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Bayesian and Adaptive Optimal Policy under Model Uncertainty

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  • Lars E.O. Svensson
  • Noah M. Williams

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 he optimally learns from observations of the economy. This is a classic problem of learning and control, variants of which have been studied in the past, but seldom 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, computing 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 some simple examples to illustrate the role of learning and experimentation in an MJLQ framework.

Suggested Citation

  • Lars E.O. Svensson & Noah M. Williams, 2007. "Bayesian and Adaptive Optimal Policy under Model Uncertainty," NBER Working Papers 13414, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:13414
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    References listed on IDEAS

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    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. 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.
    3. 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.
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    7. 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.
    8. 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.
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    14. 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.
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    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • 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

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