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Methods for robust control

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  • Richard Dennis
  • Kai Leitemo
  • Ulf Söderström

Abstract

Robust control allows policymakers to formulate policies that guard against model misspecification. The principal tools used to solve robust control problems are state-space methods (see Hansen and Sargent 2006 and Giordani and Soderlind 2004). In this paper we show that the structural-form methods developed by Dennis (2006) to solve control problems with rational expectations can also be applied to robust control problems, with the advantage that they bypass the task, often onerous, of having to express the reference model in statespace form. Interestingly, because state-space forms and structural forms are not unique the two approaches do not necessarily return the same equilibria for robust control problems. We apply both state-space and structural solution methods to an empirical New Keynesian business cycle model and find that the differences between the methods are both qualitatively and quantitatively important. In particular, with the structural-form solution methods the specification errors generally involve changes to the conditional variances in addition to the conditional means of the shock processes.

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Bibliographic Info

Paper provided by Federal Reserve Bank of San Francisco in its series Working Paper Series with number 2006-10.

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Date of creation: 2006
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Handle: RePEc:fip:fedfwp:2006-10

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Keywords: Robust control ; Monetary policy ; Econometric models;

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References

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  1. Leitemo, Kai & Söderström, Ulf, 2008. "Robust Monetary Policy In The New Keynesian Framework," Macroeconomic Dynamics, Cambridge University Press, vol. 12(S1), pages 126-135, April.
  2. Evan W. Anderson & Lars Peter Hansen & Thomas J. Sargent, 2003. "A Quartet of Semigroups for Model Specification, Robustness, Prices of Risk, and Model Detection," Journal of the European Economic Association, MIT Press, vol. 1(1), pages 68-123, 03.
  3. Giordani, Paolo & Söderlind, Paul, 2002. "Solution of Macromodels with Hansen-Sargent Robust Policies: Some Extensions," Working Paper Series in Economics and Finance 499, Stockholm School of Economics, revised 15 May 2003.
  4. Jeffrey C. Fuhrer & Glenn D. Rudebusch, 2002. "Estimating the Euler equation for output," Working Papers 02-3, Federal Reserve Bank of Boston.
  5. Hansen, Lars Peter & Sargent, Thomas J., 2003. "Robust control of forward-looking models," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 581-604, April.
  6. Buiter,Willem H. & Marston,Richard C., 1986. "International Economic Policy Coordination," Cambridge Books, Cambridge University Press, number 9780521337809, April.
  7. Dennis, Richard & Söderström, Ulf, 2002. "How Important Is Precommitment for Monetary Policy?," Working Paper Series 139, Sveriges Riksbank (Central Bank of Sweden).
  8. Kydland, Finn E. & Prescott, Edward C., 1980. "Dynamic optimal taxation, rational expectations and optimal control," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 79-91, May.
  9. Anderson, Evan W. & McGrattan, Ellen R. & Hansen, Lars Peter & Sargent, Thomas J., 1996. "Mechanics of forming and estimating dynamic linear economies," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 4, pages 171-252 Elsevier.
  10. Lars Peter Hansen & Thomas J. Sargent & Thomas D. Tallarini Jr., 1997. "Robust Permanent Income and Pricing," Levine's Working Paper Archive 596, David K. Levine.
  11. Engle, Robert F & Hendry, David F & Richard, Jean-Francois, 1983. "Exogeneity," Econometrica, Econometric Society, vol. 51(2), pages 277-304, March.
  12. Kai Leitemo & Ulf Söderstrom, 2005. "Robust Monetary Policy in a Small Open Economy," Working Papers 290, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  13. Andrew T. Levin & Alexei Onatski & John C. Williams & Noah Williams, 2005. "Monetary Policy Under Uncertainty in Micro-Founded Macroeconometric Models," NBER Working Papers 11523, National Bureau of Economic Research, Inc.
  14. Currie,David & Levine,Paul, 2009. "Rules, Reputation and Macroeconomic Policy Coordination," Cambridge Books, Cambridge University Press, number 9780521104609, April.
  15. Rudebusch, Glenn D., 2000. "Assessing nominal income rules for monetary policy with model and data uncertainty," Working Paper Series 0014, European Central Bank.
  16. Binder,M. & Pesaran,H.M., 1995. "Multivariate Rational Expectations Models and Macroeconomic Modelling: A Review and Some New Results," Cambridge Working Papers in Economics 9415, Faculty of Economics, University of Cambridge.
  17. Frank Smets & Raf Wouters, 2002. "An estimated dynamic stochastic general equilibrium model of the euro area," Working Paper Research 35, National Bank of Belgium.
  18. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-11, July.
  19. Glenn D. Rudebusch, 2001. "Term structure evidence on interest rate smoothing and monetary policy inertia," Working Paper Series 2001-02, Federal Reserve Bank of San Francisco.
  20. Dennis, Richard, 2007. "Optimal Policy In Rational Expectations Models: New Solution Algorithms," Macroeconomic Dynamics, Cambridge University Press, vol. 11(01), pages 31-55, February.
  21. Calvo, Guillermo A., 1983. "Staggered prices in a utility-maximizing framework," Journal of Monetary Economics, Elsevier, vol. 12(3), pages 383-398, September.
  22. Levine, Paul & Currie, David, 1985. "Optimal feedback rules in an open economy macromodel with rational expectations," European Economic Review, Elsevier, vol. 27(2), pages 141-163, March.
  23. Hansen, Lars Peter & Sargent, Thomas J. & Wang, Neng E., 2002. "Robust Permanent Income And Pricing With Filtering," Macroeconomic Dynamics, Cambridge University Press, vol. 6(01), pages 40-84, February.
  24. 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.
  25. Richard Dennis, 2005. "Robust control with commitment: a modification to Hansen-Sargent," Working Paper Series 2005-20, Federal Reserve Bank of San Francisco.
  26. repec:cup:macdyn:v:6:y:2002:i:1:p:40-84 is not listed on IDEAS
  27. Thomas J. Sargent & LarsPeter Hansen, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 60-66, May.
  28. Backus, David & Driffill, John, 1986. "The Consistency of Optimal Policy in Stochastic Rational Expectations Models," CEPR Discussion Papers 124, C.E.P.R. Discussion Papers.
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