. 96(1), pages 54-81, March.
  14. Glenn D. Rudebusch & Eric T. Swanson, 2008. "Examining the bond premium puzzle with a DSGE model," Working Paper Series 2007-25, Federal Reserve Bank of San Francisco.
  15. Troy Davig & Eric M. Leeper, 2005. "Generalizing the Taylor Principle," NBER Working Papers 11874, National Bureau of Economic Research, Inc.
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  17. Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2006. "Estimating Macroeconomic Models: A Likelihood Approach," Levine's Bibliography 122247000000000849, UCLA Department of Economics.
  18. Davig, Troy & Leeper, Eric M. & Walker, Todd B., 2010. ""Unfunded liabilities" and uncertain fiscal financing," Journal of Monetary Economics, Elsevier, vol. 57(5), pages 600-619, July.
  19. 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.
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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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