IDEAS home Printed from https://ideas.repec.org/p/sce/scecf5/134.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: http://repec.org/sce2005/up.6985.1106827445.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    3. Sharon Kozicki, 2004. "How do data revisions affect the evaluation and conduct of monetary policy?," Economic Review, Federal Reserve Bank of Kansas City, vol. 89(Q I), pages 5-38.
    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.
    6. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    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.
    13. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Noah Williams & Lars E.O. Svensson, 2005. "Monetary Policy with Model Uncertainty: Distribution Forecast Targeting," Computing in Economics and Finance 2005 108, Society for Computational Economics.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Andrew P Blake & Fabrizio Zampolli, 2006. "Optimal monetary policy in Markov-switching models with rational expectations agents," Bank of England working papers 298, Bank of England.
    2. 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.
    3. Dennis, Richard, 2004. "Solving for optimal simple rules in rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 28(8), pages 1635-1660, June.
    4. Dennis, Richard & Leitemo, Kai & Söderström, Ulf, 2009. "Methods for robust control," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1604-1616, August.
    5. Dennis, Richard, 2014. "Imperfect credibility and robust monetary policy," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 218-234.
    6. Sala, Luca & Söderström, Ulf & Trigari, Antonella, 2008. "Monetary policy under uncertainty in an estimated model with labor market frictions," Journal of Monetary Economics, Elsevier, vol. 55(5), pages 983-1006, July.
    7. Richard Dennis & Tatiana Kirsanova, 2010. "Expectations traps and coordination failures: selecting among multiple discretionary equilibria," Working Paper Series 2010-02, Federal Reserve Bank of San Francisco.
    8. Himmels, Christoph & Kirsanova, Tatiana, 2013. "Escaping expectation traps: How much commitment is required?," Journal of Economic Dynamics and Control, Elsevier, vol. 37(3), pages 649-665.
    9. Christoph Himmels & Tatiana Kirsanova, 2011. "Expectations Traps and Monetary Policy with Limited Commitment," Discussion Papers 1102, University of Exeter, Department of Economics.
    10. Richard Dennis & Kai Leitemo & Ulf Soderstrom, 2006. "Monetary Policy in a Small Open Economy with a Preference for Robustness," Working Papers 316, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    11. Richard Dennis, 2007. "Model uncertainty and monetary policy," Working Paper Series 2007-09, Federal Reserve Bank of San Francisco.
    12. Andrew Blake, 2012. "DSGE Modeling on an iPhone/iPad Using SpaceTime," Computational Economics, Springer;Society for Computational Economics, vol. 40(4), pages 313-332, December.
    13. Andrew Levin & Volker Wieland & John C. Williams, 2003. "The Performance of Forecast-Based Monetary Policy Rules Under Model Uncertainty," American Economic Review, American Economic Association, vol. 93(3), pages 622-645, June.
    14. Blake, Andrew P., 2004. "Open loop time consistency for linear rational expectations models," Economics Letters, Elsevier, vol. 82(1), pages 21-27, January.
    15. Dennis, Richard, 2022. "Computing time-consistent equilibria: A perturbation approach," Journal of Economic Dynamics and Control, Elsevier, vol. 137(C).
    16. Debortoli, Davide & Maih, Junior & Nunes, Ricardo, 2014. "Loose Commitment In Medium-Scale Macroeconomic Models: Theory And Applications," Macroeconomic Dynamics, Cambridge University Press, vol. 18(1), pages 175-198, January.
    17. Jean-Bernard Chatelain & Kirsten Ralf, 2017. "Can We Identify the Fed's Preferences?," Working Papers halshs-01549908, HAL.
    18. Dennis, Richard & Kirsanova, Tatiana, 2016. "Computing Markov-Perfect Optimal Policies In Business-Cycle Models," Macroeconomic Dynamics, Cambridge University Press, vol. 20(7), pages 1850-1872, October.
    19. Wollmershauser, Timo, 2006. "Should central banks react to exchange rate movements? An analysis of the robustness of simple policy rules under exchange rate uncertainty," Journal of Macroeconomics, Elsevier, vol. 28(3), pages 493-519, September.
    20. Svensson, Lars E. O., 1999. "Inflation targeting as a monetary policy rule," Journal of Monetary Economics, Elsevier, vol. 43(3), pages 607-654, June.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sce:scecf5:134. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Christopher F. Baum (email available below). General contact details of provider: https://edirc.repec.org/data/sceeeea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.