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Limit Points of Endogenous Misspecified Learning

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  • Drew Fudenberg
  • Giacomo Lanzani
  • Philipp Strack

Abstract

We study how an agent learns from endogenous data when their prior belief is misspecified. We show that only uniform Berk–Nash equilibria can be long‐run outcomes, and that all uniformly strict Berk–Nash equilibria have an arbitrarily high probability of being the long‐run outcome for some initial beliefs. When the agent believes the outcome distribution is exogenous, every uniformly strict Berk–Nash equilibrium has positive probability of being the long‐run outcome for any initial belief. We generalize these results to settings where the agent observes a signal before acting.

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  • Drew Fudenberg & Giacomo Lanzani & Philipp Strack, 2021. "Limit Points of Endogenous Misspecified Learning," Econometrica, Econometric Society, vol. 89(3), pages 1065-1098, May.
    • Handle: RePEc:wly:emetrp:v:89:y:2021:i:3:p:1065-1098
    DOI: 10.3982/ECTA18508
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    References listed on IDEAS

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    1. Bell, Alex & Chetty, Raj & Jaravel, Xavier & Petkova, Neviana & Van Reenen, John, 2019. "Do tax cuts produce more Einsteins? The impacts of financial incentives vs. exposure to innovation on the supply of inventors," LSE Research Online Documents on Economics 121796, London School of Economics and Political Science, LSE Library.
    2. Philippe Jehiel, 2018. "Investment Strategy and Selection Bias: An Equilibrium Perspective on Overoptimism," American Economic Review, American Economic Association, vol. 108(6), pages 1582-1597, June.
    3. George J. Mailath & Larry Samuelson, 2020. "Learning under Diverse World Views: Model-Based Inference," American Economic Review, American Economic Association, vol. 110(5), pages 1464-1501, May.
    4. 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.
    5. Fudenberg, Drew & He, Kevin, 2020. "Payoff information and learning in signaling games," Games and Economic Behavior, Elsevier, vol. 120(C), pages 96-120.
    6. Bohren, J. Aislinn, 2016. "Informational herding with model misspecification," Journal of Economic Theory, Elsevier, vol. 163(C), pages 222-247.
    7. Bray, Margaret, 1982. "Learning, estimation, and the stability of rational expectations," Journal of Economic Theory, Elsevier, vol. 26(2), pages 318-339, April.
    8. Benaim, Michel & Hirsch, Morris W., 1999. "Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 36-72, October.
    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. Kevin He & Jonathan Libgober, 2020. "Evolutionarily Stable (Mis)specifications: Theory and Applications," Papers 2012.15007, arXiv.org, revised Feb 2023.
    11. Drew Fudenberg & Kevin He & Lorens Imhof, 2016. "Bayesian Posteriors For Arbitrarily Rare Events," Papers 1608.05002, arXiv.org, revised Apr 2017.
    12. Mira Frick & Ryota Iijima & Yuhta Ishii, 2020. "Stability and Robustness in Misspecified Learning Models," Cowles Foundation Discussion Papers 2235, Cowles Foundation for Research in Economics, Yale University.
    13. Pooya Molavi, 2019. "Macroeconomics with Learning and Misspecification: A General Theory and Applications," 2019 Meeting Papers 1584, Society for Economic Dynamics.
    14. Paul Heidhues & Botond KH{o}szegi & Philipp Strack, 2019. "Overconfidence and Prejudice," Papers 1909.08497, arXiv.org.
    15. Kagel, John H. & Levin, Dan, 1986. "The Winner's Curse and Public Information in Common Value Auctions," American Economic Review, American Economic Association, vol. 76(5), pages 894-920, December.
    16. Matthew Rabin & Joel L. Schrag, 1999. "First Impressions Matter: A Model of Confirmatory Bias," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(1), pages 37-82.
    17. William Morrison & Dmitry Taubinsky, 2023. "Rules of Thumb and Attention Elasticities: Evidence from Under- and Overreaction to Taxes," The Review of Economics and Statistics, MIT Press, vol. 105(5), pages 1110-1127, September.
    18. Bray, Margaret M & Savin, Nathan E, 1986. "Rational Expectations Equilibria, Learning, and Model Specification," Econometrica, Econometric Society, vol. 54(5), pages 1129-1160, September.
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    3. In-Koo Cho & Jonathan Libgober, 2022. "Learning Underspecified Models," Papers 2207.10140, arXiv.org.
    4. Duarte Gonc{c}alves, 2022. "Sequential Sampling Equilibrium," Papers 2212.07725, arXiv.org, revised Nov 2023.
    5. Chen, Jaden Yang, 2022. "Biased learning under ambiguous information," Journal of Economic Theory, Elsevier, vol. 203(C).
    6. Fudenberg, Drew & Gao, Ying & Pei, Harry, 2022. "A reputation for honesty," Journal of Economic Theory, Elsevier, vol. 204(C).
    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.

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