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Certainty equivalence and model uncertainty

  • Lars Peter Hansen
  • Thomas J. Sargent

Simon’s and Theil’s certainty equivalence property justifies a convenient algorithm for solving dynamic programming problems with quadratic objectives and linear transition laws: first, optimize under perfect foresight, then substitute optimal forecasts for unknown future values. A similar decomposition into separate optimization and forecasting steps prevails when a decision maker wants a decision rule that is robust to model misspecification. Concerns about model misspecification leave the first step of the algorithm intact and affect only the second step of forecasting the future. The decision maker attains robustness by making forecasts with a distorted model that twists probabilities relative to his approximating model. The appropriate twisting emerges from a two-player zero-sum dynamic game.

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Article provided by Board of Governors of the Federal Reserve System (U.S.) in its journal Proceedings.

Volume (Year): (2005)
Issue (Month): ()
Pages: 17-38

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Handle: RePEc:fip:fedgpr:y:2005:p:17-38
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  1. Lucas, Robert Jr, 1976. "Econometric policy evaluation: A critique," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 1(1), pages 19-46, January.
  2. Itzhak Gilboa & David Schmeidler, 1989. "Maxmin Expected Utility with Non-Unique Prior," Post-Print hal-00753237, HAL.
  3. Lars Peter Hansen & Thomas J. Sargent & Thomas D. Tallarini, 1999. "Robust Permanent Income and Pricing," Review of Economic Studies, Oxford University Press, vol. 66(4), pages 873-907.
  4. Lucas, Robert E, Jr & Prescott, Edward C, 1971. "Investment Under Uncertainty," Econometrica, Econometric Society, vol. 39(5), pages 659-81, September.
  5. Epstein, Larry G & Zin, Stanley E, 1989. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework," Econometrica, Econometric Society, vol. 57(4), pages 937-69, July.
  6. 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.
  7. Philippe Weil, 1993. "Precautionary Savings and the Permanent Income Hypothesis," Review of Economic Studies, Oxford University Press, vol. 60(2), pages 367-383.
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