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Robust hidden Markov LQG problems

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Author Info

  • Hansen, Lars Peter
  • Mayer, Ricardo
  • Sargent, Thomas

Abstract

For linear quadratic Gaussian problems, this paper uses two risk-sensitivity operators defined by Hansen and Sargent (2007b) to construct decision rules that are robust to misspecifications of (1) transition dynamics for state variables and (2) a probability density over hidden states induced by Bayes' law. Duality of risk sensitivity to the multiplier version of min-max expected utility theory of Hansen and Sargent (2001) allows us to compute risk-sensitivity operators by solving two-player zero-sum games. Because the approximating model is a Gaussian probability density over sequences of signals and states, we can exploit a modified certainty equivalence principle to solve four games that differ in continuation value functions and discounting of time t increments to entropy. The different games express different dimensions of concerns about robustness. All four games give rise to time consistent worst-case distributions for observed signals. But in Games I-III, the minimizing players' worst-case densities over hidden states are time inconsistent, while Game IV is an LQG version of a game of Hansen and Sargent (2005) that builds in time consistency. We show how detection error probabilities can be used to calibrate the risk-sensitivity parameters that govern fear of model misspecification in hidden Markov models.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 34 (2010)
Issue (Month): 10 (October)
Pages: 1951-1966

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Handle: RePEc:eee:dyncon:v:34:y:2010:i:10:p:1951-1966

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Web page: http://www.elsevier.com/locate/jedc

Related research

Keywords: Hidden Markov models Misspecification Kalman filter Robustness Entropy Certainty equivalence;

References

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  1. 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.
  2. Christina D. Romer & David H. Romer, 2008. "The FOMC versus the Staff: Where Can Monetary Policymakers Add Value?," American Economic Review, American Economic Association, vol. 98(2), pages 230-35, May.
  3. Martin Ellison & Thomas J. Sargent, 2009. "A defence of the FOMC," Economics Series Working Papers 457, University of Oxford, Department of Economics.
    • Martin Ellison & Thomas J. Sargent, 2012. "A Defense Of The Fomc," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(4), pages 1047-1065, November.
  4. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, December.
  5. Christopher A. Sims & Tao Zha, 2005. "Were There Regime Switches in U.S. Monetary Policy?," Working Papers 92, Princeton University, Department of Economics, Center for Economic Policy Studies..
  6. Thomas J. Sargent & LarsPeter Hansen, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 60-66, May.
  7. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
  8. Hansen, Lars Peter & Sargent, Thomas J., 2005. "Robust estimation and control under commitment," Journal of Economic Theory, Elsevier, vol. 124(2), pages 258-301, October.
  9. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
  10. Kenneth Kasa, 1999. "Model uncertainty, robust policies, and the value of commitment," Working Paper Series 99-14, Federal Reserve Bank of San Francisco.
  11. Hansen, Lars Peter & Sargent, Thomas J., 2007. "Recursive robust estimation and control without commitment," Journal of Economic Theory, Elsevier, vol. 136(1), pages 1-27, September.
  12. Larry Epstein & Martin Schneider, 2006. "Learning Under Ambiguity," RCER Working Papers 527, University of Rochester - Center for Economic Research (RCER).
  13. 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.
  14. repec:nbr:nberwo:13892 is not listed on IDEAS
  15. Timothy Cogley & Riccardo Colacito & Lars Peter Hansen & Thomas J. Sargent, 2008. "Robustness and U.S. Monetary Policy Experimentation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 40(8), pages 1599-1623, December.
  16. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2008. "Uncertainty Averse Preferences," Carlo Alberto Notebooks 77, Collegio Carlo Alberto.
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Cited by:
  1. Yulei Luo & Jun Nie & Eric R. Young, 2013. "Robust Control, Informational Frictions, and International Consumption Correlations," Working Papers 212013, Hong Kong Institute for Monetary Research.
  2. Martin Ellison & Thomas J. Sargent, 2012. "A Defense Of The Fomc," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(4), pages 1047-1065, November.

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