Robust hidden Markov LQG problems
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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- 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.
- Hansen, Lars Peter & Sargent, Thomas J., 2005. "Recursive robust estimation and control without commitment," Discussion Paper Series 1: Economic Studies 2005,28, Deutsche Bundesbank, Research Centre.
- Christopher A. Sims & Tao Zha, 2005.
"Were There Regime Switches in U.S. Monetary Policy?,"
92, Princeton University, Department of Economics, Center for Economic Policy Studies..
- Christopher A. Sims & Tao Zha, 2006. "Were There Regime Switches in U.S. Monetary Policy?," American Economic Review, American Economic Association, vol. 96(1), pages 54-81, March.
- Christopher A. Sims & Tao Zha, 2004. "Were there regime switches in U.S. monetary policy?," FRB Atlanta Working Paper 2004-14, Federal Reserve Bank of Atlanta.
- 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.
- 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.
- Christina D. Romer & David H. Romer, 2008. "The FOMC versus the Staff: Where Can Monetary Policymakers Add Value?," NBER Working Papers 13751, National Bureau of Economic Research, Inc.
- Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, December.
- Larry Epstein & Martin Schneider, 2006.
"Learning Under Ambiguity,"
RCER Working Papers
527, University of Rochester - Center for Economic Research (RCER).
- Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M. & Montrucchio, L., 2011.
"Uncertainty averse preferences,"
Journal of Economic Theory,
Elsevier, vol. 146(4), pages 1275-1330, July.
- Kenneth Kasa, 1999.
"Model uncertainty, robust policies, and the value of commitment,"
Working Paper Series
99-14, Federal Reserve Bank of San Francisco.
- Kasa, Kenneth, 2002. "Model Uncertainty, Robust Policies, And The Value Of Commitment," Macroeconomic Dynamics, Cambridge University Press, vol. 6(01), pages 145-166, February.
- 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.
- Epstein, Larry G. & Schneider, Martin, 2003.
Journal of Economic Theory,
Elsevier, vol. 113(1), pages 1-31, November.
- 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.
- Martin Ellison & Thomas J. Sargent, 2009.
"A defence of the FOMC,"
Economics Series Working Papers
457, University of Oxford, Department of Economics.
- Thomas J. Sargent & LarsPeter Hansen, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 60-66, May.
- 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.
- 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.
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