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State-Dependent Probability Distributions in Non Linear Rational Expectations Models

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  • Barthélemy, J.
  • Marx, M.

Abstract

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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Bibliographic Info

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

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Keywords: Perturbation methods; monetary policy; indeterminacy; regime switching; DSGE.;

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  1. Lawrence J. Christiano & Jonas D.M. Fisher, 1997. "Algorithms for Solving Dynamic Models with Occasionally Binding Constraints," NBER Technical Working Papers 0218, National Bureau of Economic Research, Inc.
  2. Eric M. Leeper & Tao Zha, 2002. "Modest Policy Interventions," NBER Working Papers 9192, National Bureau of Economic Research, Inc.
  3. Troy Davig & Eric M. Leeper, 2007. "Generalizing the Taylor Principle," American Economic Review, American Economic Association, vol. 97(3), pages 607-635, June.
  4. 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.
  5. Christopher A. Sims & Tao Zha, 2005. "Were There Regime Switches in U.S. Monetary Policy?," Working Papers 92, Princeton University, Department of Economics, Center for Economic Policy Studies..
  6. 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.
  7. 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.
  8. 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.
  9. Troy Davig & Taeyoung Doh, 2008. "Monetary policy regime shifts and inflation persistence," Research Working Paper RWP 08-16, Federal Reserve Bank of Kansas City.
  10. Barthélemy, J. & Marx, M., 2012. "Generalizing the Taylor Principle: New Comment," Working papers 403, Banque de France.
  11. 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.
  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. 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).
  14. Andrew J. Filardo & Stephen F. Gordon, 1993. "Business cycle durations," Research Working Paper 93-11, Federal Reserve Bank of Kansas City.
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