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Mislearning from censored data: The gambler's fallacy and other correlational mistakes in optimal-stopping problems

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  • He, Kevin

    (Department of Economics, University of Pennsylvania)

Abstract

I study endogenous learning dynamics for people who misperceive intertemporal correlations in random sequences. Biased agents face an optimal-stopping problem. They are uncertain about the underlying distribution and learn its parameters from predecessors. Agents stop when early draws are "good enough," so predecessors' experiences contain negative streaks but not positive streaks. When agents wrongly expect systematic reversals (the "gambler's fallacy"), they understate the likelihood of consecutive below-average draws, converge to over-pessimistic beliefs about the distribution's mean, and stop too early. Agents uncertain about the distribution's variance overestimate it to an extent that depends on predecessors' stopping thresholds. I also analyze how other misperceptions of intertemporal correlation interact with endogenous data censoring.

Suggested Citation

  • He, Kevin, 2022. "Mislearning from censored data: The gambler's fallacy and other correlational mistakes in optimal-stopping problems," Theoretical Economics, Econometric Society, vol. 17(3), July.
    • Handle: RePEc:the:publsh:4657
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    Cited by:

    1. J. Aislinn Bohren & Daniel N. Hauser, 2023. "Behavioral Foundations of Model Misspecification," PIER Working Paper Archive 23-007, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    2. Kevin He & Jonathan Libgober, 2020. "Evolutionarily Stable (Mis)specifications: Theory and Applications," Papers 2012.15007, arXiv.org, revised Feb 2023.
    3. Takeshi Murooka & Yuichi Yamamoto, 2021. "Misspecified Bayesian Learning by Strategic Players: First-Order Misspecification and Higher-Order Misspecification," OSIPP Discussion Paper 21E008, Osaka School of International Public Policy, Osaka University.
    4. Ba, Cuimin & Gindin, Alice, 2023. "A multi-agent model of misspecified learning with overconfidence," Games and Economic Behavior, Elsevier, vol. 142(C), pages 315-338.
    5. Mira Frick & Ryota Iijima & Yuhta Ishii, 2020. "Misinterpreting Others and the Fragility of Social Learning," Econometrica, Econometric Society, vol. 88(6), pages 2281-2328, November.
    6. Luca Braghieri, 2023. "Biased Decoding and the Foundations of Communication," CESifo Working Paper Series 10432, CESifo.
    7. Ignacio Esponda & Demian Pouzo & Yuichi Yamamoto, 2019. "Asymptotic Behavior of Bayesian Learners with Misspecified Models," Papers 1904.08551, arXiv.org, revised Oct 2019.
    8. Yingkai Li & Harry Pei, 2020. "Misspecified Beliefs about Time Lags," Papers 2012.07238, arXiv.org.
    9. Gagnon-Bartsch, Tristan & Bushong, Benjamin, 2022. "Learning with misattribution of reference dependence," Journal of Economic Theory, Elsevier, vol. 203(C).
    10. Itai Arieli & Yakov Babichenko & Stephan Muller & Farzad Pourbabaee & Omer Tamuz, 2023. "The Hazards and Benefits of Condescension in Social Learning," Papers 2301.11237, arXiv.org, revised Feb 2024.
    11. Fudenberg, Drew & Lanzani, Giacomo & Strack, Philipp, 2023. "Pathwise concentration bounds for Bayesian beliefs," Theoretical Economics, Econometric Society, vol. 18(4), November.
    12. Mira Frick & Ryota Iijima & Yuhta Ishii, 2023. "Belief Convergence under Misspecified Learning: A Martingale Approach," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(2), pages 781-814.

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    More about this item

    Keywords

    Misspecified learning; gambler’s fallacy; Berk-Nash equilibrium; endogenous data censoring; fictitious variation;
    All these keywords.

    JEL classification:

    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

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