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State-Dependent Probability Distributions in Non Linear Rational Expectations Models

  • Barthélemy, J.
  • Marx, M.

In this paper, we provide solution methods for non-linear rational expectations models in which regime-switching or the shocks themselves may be "endogenous", i.e. follow state-dependent probability distributions. We use the perturbation approach to find determinacy conditions, i.e. conditions for the existence of a unique stable equilibrium. We show that these conditions directly follow from the corresponding conditions in the exogenous regime-switching model. Whereas these conditions are difficult to check in the general case, we provide for easily verifiable and sufficient determinacy conditions and first-order approximation of the solution for purely forward-looking models. Finally, we illustrate our results with a Fisherian model of inflation determination in which the monetary policy rule may change across regimes according to a state-dependent transition probability matrix.

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Paper provided by Banque de France in its series Working papers with number 347.

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Length: 30 pages
Date of creation: 2011
Date of revision:
Handle: RePEc:bfr:banfra:347
Contact details of provider: Postal: Banque de France 31 Rue Croix des Petits Champs LABOLOG - 49-1404 75049 PARIS
Web page: http://www.banque-france.fr/

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  1. 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.
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  3. Roger E.A. Farmer & Daniel F. Waggoner & Tao Zha, 2007. "Understanding the New Keynesian model when monetary policy switches regimes," FRB Atlanta Working Paper No. 2007-12, Federal Reserve Bank of Atlanta.
  4. Zheng Liu & Daniel F. Waggoner & Tao Zha, 2010. "Sources of Macroeconomic Fluctuations: A Regime-switching DSGE Approach," Emory Economics 1002, Department of Economics, Emory University (Atlanta).
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  6. Eric M. Leeper & Tao Zha, 2002. "Modest Policy Interventions," NBER Working Papers 9192, National Bureau of Economic Research, Inc.
  7. Troy Davig & Taeyoung Doh, 2008. "Monetary policy regime shifts and inflation persistence," Research Working Paper RWP 08-16, Federal Reserve Bank of Kansas City.
  8. Kim, Chang-Jin & Piger, Jeremy & Startz, Richard, 2008. "Estimation of Markov regime-switching regression models with endogenous switching," Journal of Econometrics, Elsevier, vol. 143(2), pages 263-273, April.
  9. Filardo, Andrew J, 1994. "Business-Cycle Phases and Their Transitional Dynamics," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 299-308, July.
  10. Christopher A. Sims & Tao Zha, 2006. "Were There Regime Switches in U.S. Monetary Policy?," American Economic Review, American Economic Association, vol. 96(1), pages 54-81, March.
  11. 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.
  12. Coe, Patrick J, 2002. "Financial Crisis and the Great Depression: A Regime Switching Approach," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 34(1), pages 76-93, February.
  13. Lars E.O. Svensson & Noah Williams, 2008. "Optimal Monetary Policy Under Uncertainty in DSGE Models: A Markov Jump-Linear-Quadratic Approach," Working Papers Central Bank of Chile 484, Central Bank of Chile.
  14. 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.
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  16. Lawrence J. Christiano & Jonas D.M. Fisher, 1997. "Algorithms for solving dynamic models with occasionally binding constraints," Working Paper Series, Macroeconomic Issues WP-97-15, Federal Reserve Bank of Chicago.
  17. Barthélemy, J. & Marx, M., 2012. "Generalizing the Taylor Principle: New Comment," Working papers 403, Banque de France.
  18. Taylor, John B., 1993. "Discretion versus policy rules in practice," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 39(1), pages 195-214, December.
  19. 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.
  20. Michel Juillard, 2003. "What is the contribution of a k order approximation," Computing in Economics and Finance 2003 286, Society for Computational Economics.
  21. Jesús Fernández-Villaverde & Pablo Guerrón-Quintana & Juan F. Rubio-Ramírez, 2010. "Reading the recent monetary history of the United States, 1959-2007," Review, Federal Reserve Bank of St. Louis, issue May, pages 311-338.
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