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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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    1. Rachel Croson & James Sundali, 2005. "The Gambler’s Fallacy and the Hot Hand: Empirical Data from Casinos," Journal of Risk and Uncertainty, Springer, vol. 30(3), pages 195-209, May.
    2. Sigrid Suetens & Claus B. Galbo-Jørgensen & Jean-Robert Tyran, 2016. "Predicting Lotto Numbers: A Natural Experiment on the Gambler's Fallacy and the Hot-Hand Fallacy," Journal of the European Economic Association, European Economic Association, vol. 14(3), pages 584-607.
    3. Matthew Rabin, 2002. "Inference by Believers in the Law of Small Numbers," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(3), pages 775-816.
    4. Chen, Daniel L. & Moskowitz, Tobias J. & Shue, Kelly, 2016. "Decision-Making Under the Gambler’s Fallacy: Evidence From Asylum Courts, Loan Officers, and Baseball Umpires," IAST Working Papers 16-43, Institute for Advanced Study in Toulouse (IAST).
    5. Benjamin Enke, 2020. "What You See Is All There Is," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 135(3), pages 1363-1398.
    6. Ignacio Esponda & Demian Pouzo, 2014. "Berk-Nash Equilibrium: A Framework for Modeling Agents with Misspecified Models," Papers 1411.1152, arXiv.org, revised Nov 2019.
    7. Daniel L. Chen & Tobias J. Moskowitz & Kelly Shue, 2016. "Decision Making Under the Gambler’s Fallacy: Evidence from Asylum Judges, Loan Officers, and Baseball Umpires," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(3), pages 1181-1242.
    8. Ignacio Esponda, 2008. "Behavioral Equilibrium in Economies with Adverse Selection," American Economic Review, American Economic Association, vol. 98(4), pages 1269-1291, September.
    9. Terrell, Dek, 1994. "A Test of the Gambler's Fallacy: Evidence from Pari-mutuel Games," Journal of Risk and Uncertainty, Springer, vol. 8(3), pages 309-317, May.
    10. Sridhar Narayanan & Puneet Manchanda, 2012. "An empirical analysis of individual level casino gambling behavior," Quantitative Marketing and Economics (QME), Springer, vol. 10(1), pages 27-62, March.
    11. Camerer, Colin F, 1987. "Do Biases in Probability Judgment Matter in Markets? Experimental Evidence," American Economic Review, American Economic Association, vol. 77(5), pages 981-997, December.
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    Cited by:

    1. Kevin He & Jonathan Libgober, 2020. "Evolutionarily Stable (Mis)specifications: Theory and Applications," Papers 2012.15007, arXiv.org, revised Feb 2023.
    2. Luca Braghieri, 2023. "Biased Decoding and the Foundations of Communication," CESifo Working Paper Series 10432, CESifo.
    3. Gagnon-Bartsch, Tristan & Bushong, Benjamin, 2022. "Learning with misattribution of reference dependence," Journal of Economic Theory, Elsevier, vol. 203(C).
    4. 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.
    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. 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.
    7. 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.
    8. 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.
    9. Ignacio Esponda & Demian Pouzo & Yuichi Yamamoto, 2019. "Asymptotic Behavior of Bayesian Learners with Misspecified Models," Papers 1904.08551, arXiv.org, revised Oct 2019.
    10. Yingkai Li & Harry Pei, 2020. "Misspecified Beliefs about Time Lags," Papers 2012.07238, arXiv.org.
    11. 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

    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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