IDEAS home Printed from https://ideas.repec.org/p/red/sed007/446.html
   My bibliography  Save this paper

Bayesian and Adaptive Optimal Policy under Model Uncertainty

Author

Listed:
  • Noah Williams

    (Princeton University)

  • Lars E.O. Svensson

    (Princeton University)

Abstract

We study the problem of a policymaker who seeks to set policy optimally in an economy where the true economic structure is unobserved, and policymakers optimally learn from their observations of the economy. This is a classic problem of learning and control, variants of which have been studied in the past, but little with forward-looking variables which are a key component of modern policy-relevant models. As in most Bayesian learning problems, the optimal policy typically includes an experimentation component reflecting the endogeneity of information. We develop algorithms to solve numerically for the Bayesian optimal policy (BOP). However the BOP is only feasible in relatively small models, and thus we also consider a simpler specification we term adaptive optimal policy (AOP) which allows policymakers to update their beliefs but shortcuts the experimentation motive. In our setting, the AOP is significantly easier to compute, and in many cases provides a good approximation to the BOP. We provide a simple example to illustrate the role of learning and experimentation in an MJLQ framework.

Suggested Citation

  • Noah Williams & Lars E.O. Svensson, 2007. "Bayesian and Adaptive Optimal Policy under Model Uncertainty," 2007 Meeting Papers 446, Society for Economic Dynamics.
  • Handle: RePEc:red:sed007:446
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Timothy Cogley & Riccardo Colacito & Thomas J. Sargent, 2007. "Benefits from U.S. Monetary Policy Experimentation in the Days of Samuelson and Solow and Lucas," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 67-99, February.
    2. Albert Marcet & Ramon Marimon, 2019. "Recursive Contracts," Econometrica, Econometric Society, vol. 87(5), pages 1589-1631, September.
    3. Lars Svensson & Noah Williams, 2005. "Monetary Policy with Model Uncertainty: Distribution Forecast Targeting," NBER Working Papers 11733, National Bureau of Economic Research, Inc.
    4. Zampolli, Fabrizio, 2006. "Optimal monetary policy in a regime-switching economy: The response to abrupt shifts in exchange rate dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1527-1567.
    5. Volker Wieland, "undated". "Monetary Policy and Uncertainty about the Natural Unemployment Rate," Computing in Economics and Finance 1997 11, Society for Computational Economics.
    6. Kiefer, Nicholas M., 1989. "A value function arising in the economics of information," Journal of Economic Dynamics and Control, Elsevier, vol. 13(2), pages 201-223, April.
    7. Ellison, Martin & Valla, Natacha, 2001. "Learning, uncertainty and central bank activism in an economy with strategic interactions," Journal of Monetary Economics, Elsevier, vol. 48(1), pages 153-171, August.
    8. Mewael F. Tesfaselassie & Eric Schaling & Sylvester Eijffinger, 2011. "Learning about the Term Structure and Optimal Rules for Inflation Targeting," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 43(8), pages 1685-1706, December.
    9. Wieland, Volker, 2000. "Learning by doing and the value of optimal experimentation," Journal of Economic Dynamics and Control, Elsevier, vol. 24(4), pages 501-534, April.
    10. Glenn Rudebusch & Lars E.O. Svensson, 1999. "Policy Rules for Inflation Targeting," NBER Chapters, in: Monetary Policy Rules, pages 203-262, National Bureau of Economic Research, Inc.
    11. Beck, Gunter W. & Wieland, Volker, 2002. "Learning and control in a changing economic environment," Journal of Economic Dynamics and Control, Elsevier, vol. 26(9-10), pages 1359-1377, August.
    12. do Val, Joao B. R. & Basar, Tamer, 1999. "Receding horizon control of jump linear systems and a macroeconomic policy problem," Journal of Economic Dynamics and Control, Elsevier, vol. 23(8), pages 1099-1131, August.
    13. Fabrizio Zampolli & Andrew P. Blake, 2005. "Time Consistent Policy in Markov Switching Models," Computing in Economics and Finance 2005 134, Society for Computational Economics.
    14. John B. Taylor, 1999. "Monetary Policy Rules," NBER Books, National Bureau of Economic Research, Inc, number tayl99-1, January.
    15. Linde, Jesper, 2005. "Estimating New-Keynesian Phillips curves: A full information maximum likelihood approach," Journal of Monetary Economics, Elsevier, vol. 52(6), pages 1135-1149, September.
    16. Albert Marcet & Ramon Marimon, 2019. "Recursive Contracts," Econometrica, Econometric Society, vol. 87(5), pages 1589-1631, September.
