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IID: Independently and Indistinguishably Distributed




The inability of the Bayesian model to accomodate Ellsberg-type behavior is well known. This paper focuses on another limitation of the Bayesian model, specific to a dynamic setting, namely the inability to permit a distinction between experiments that are identical and those that are only indistinguishable. It is shown that such a distinction is afforded by recursive multiple-priors utility. Two related technical contributions are the proff of a strong LLN for recursive multiple-priors utility and the extension to sets of priors of the notion of regularity of a probability measure.

Suggested Citation

  • Larry Epstein & Martin Schneider, 2002. "IID: Independently and Indistinguishably Distributed," RCER Working Papers 496, University of Rochester - Center for Economic Research (RCER).
  • Handle: RePEc:roc:rocher:496

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    References listed on IDEAS

    1. Epstein Larry G. & Wang Tan, 1995. "Uncertainty, Risk-Neutral Measures and Security Price Booms and Crashes," Journal of Economic Theory, Elsevier, vol. 67(1), pages 40-82, October.
    2. Marinacci, Massimo, 1999. "Limit Laws for Non-additive Probabilities and Their Frequentist Interpretation," Journal of Economic Theory, Elsevier, vol. 84(2), pages 145-195, February.
    3. Ghirardato, Paolo, 1997. "On Independence for Non-Additive Measures, with a Fubini Theorem," Journal of Economic Theory, Elsevier, vol. 73(2), pages 261-291, April.
    4. Sarin, Rakesh & Wakker, Peter P, 1998. "Dynamic Choice and NonExpected Utility," Journal of Risk and Uncertainty, Springer, vol. 17(2), pages 87-119, November.
    5. Hendon, Ebbe & Jacobsen, Hans Jorgen & Sloth, Birgitte & Tranaes, Torben, 1996. "The product of capacities and belief functions," Mathematical Social Sciences, Elsevier, vol. 32(2), pages 95-108, October.
    6. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    7. D. Blackwell & L. Dubins, 2010. "Merging of Opinions with Increasing Information," Levine's Working Paper Archive 565, David K. Levine.
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    Cited by:

    1. Klibanoff, Peter & Marinacci, Massimo & Mukerji, Sujoy, 2009. "Recursive smooth ambiguity preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 930-976, May.
    2. Frank Riedel & Linda Sass, 2014. "Ellsberg games," Theory and Decision, Springer, vol. 76(4), pages 469-509, April.
    3. Larry G. Epstein & Martin Schneider, 2007. "Learning Under Ambiguity," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1275-1303.
    4. Paul Viefers, 2012. "Should I Stay or Should I Go?: A Laboratory Analysis of Investment Opportunities under Ambiguity," Discussion Papers of DIW Berlin 1228, DIW Berlin, German Institute for Economic Research.
    5. Tatjana Chudjakow & Frank Riedel, 2013. "The best choice problem under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 77-97, September.
    6. 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.
    7. Daniele Pennesi, 2013. "Asset Prices in an Ambiguous Economy," Carlo Alberto Notebooks 315, Collegio Carlo Alberto.
    8. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2012. "On the Smooth Ambiguity Model: A Reply," Econometrica, Econometric Society, vol. 80(3), pages 1303-1321, May.
    9. Zerihun, Mulatu F. & Breitenbach, Marthinus C., 2016. "Nonlinear approaches in testing PPP: Evidence from Southern African development community," Economic Modelling, Elsevier, vol. 56(C), pages 162-167.
    10. Martin Schneider, 2010. "The Research Agenda: Martin Schneider on Multiple Priors Preferences and Financial Markets," EconomicDynamics Newsletter, Review of Economic Dynamics, vol. 11(2), April.
    11. Larry G. Epstein & Martin Schneider, 2008. "Ambiguity, Information Quality, and Asset Pricing," Journal of Finance, American Finance Association, vol. 63(1), pages 197-228, February.

    More about this item


    ambiguity; multiple-priors; Ellsberg Paradox; recursive utility; law of large numbers; independent experiments; exchangeable experiments;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D9 - Microeconomics - - Micro-Based Behavioral Economics

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