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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.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 13414.

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Date of creation: Sep 2007
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Handle: RePEc:nbr:nberwo:13414

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  1. Marcet, A. & Marimon, R., 1998. "Recursive Contracts," Economics Working Papers, European University Institute eco98/37, European University Institute.
  2. 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, Elsevier, vol. 30(9-10), pages 1527-1567.
  3. 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, Elsevier, vol. 23(8), pages 1099-1131, August.
  4. Glenn D. Rudebusch & Lars E. O. Svensson, 1998. "Policy Rules for Inflation Targeting," NBER Working Papers 6512, National Bureau of Economic Research, Inc.
  5. Mewael F. Tesfaselassie & Eric Schaling & Sylvester Eijffinger, 2007. "Learning About the Term Structure and Optimal Rules for Inflation Targeting," Working Papers 62, Economic Research Southern Africa.
  6. Beck, Gunter W. & Wieland, Volker, 2002. "Learning and control in a changing economic environment," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 26(9-10), pages 1359-1377, August.
  7. Martin Ellison & Natacha Valla, 2000. "Learning, Uncertainty And Central Bank Activism In An Economy With Strategic Interactions," Computing in Economics and Finance 2000, Society for Computational Economics 183, Society for Computational Economics.
  8. Timothy Cogley & Riccardo Colacito & Thomas J. Sargent, 2005. "Benefits from U.S. monetary policy experimentation in the days of Samuelson and Solow and Lucas," Proceedings, Board of Governors of the Federal Reserve System (U.S.), Board of Governors of the Federal Reserve System (U.S.).
  9. 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.
  10. 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, De Gruyter, vol. 6(1), pages 1-34, March.
  11. Fabrizio Zampolli & Andrew P. Blake, 2005. "Time Consistent Policy in Markov Switching Models," Computing in Economics and Finance 2005, Society for Computational Economics 134, Society for Computational Economics.
  12. Svensson, Lars E O & Williams, Noah, 2007. "Monetary Policy with Model Uncertainty: Distribution Forecast Targeting," CEPR Discussion Papers, C.E.P.R. Discussion Papers 6331, C.E.P.R. Discussion Papers.
  13. Volker Wieland, 1996. "Learning by doing and the value of optimal experimentation," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 96-5, Board of Governors of the Federal Reserve System (U.S.).
  14. Kiefer, Nicholas M., 1989. "A value function arising in the economics of information," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 13(2), pages 201-223, April.
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