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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. 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.
  2. 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).
  3. 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.
  4. Lawrence J. Christiano & Jonas D.M. Fisher, 1997. "Algorithms for solving dynamic models with occasionally binding constraints," Working Paper 9711, Federal Reserve Bank of Cleveland.
  5. Roger E.A. Farmer & Daniel F. Waggoner & Tao Zha, 2007. "Understanding the New-Keynesian Model when Monetary Policy Switches Regimes," NBER Working Papers 12965, National Bureau of Economic Research, Inc.
  6. 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.
  7. Filardo, Andrew J. & Gordon, Stephen F., 1998. "Business cycle durations," Journal of Econometrics, Elsevier, vol. 85(1), pages 99-123, July.
  8. Troy Davig & Eric M. Leeper, 2007. "Generalizing the Taylor Principle," American Economic Review, American Economic Association, vol. 97(3), pages 607-635, June.
  9. Taeyoung Doh & Troy Davig, 2009. "Monetary Policy Regime Shifts and Inflation Persistence," 2009 Meeting Papers 182, Society for Economic Dynamics.
  10. Eric M. Leeper & Tao Zha, 2002. "Modest policy interventions," Working Paper 2002-19, Federal Reserve Bank of Atlanta.
  11. Christopher A. Sims & Tao Zha, 2004. "Were there regime switches in U.S. monetary policy?," Working Paper 2004-14, Federal Reserve Bank of Atlanta.
  12. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September.
  13. Barthélemy, J. & Marx, M., 2012. "Generalizing the Taylor Principle: New Comment," Working papers 403, Banque de France.
  14. 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.
  15. Christopher A. Sims, 1982. "Policy Analysis with Econometric Models," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 13(1), pages 107-164.
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