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Understanding Markov-switching rational expectations models

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  • Farmer, Roger E.A.
  • Waggoner, Daniel F.
  • Zha, Tao

Abstract

We develop a set of necessary and sufficient conditions for equilibria to be determinate in a class of forward-looking Markov-switching rational expectations models and we develop an algorithm to check these conditions in practice. We use three examples, based on the new-Keynesian model of monetary policy, to illustrate our technique. Our work connects applied econometric models of Markov-switching with forward looking rational expectations models and allows an applied researcher to construct the likelihood function for models in this class over a parameter space that includes a determinate region and an indeterminate region.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jetheo:v:144:y:2009:i:5:p:1849-1867
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    1. Timothy Cogley & Thomas J. Sargent, 2005. "Drift and Volatilities: Monetary Policies and Outcomes in the Post WWII U.S," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(2), pages 262-302, April.
    2. Leeper, Eric M. & Zha, Tao, 2003. "Modest policy interventions," Journal of Monetary Economics, Elsevier, vol. 50(8), pages 1673-1700, November.
    3. McCallum, Bennett T., 1983. "On non-uniqueness in rational expectations models : An attempt at perspective," Journal of Monetary Economics, Elsevier, vol. 11(2), pages 139-168.
    4. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory," The Quarterly Journal of Economics, Oxford University Press, vol. 115(1), pages 147-180.
    5. Troy Davig & Eric M. Leeper, 2007. "Generalizing the Taylor Principle," American Economic Review, American Economic Association, vol. 97(3), pages 607-635, June.
    6. Thomas A. Lubik & Frank Schorfheide, 2004. "Testing for Indeterminacy: An Application to U.S. Monetary Policy," American Economic Review, American Economic Association, vol. 94(1), pages 190-217, March.
    7. Troy Davig & Eric M. Leeper, 2007. "Fluctuating Macro Policies and the Fiscal Theory," NBER Chapters,in: NBER Macroeconomics Annual 2006, Volume 21, pages 247-316 National Bureau of Economic Research, Inc.
    8. Andrew P Blake & Fabrizio Zampolli, 2006. "Optimal monetary policy in Markov-switching models with rational expectations agents," Bank of England working papers 298, Bank of England.
    9. Roger E. A. Farmer & Daniel F. Waggoner & Tao Zha, 2010. "Generalizing the Taylor Principle: Comment," American Economic Review, American Economic Association, vol. 100(1), pages 608-617, March.
    10. Leeper, Eric M., 1991. "Equilibria under 'active' and 'passive' monetary and fiscal policies," Journal of Monetary Economics, Elsevier, vol. 27(1), pages 129-147, February.
    11. Lubik, Thomas A. & Schorfheide, Frank, 2003. "Computing sunspot equilibria in linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 28(2), pages 273-285, November.
    12. Zheng Liu & Daniel Waggoner & Tao Zha, 2009. "Asymmetric Expectation Effects of Regime Shifts in Monetary Policy," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 12(2), pages 284-303, April.
    13. Roger E. A. Farmer & Daniel F. Waggoner & Tao Zha, 2009. "Indeterminacy in a forward-looking regime switching model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(1), pages 69-84.
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    Keywords

    Stability Non-linearity Unique equilibrium Cross-regime indeterminacy Expectations formation Necessary and sufficient conditions;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • E0 - Macroeconomics and Monetary Economics - - General
    • E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates

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