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Minimal state variable solutions to Markov-switching rational expectations models

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Author Info
Roger E.A. Farmer
Daniel F. Waggoner
Tao Zha

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Abstract

We develop a new method for computing minimal state variable solutions (MSV) to Markov-switching rational expectations models. We provide an algorithm to compute an MSV solution and show how to test a given solution for uniqueness and boundedness. We construct an example that is calibrated to U.S. data and show that the MSV solution in our example is unique. This solution can potentially explain in three different ways the observed reduction in the variance of inflation and the interest rate after 1980: The policy rule might have changed, the variance of the fundamental shocks might have fallen, or the private sector equations might have been different across regimes. We compare these three explanations for the change in variance and show that any one of them can potentially account for the facts. Our paper provides the necessary tools for a future empirical study of this issue.

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Paper provided by Federal Reserve Bank of Atlanta in its series Working Paper with number 2008-23.

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Date of creation: 2008
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Handle: RePEc:fip:fedawp:2008-23

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Keywords: Econometric models;

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This paper has been announced in the following NEP Reports: References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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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  2. Lars Svensson & Noah Williams, 2005. "Monetary Policy with Model Uncertainty: Distribution Forecast Targeting," NBER Working Papers 11733, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  3. Beyer, Andreas & Farmer, Roger E A, 2003. "Identifying the Monetary Transmission Mechanism Using Structural Breaks," CEPR Discussion Papers 4106, 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. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January. [Downloadable!] (restricted)
  6. Harald Uhlig, 1997. "Bayesian Vector Autoregressions with Stochastic Volatility," Econometrica, Econometric Society, vol. 65(1), pages 59-74, January.
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  7. Cass, David & Shell, Karl, 1983. "Do Sunspots Matter?," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 193-227, April. [Downloadable!] (restricted)
  8. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March. [Downloadable!] (restricted)
  9. Bennett T. McCallum, 1983. "On Non-Uniqueness in Rational Expectations Models: An Attempt at Perspective," NBER Working Papers 0684, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  10. Martin Fukac & Adrian Pagan, 2006. "Issues In Adopting Dsge Models For Use In The Policy Process," CAMA Working Papers 2006-10, Australian National University, Centre for Applied Macroeconomic Analysis. [Downloadable!]
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  11. Troy Davig & Eric M. Leeper, 2005. "Generalizing the Taylor Principle," NBER Working Papers 11874, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  12. Timothy Cogley & Thomas J. Sargent, 2003. "Drifts and volatilities: monetary policies and outcomes in the post WWII U.S," Working Paper 2003-25, Federal Reserve Bank of Atlanta. [Downloadable!]
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  13. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules And Macroeconomic Stability: Evidence And Some Theory," The Quarterly Journal of Economics, MIT Press, vol. 115(1), pages 147-180, February. [Downloadable!] (restricted)
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  14. Christopher Sims & Tao Zha, 2002. "Macroeconomic switching," Proceedings, Federal Reserve Bank of San Francisco, issue Mar. [Downloadable!]
  15. 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. [Downloadable!] (restricted)
  16. 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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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Fernando Alexandre & Pedro Bação & John Driffill, 2007. "Optimal monetary policy with a regime-switching exchange rate in a forward-looking model," GEMF Working Papers 2007-09, GEMF - Faculdade de Economia, Universidade de Coimbra. [Downloadable!]
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  2. 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)
    Other versions:
  3. Eo, Yunjong, 2008. "Bayesian Analysis of DSGE Models with Regime Switching," MPRA Paper 13910, University Library of Munich, Germany, revised 11 Feb 2009. [Downloadable!]
  4. Beatrice Pataracchia, 2008. "Design Limits in Regime-Switching Cases," Department of Economics University of Siena 529, Department of Economics, University of Siena. [Downloadable!]
  5. Zheng Liu & Daniel F. Waggoner & Tao Zha, 2007. "Asymmetric expectation effects of regime shifts and the Great Moderation," Working Paper 2007-23, Federal Reserve Bank of Atlanta. [Downloadable!]
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