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Generalized Entropy and Model Uncertainty

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  • Alexander Meyer-Gohde

Abstract

I entertain a generalization of the standard Bolzmann-Gibbs-Shannon measure of entropy in multiplier preferences of model uncertainty. Using this measure, I derive a generalized exponential certainty equivalent, which nests the exponential certainty equivalent of the standard Hansen-Sargent model uncertainty formulation and the power certainty equivalent of the popular Epstein-Zin-Weil recursive preferences as special cases. Besides providing a model uncertainty rationale to these risk-sensitive preferences, the generalized exponential equivalent provides additional flexibility in modeling uncertainty through its introduction of pessimism into agents, causing them to overweight events made more likely in the worst case model when forming expectations. In a standard neoclassical growth model, I close the gap to the Hansen-Jagannathan bounds with plausible detection error probabilities using the generalized exponential equivalent and show that Hansen-Sargent and Epstein-Zin-Weil preferences yield comparable market prices of risk for given detection error probabilities.

Suggested Citation

  • Alexander Meyer-Gohde, 2017. "Generalized Entropy and Model Uncertainty," SFB 649 Discussion Papers SFB649DP2017-017, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2017-017
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    References listed on IDEAS

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    1. Hansen, Lars Peter & Jagannathan, Ravi, 1997. " Assessing Specification Errors in Stochastic Discount Factor Models," Journal of Finance, American Finance Association, vol. 52(2), pages 557-590, June.
    2. Rhys Bidder & Ian Dew-Becker, 2016. "Long-Run Risk Is the Worst-Case Scenario," American Economic Review, American Economic Association, vol. 106(9), pages 2494-2527, September.
    3. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    4. Backus, David & Ferriere, Axelle & Zin, Stanley, 2015. "Risk and ambiguity in models of business cycles," Journal of Monetary Economics, Elsevier, vol. 69(C), pages 42-63.
    5. Bidder, R.M. & Smith, M.E., 2012. "Robust animal spirits," Journal of Monetary Economics, Elsevier, vol. 59(8), pages 738-750.
    6. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    7. Martin Ellison & Thomas J. Sargent, 2015. "Welfare Cost of Business Cycles with Idiosyncratic Consumption Risk and a Preference for Robustness," American Economic Journal: Macroeconomics, American Economic Association, vol. 7(2), pages 40-57, April.
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    More about this item

    Keywords

    model uncertainty; robust control; recursive preferences; equity premium puzzle; Tsallis entropy;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications

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