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Recursive utility and parameter uncertainty

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  • Al-Najjar, Nabil I.
  • Shmaya, Eran

Abstract

We explore how the Epstein–Zin utility captures an agent's sensitivity to parameter uncertainty. Our main result is a closed-form representation of the Epstein–Zin utility for an i.i.d. consumption process with unknown parameter, as the discount factor approaches 1. Using this representation, and under the usual assumption about the relationship between risk aversion and the attitude towards time smoothing, we show that the agent is averse to parameter uncertainty.

Suggested Citation

  • Al-Najjar, Nabil I. & Shmaya, Eran, 2019. "Recursive utility and parameter uncertainty," Journal of Economic Theory, Elsevier, vol. 181(C), pages 274-288.
    • Handle: RePEc:eee:jetheo:v:181:y:2019:i:c:p:274-288
    DOI: 10.1016/j.jet.2019.02.005
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    References listed on IDEAS

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    1. Larry G. Epstein & Emmanuel Farhi & Tomasz Strzalecki, 2014. "How Much Would You Pay to Resolve Long-Run Risk?," American Economic Review, American Economic Association, vol. 104(9), pages 2680-2697, September.
    2. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    3. Marinacci, Massimo & Montrucchio, Luigi, 2010. "Unique solutions for stochastic recursive utilities," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1776-1804, September.
    4. Nabil I. Al-Najjar & Eran Shmaya, 2015. "Uncertainty and Disagreement in Equilibrium Models," Journal of Political Economy, University of Chicago Press, vol. 123(4), pages 778-808.
    5. Antoine Bommier & Asen Kochov & François Le Grand, 2017. "On Monotone Recursive Preferences," Econometrica, Econometric Society, vol. 85, pages 1433-1466, September.
    6. Bruno Ziliotto, 2016. "A Tauberian Theorem for Nonexpansive Operators and Applications to Zero-Sum Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1522-1534, November.
    7. Al-Najjar, Nabil I. & Shmaya, Eran, 2018. "Learning the fundamentals in a stationary environment," Games and Economic Behavior, Elsevier, vol. 109(C), pages 616-624.
    8. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
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    Cited by:

    1. Asen Kochov & Yangwei Song, 2023. "Intertemporal Hedging and Trade in Repeated Games With Recursive Utility," Econometrica, Econometric Society, vol. 91(6), pages 2333-2369, November.
    2. Thomas J. Sargent & John Stachurski, 2024. "Dynamic Programming: Finite States," Papers 2401.10473, arXiv.org.
    3. Fudenberg, Drew & Lanzani, Giacomo & Strack, Philipp, 2023. "Pathwise concentration bounds for Bayesian beliefs," Theoretical Economics, Econometric Society, vol. 18(4), November.

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    More about this item

    Keywords

    Recursive utility; Parameter uncertainty;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • E7 - Macroeconomics and Monetary Economics - - Macro-Based Behavioral Economics

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