    17. Wieland Volker, 2006. "Monetary Policy and Uncertainty about the Natural Unemployment Rate: Brainard-Style Conservatism versus Experimental Activism," The B.E. Journal of Macroeconomics, De Gruyter, vol. 6(1), pages 1-34, March.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. 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.
    3. Lars E.O. Svensson & Noah Williams, 2009. "Optimal Monetary Policy under Uncertainty in DSGE Models: A Markov Jump-Linear-Quadratic Approach," Central Banking, Analysis, and Economic Policies Book Series, in: Klaus Schmidt-Hebbel & Carl E. Walsh & Norman Loayza (Series Editor) & Klaus Schmidt-Hebbel (Series (ed.),Monetary Policy under Uncertainty and Learning, edition 1, volume 13, chapter 3, pages 077-114, Central Bank of Chile.
    4. Svensson, Lars E. O. & Williams, Noah, 2005. "Monetary policy with model uncertainty: distribution forecast targeting," Discussion Paper Series 1: Economic Studies 2005,35, Deutsche Bundesbank.
    5. Williams, Noah, 2012. "Monetary policy under financial uncertainty," Journal of Monetary Economics, Elsevier, vol. 59(5), pages 449-465.
    6. Lars E O Svensson, 2005. "Monetary Policy with Judgment: Forecast Targeting," International Journal of Central Banking, International Journal of Central Banking, vol. 1(1), May.
    7. Tim Willems, 2017. "Actively Learning by Pricing: A Model of an Experimenting Seller," Economic Journal, Royal Economic Society, vol. 127(604), pages 2216-2239, September.
    8. 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.
    9. Tesfaselassie, M.F. & Schaling, E., 2010. "Managing disinflation under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(12), pages 2568-2577, December.
    10. Stefan Laséen & Lars E.O. Svensson, 2011. "Anticipated Alternative policy Rate Paths in Plicy Simulations," International Journal of Central Banking, International Journal of Central Banking, vol. 7(3), pages 1-35, September.
    11. Stefan Laséen & Lars E.O. Svensson, 2009. "Anticipated Alternative Instrument-Rate Paths in Policy Simulations," NBER Working Papers 14902, National Bureau of Economic Research, Inc.
    12. Rondina, Francesca, 2012. "The role of model uncertainty and learning in the US postwar policy response to oil prices," Journal of Economic Dynamics and Control, Elsevier, vol. 36(7), pages 1009-1041.
    13. Matteo Cacciatore & Dmitry Matveev & Rodrigo Sekkel, 2022. "Uncertainty and Monetary Policy Experimentation: Empirical Challenges and Insights from Academic Literature," Discussion Papers 2022-9, Bank of Canada.
    14. Maria Antonieta Cunha-e-Sa & Vasco Santos, 2007. "Experimentation with accumulation," Nova SBE Working Paper Series wp503, Universidade Nova de Lisboa, Nova School of Business and Economics.
    15. Volker Wieland, 2009. "Learning, Endogenous Indexation, and Disinflation in the New-Keynesian Model," Central Banking, Analysis, and Economic Policies Book Series, in: Klaus Schmidt-Hebbel & Carl E. Walsh & Norman Loayza (Series Editor) & Klaus Schmidt-Hebbel (Series (ed.),Monetary Policy under Uncertainty and Learning, edition 1, volume 13, chapter 11, pages 413-450, Central Bank of Chile.
    16. Cunha-e-Sa, Maria A. & Santos, Vasco, 2008. "Experimentation with accumulation," Journal of Economic Dynamics and Control, Elsevier, vol. 32(2), pages 470-496, February.
    17. Ellison, Martin, 2006. "The learning cost of interest rate reversals," Journal of Monetary Economics, Elsevier, vol. 53(8), pages 1895-1907, November.
    18. Timothy Cogley, 2008. "Commentary on \\"Optimal monetary policy under uncertainty: a Markov jump-linear-quadratic approach\\"," Review, Federal Reserve Bank of St. Louis, vol. 90(Jul), pages 295-300.
    19. Mewael F. Tesfaselassie & Eric Schaling & Sylvester Eijffinger, 2011. "Learning about the Term Structure and Optimal Rules for Inflation Targeting," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 43(8), pages 1685-1706, December.
    20. Beck, Guenter W. & Wieland, Volker, 2008. "Central bank misperceptions and the role of money in interest-rate rules," Journal of Monetary Economics, Elsevier, vol. 55(Supplemen), pages 1-17, October.

    More about this item

    JEL classification:

    • E42 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Monetary Sytsems; Standards; Regimes; Government and the Monetary System
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
    • E58 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Central Banks and Their Policies

    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:red:sed007:446. 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: Christian Zimmermann (email available below). General contact details of provider: https://edirc.repec.org/data/sedddea.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.