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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 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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  1. 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.
  2. 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.
  3. Troy Davig & Eric M. Leeper & Hess Chung, 2005. "Monetary and fiscal policy switching," Research Working Paper RWP 05-12, Federal Reserve Bank of Kansas City.
  4. 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.
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  6. Christopher Sims & Tao Zha, 2002. "Macroeconomic switching," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
  7. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  8. Roger E.A. Farmer & Daniel F. Waggoner & Tao Zha, 2007. "Indeterminacy in a forward-looking regime-switching model," Working Paper 2006-19, Federal Reserve Bank of Atlanta.
  9. Troy Davig & Eric M. Leeper, 2005. "Generalizing the Taylor principle," Research Working Paper RWP 05-13, Federal Reserve Bank of Kansas City.
  10. Roberto Motto & Massimo Rostagno & Lawrence J. Christiano, 2010. "Financial Factors in Economic Fluctuations," 2010 Meeting Papers 141, Society for Economic Dynamics.
  11. 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.
  12. Cooley, Thomas F & LeRoy, Stephen F & Raymon, Neil, 1984. "Econometric Policy Evaluation: Note," American Economic Review, American Economic Association, vol. 74(3), pages 467-70, June.
  13. Bernanke, B. & Gertler, M. & Gilchrist, S., 1998. "The Financial Accelerator in a Quantitative Business Cycle Framework," Working Papers 98-03, C.V. Starr Center for Applied Economics, New York University.
  14. Thomas Lubik & Frank Schorfheide, 2002. "Testing for Indeterminacy:An Application to U.S. Monetary Policy," Economics Working Paper Archive 480, The Johns Hopkins University,Department of Economics, revised Jun 2003.
  15. Richard Clarida & Jordi Galí & Mark Gertler, 1997. "Monetary policy rules and macroeconomic stability: Evidence and some theory," Economics Working Papers 350, Department of Economics and Business, Universitat Pompeu Fabra, revised May 1999.
  16. Bennett T. McCallum, 1981. "On Non-Uniqueness in Rational Expectations Models: An Attempt at Perspective," NBER Working Papers 0684, National Bureau of Economic Research, Inc.
  17. Cass, David & Shell, Karl, 1983. "Do Sunspots Matter?," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 193-227, April.
  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. Harald Uhlig, 1997. "Bayesian Vector Autoregressions with Stochastic Volatility," Econometrica, Econometric Society, vol. 65(1), pages 59-74, January.
  20. Martin Fukac & Adrian Pagan, 2006. "Issues In Adopting Dsge Models For Use In The Policy Process," CAMA Working Papers 2006-10, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  21. 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.
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