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Expectational stability in regime-switching rational expectations models

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William A. Branch
Troy Davig
Bruce McGough

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Abstract

Regime-switching rational expectations models, in which the parameters of the model evolve according to a finite state Markov process, have properties that differentiate them from linear models. Issues that are well understood in linear contexts, such as equilibrium determinacy and stability under adaptive learning, re-emerge in this new context. This paper outlines these issues and defines two classes of equilibria that emerge from regime-switching models. The distinguishing feature between the two classes is whether the conditional density of the endogenous state variables depends on past regimes. An assumption on whether agents condition their expectations on past regimes has important implications for determinacy and equilibrium dynamics. The paper addresses the stability properties of the different classes of equilibria under adaptive learning, extending the learning literature to a non-linear framework.

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Paper provided by Federal Reserve Bank of Kansas City in its series Research Working Paper with number RWP 07-09.

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Date of creation: 2007
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Handle: RePEc:fip:fedkrw:rwp07-09

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Keywords: Rational expectations (Economic theory);

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  1. Evans, George W. & McGough, Bruce, 2005. "Stable sunspot solutions in models with predetermined variables," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 601-625, April. [Downloadable!] (restricted)
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  2. James Bullard & Kaushik Mitra, 2002. "Learning about monetary policy rules," Working Papers 2000-001, Federal Reserve Bank of St. Louis. [Downloadable!]
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  3. Farmer, Roger E A & Waggoner, Daniel F & Zha, Tao, 2006. "Indeterminacy in a Forward Looking Regime Switching Model," CEPR Discussion Papers 5919, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  4. Hess Chung & Troy Davig & Eric M. Leeper, 2007. "Monetary and Fiscal Policy Switching," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(4), pages 809-842, 06. [Downloadable!] (restricted)
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  5. Eric M. Leeper & Tao Zha, 1999. "Modest policy interventions," Working Paper 99-22, Federal Reserve Bank of Atlanta. [Downloadable!]
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  6. Davig, Troy, 2004. "Regime-switching debt and taxation," Journal of Monetary Economics, Elsevier, vol. 51(4), pages 837-859, May. [Downloadable!] (restricted)
  7. Marcet, Albert & Sargent, Thomas J., 1989. "Convergence of least squares learning mechanisms in self-referential linear stochastic models," Journal of Economic Theory, Elsevier, vol. 48(2), pages 337-368, August. [Downloadable!] (restricted)
  8. Svensson, Lars E O & Williams, Noah, 2007. "Monetary Policy with Model Uncertainty: Distribution Forecast Targeting," CEPR Discussion Papers 6331, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  9. Bray, Margaret M & Savin, Nathan E, 1986. "Rational Expectations Equilibria, Learning, and Model Specification," Econometrica, Econometric Society, vol. 54(5), pages 1129-60, September. [Downloadable!] (restricted)
  10. Zampolli, Fabrizio, 2006. "Optimal monetary policy in a regime-switching economy: The response to abrupt shifts in exchange rate dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1527-1567. [Downloadable!] (restricted)
  11. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-11, July. [Downloadable!] (restricted)
  12. Troy Davig & Eric M. Leeper, 2007. "Generalizing the Taylor Principle," American Economic Review, American Economic Association, vol. 97(3), pages 607-635, June. [Downloadable!]
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  13. 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. [Downloadable!]
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