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Bayesian and Adaptive Optimal Policy under Model Uncertainty

  • Noah Williams

    (Princeton University)

  • Lars E.O. Svensson

    (Princeton University)

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.

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Paper provided by Society for Economic Dynamics in its series 2007 Meeting Papers with number 446.

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Date of creation: 2007
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Handle: RePEc:red:sed007:446
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Society for Economic Dynamics Marina Azzimonti Department of Economics Stonybrook University 10 Nicolls Road Stonybrook NY 11790 USA

Web page: http://www.EconomicDynamics.org/
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  1. Rudebusch, G.D. & Svensson, L.E.O., 1998. "Policy Rules for Inflation Targeting," Papers 637, Stockholm - International Economic Studies.
  2. Lars Svensson & Noah Williams, 2005. "Monetary Policy with Model Uncertainty: Distribution Forecast Targeting," NBER Working Papers 11733, National Bureau of Economic Research, Inc.
  3. Marcet, A. & Marimon, R., 1998. "Recursive Contracts," Economics Working Papers eco98/37, European University Institute.
  4. Lindé, Jesper, 2001. "Estimating New-Keynesian Phillips Curves: A Full Information Maximum Likelihood Approach," Working Paper Series 129, Sveriges Riksbank (Central Bank of Sweden), revised 30 Apr 2001.
  5. 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.
  6. Tesfaselassie, M.F. & Schaling, E. & Eijffinger, S.C.W., 2006. "Learning About the Term Structure and Optimal Rules for Inflation Targeting," ERIM Report Series Research in Management ERS-2006-058-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
  7. Ellison, Martin & Valla, Natacha, 2000. "Learning, uncertainty and central bank activism in an economy with strategic interactions," Working Paper Series 0028, European Central Bank.
  8. 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.
  9. 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, 02.
  10. 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.
  11. Fabrizio Zampolli & Andrew P. Blake, 2005. "Time Consistent Policy in Markov Switching Models," Computing in Economics and Finance 2005 134, Society for Computational Economics.
  12. Fabrizio Zampolli, 2006. "Optimal monetary policy in a regime-switching economy: the response to abrupt shifts in exchange rate dynamics," Bank of England working papers 297, Bank of England.
  13. 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.
  14. 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.
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