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Time Consistent Policy in Markov Switching Models

Author

Listed:
  • 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).

Suggested Citation

  • Fabrizio Zampolli & Andrew P. Blake, 2005. "Time Consistent Policy in Markov Switching Models," Computing in Economics and Finance 2005 134, Society for Computational Economics.
    • Handle: RePEc:sce:scecf5:134
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    References listed on IDEAS

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    1. 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.
    2. Swanson, Eric T., 2004. "Signal Extraction And Non-Certainty-Equivalence In Optimal Monetary Policy Rules," Macroeconomic Dynamics, Cambridge University Press, vol. 8(1), pages 27-50, February.
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    4. 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.
    5. Fershtman, Chaim, 1989. "Fixed rules and decision rules : Time consistency and subgame perfection," Economics Letters, Elsevier, vol. 30(3), pages 191-194, September.
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    7. repec:cup:macdyn:v:8:y:2004:i:1:p:27-50 is not listed on IDEAS
    8. Leitemo, Kai & Soderstrom, Ulf, 2005. "Simple monetary policy rules and exchange rate uncertainty," Journal of International Money and Finance, Elsevier, vol. 24(3), pages 481-507, April.
    9. Dennis, Richard, 2007. "Optimal Policy In Rational Expectations Models: New Solution Algorithms," Macroeconomic Dynamics, Cambridge University Press, vol. 11(1), pages 31-55, February.
    10. Roberds, William, 1987. "Models of Policy under Stochastic Replanning," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(3), pages 731-755, October.
    11. Batini, Nicoletta & Nelson, Edward, 2000. "When the Bubble Bursts: Monetary Policy Rules and Foreign Exchange Market Behavior," Working Papers 2000-01, University of Sydney, School of Economics.
    12. Fabrizio Zampolli, 2004. "Optimal monetary policy in a regime-switching economy," Computing in Economics and Finance 2004 166, Society for Computational Economics.
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    Cited by:

    1. Lars Svensson & Noah Williams, 2005. "Monetary Policy with Model Uncertainty: Distribution Forecast Targeting," NBER Working Papers 11733, National Bureau of Economic Research, Inc.
    2. 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, vol. 90(Jul), pages 275-294.
    3. Moessner, Richhild, 2006. "Optimal monetary policy with uncertainty about financial frictions," Working Paper Series 639, European Central Bank.
    4. Svensson, Lars E. O. & Williams, Noah, 2006. "Bayesian and adaptive optimal policy under model uncertainty," CFS Working Paper Series 2007/11, Center for Financial Studies (CFS).
    5. Rodríguez Arnulfo & González Fidel & González García Jesús R., 2007. "Uncertainty about the Persistence of Cost-Push Shocks and the Optimal Reaction of the Monetary Authority," Working Papers 2007-05, Banco de México.
    6. 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.
    7. Williams, Noah, 2012. "Monetary policy under financial uncertainty," Journal of Monetary Economics, Elsevier, vol. 59(5), pages 449-465.
    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.
    9. Blake, Andrew P. & Zampolli, Fabrizio, 2011. "Optimal policy in Markov-switching rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(10), pages 1626-1651, October.

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    More about this item

    Keywords

    monetary policy; regime switching; model uncertainty; time consistency;
    All these keywords.

    JEL classification:

    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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