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Time Consistent Policy in Markov Switching Models

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  • Fabrizio Zampolli
  • Andrew P. Blake

    ()
    (Monetary Assessment and Strategy Bank of England)

Abstract

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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Bibliographic Info

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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Keywords: monetary policy; regime switching; model uncertainty; time consistency;

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References

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  1. Ulf Soderstrom & Richard Dennis, 2003. "How Important is Precommitment for Monetary Policy?," Computing in Economics and Finance 2003 49, Society for Computational Economics.
  2. Fershtman, C., 1988. "Fixed Rules And Decision Rules: Time Consistency And Subgame Perfection," Papers 12-88, Tel Aviv.
  3. William Roberds, 1986. "Models of policy under stochastic replanning," Staff Report 104, Federal Reserve Bank of Minneapolis.
  4. Fabrizio Zampolli, 2004. "Optimal monetary policy in a regime-switching economy," Computing in Economics and Finance 2004 166, Society for Computational Economics.
  5. Kai Leitemo & Ulf Soderstrom, 2001. "Simple monetary policy rules and exchange rate uncertainty," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
  6. Dennis, Richard, 2007. "Optimal Policy In Rational Expectations Models: New Solution Algorithms," Macroeconomic Dynamics, Cambridge University Press, vol. 11(01), pages 31-55, February.
  7. 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.
  8. 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.
  9. 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.
  10. repec:cup:macdyn:v:8:y:2004:i:1:p:27-50 is not listed on IDEAS
  11. 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.
  12. 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.
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Cited by:
  1. Svensson, Lars E.O., 2010. "Inflation Targeting," Handbook of Monetary Economics, in: Benjamin M. Friedman & Michael Woodford (ed.), Handbook of Monetary Economics, edition 1, volume 3, chapter 22, pages 1237-1302 Elsevier.
  2. 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.
  3. Lars E.O. Svensson & Noah Williams, 2008. "Optimal monetary policy under uncertainty: a Markov jump-linear-quadratic approach," Review, Federal Reserve Bank of St. Louis, issue Jul, pages 275-294.
  4. Noah Williams & Lars E.O. Svensson, 2007. "Bayesian and Adaptive Optimal Policy under Model Uncertainty," 2007 Meeting Papers 446, Society for Economic Dynamics.
  5. Lars E.O. Svensson & Noah Williams, 2008. "Optimal Monetary Policy under Uncertainty in DSGE Models: A Markov Jump-Linear-Quadratic Approach," NBER Working Papers 13892, National Bureau of Economic Research, Inc.
  6. Moessner, Richhild, 2006. "Optimal monetary policy with uncertainty about financial frictions," Working Paper Series 0639, European Central Bank.
  7. Arnulfo Rodríguez & Fidel González & Jesús R. González García, 2007. "Uncertainty about the Persistence of Cost-Push Shocks and the Optimal Reaction of the Monetary Authority," Working Papers 2007-05, Banco de México.
  8. Gonzalez F. & Rodriguez A. & Gonzalez-Garcia J.R., 2005. "Uncertainty about the Persistence of Periods with Large Price Shocks and the Optimal Reaction of the Monetary Authority," Computing in Economics and Finance 2005 402, Society for Computational Economics.

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