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Minimal state variable solutions to Markov-switching rational expectations models

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

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 FRB Atlanta Working Paper No. 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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  2. Clarida, Richard & Galí, Jordi & Gertler, Mark, 1998. "Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory," CEPR Discussion Papers 1908, C.E.P.R. Discussion Papers.
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  9. Lawrence Christiano & Martin Eichenbaum & Sergio Rebelo, 2011. "When Is the Government Spending Multiplier Large?," Journal of Political Economy, University of Chicago Press, vol. 119(1), pages 78 - 121.
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  12. 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.
  13. 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.
  14. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  15. Roberto Motto & Massimo Rostagno & Lawrence J. Christiano, 2010. "Financial Factors in Economic Fluctuations," 2010 Meeting Papers 141, Society for Economic Dynamics.
  16. 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.
  17. 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.
  18. Giorgio E. Primiceri, 2005. "Time Varying Structural Vector Autoregressions and Monetary Policy," Review of Economic Studies, Oxford University Press, vol. 72(3), pages 821-852.
  19. 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.
  20. Christopher Sims & Tao Zha, 2002. "Macroeconomic switching," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
  21. Harald Uhlig, 1997. "Bayesian Vector Autoregressions with Stochastic Volatility," Econometrica, Econometric Society, vol. 65(1), pages 59-74, January.
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