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Time Consistent Policy in Markov Switching Models

  • Fabrizio Zampolli
  • Andrew P. Blake

    ()

    (Monetary Assessment and Strategy Bank of England)

In this paper we consider the quadratic optimal control problem with regime shifts and forward-looking agents. This extends the results of Zampolli (2003) who considered models without forward-looking expectations. Two algorithms are presented: The first algorithm computes the solution of a rational expectation model with random parameters or regime shifts. The second algorithm computes the time-consistent policy and the resulting Nash-Stackelberg equilibrium. The formulation of the problem is of general form and allows for model uncertainty and incorporation of policymaker’s judgement. We apply these methods to compute the optimal (non-linear) monetary policy in a small open economy subject to (symmetric or asymmetric) risks of change in some of its key parameters such as inflation inertia, degree of exchange rate pass-through, elasticity of aggregate demand to interest rate, etc.. We normally find that the time-consistent response to risk is more cautious. Furthermore, the optimal response is in some cases non-monotonic as a function of uncertainty. We also simulate the model under assumptions that the policymaker and the private sector hold the same beliefs over the probabilities of the structural change and different beliefs (as well as different assumptions about the knowledge of each other’s reaction function).

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Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2005 with number 134.

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Date of creation: 11 Nov 2005
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Handle: RePEc:sce:scecf5:134
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  1. Richard Dennis, 2001. "Optimal policy in rational-expectations models: new solution algorithms," Working Paper Series 2001-09, Federal Reserve Bank of San Francisco.
  2. Dennis, Richard & Soderstrom, Ulf, 2006. "How Important Is Precommitment for Monetary Policy?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(4), pages 847-872, June.
  3. William Roberds, 1986. "Models of policy under stochastic replanning," Staff Report 104, Federal Reserve Bank of Minneapolis.
  4. Fershtman, C., 1988. "Fixed Rules And Decision Rules: Time Consistency And Subgame Perfection," Papers 12-88, Tel Aviv.
  5. Sharon Kozicki, 2004. "How do data revisions affect the evaluation and conduct of monetary policy?," Economic Review, Federal Reserve Bank of Kansas City, issue Q I, pages 5-38.
  6. Kai Leitemo & Ulf Soderstrom, 2001. "Simple monetary policy rules and exchange rate uncertainty," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
  7. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-11, July.
  8. repec:cup:macdyn:v:8:y:2004:i:1:p:27-50 is not listed on IDEAS
  9. Fabrizio Zampolli, 2004. "Optimal monetary policy in a regime-switching economy," Computing in Economics and Finance 2004 166, Society for Computational Economics.
  10. Swanson, Eric T., 2004. "Signal Extraction And Non-Certainty-Equivalence In Optimal Monetary Policy Rules," Macroeconomic Dynamics, Cambridge University Press, vol. 8(01), pages 27-50, February.
  11. Gilles Oudiz & Jeffrey Sachs, 1985. "International Policy Coordination in Dynamic Macroeconomic Models," NBER Chapters, in: International Economic Policy Coordination, pages 274-330 National Bureau of Economic Research, Inc.
  12. Christophe Planas & Alessandro Rossi, 2004. "Can inflation data improve the real-time reliability of output gap estimates?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(1), pages 121-133.
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