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Learning With Heterogeneous Misspecified Models: Characterization and Robustness

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  • J. Aislinn Bohren
  • Daniel N. Hauser

Abstract

This paper develops a general framework to study how misinterpreting information impacts learning. Our main result is a simple criterion to characterize long‐run beliefs based on the underlying form of misspecification. We present this characterization in the context of social learning, then highlight how it applies to other learning environments, including individual learning. A key contribution is that our characterization applies to settings with model heterogeneity and provides conditions for entrenched disagreement. Our characterization can be used to determine whether a representative agent approach is valid in the face of heterogeneity, study how differing levels of bias or unawareness of others' biases impact learning, and explore whether the impact of a bias is sensitive to parametric specification or the source of information. This unified framework synthesizes insights gleaned from previously studied forms of misspecification and provides novel insights in specific applications, as we demonstrate in settings with partisan bias, overreaction, naive learning, and level‐k reasoning.

Suggested Citation

  • J. Aislinn Bohren & Daniel N. Hauser, 2021. "Learning With Heterogeneous Misspecified Models: Characterization and Robustness," Econometrica, Econometric Society, vol. 89(6), pages 3025-3077, November.
  • Handle: RePEc:wly:emetrp:v:89:y:2021:i:6:p:3025-3077
    DOI: 10.3982/ECTA15318
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    References listed on IDEAS

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    1. Mira Frick & Ryota Iijima & Yuhta Ishii, 2018. "Dispersed Behavior and Perceptions in Assortative Societies," Cowles Foundation Discussion Papers 2128R2, Cowles Foundation for Research in Economics, Yale University, revised Oct 2021.
    2. Jehiel, Philippe & Mohlin, Erik, 2021. "Cycling and Categorical Learning in Decentralized Adverse Selection Economies," Working Papers 2021:11, Lund University, Department of Economics.
    3. Jia, Chengcheng & Wu, Jing Cynthia, 2023. "Average inflation targeting: Time inconsistency and ambiguous communication," Journal of Monetary Economics, Elsevier, vol. 138(C), pages 69-86.
    4. Abhijit Banerjee & Olivier Compte, 2022. "Consensus and Disagreement: Information Aggregation under (not so) Naive Learning," NBER Working Papers 29897, National Bureau of Economic Research, Inc.
    5. Luca Braghieri, 2023. "Biased Decoding and the Foundations of Communication," CESifo Working Paper Series 10432, CESifo.
    6. Ing-Haw Cheng & Alice Hsiaw, 2023. "Bayesian Doublespeak," Working Papers 135, Brandeis University, Department of Economics and International Business School.
    7. Mira Frick & Ryota Iijima & Yuhta Ishii, 2018. "Dispersed Behavior and Perceptions in Assortative Societies," Cowles Foundation Discussion Papers 2128R3, Cowles Foundation for Research in Economics, Yale University, revised Jun 2022.
    8. Gagnon-Bartsch, Tristan & Bushong, Benjamin, 2022. "Learning with misattribution of reference dependence," Journal of Economic Theory, Elsevier, vol. 203(C).
    9. Zikai Xu, 2022. "Observational Learning with Competitive Prices," Papers 2202.06425, arXiv.org, revised May 2022.
    10. Philippe Jehiel & Erik Mohlin, 2023. "Categorization in Games: A Bias-Variance Perspective," Working Papers halshs-04154272, HAL.
    11. Chen, Jaden Yang, 2022. "Biased learning under ambiguous information," Journal of Economic Theory, Elsevier, vol. 203(C).
    12. Mira Frick & Ryota Iijima & Yuhta Ishii, 2020. "Belief Convergence under Misspecified Learning: A Martingale Approach," Cowles Foundation Discussion Papers 2235R2, Cowles Foundation for Research in Economics, Yale University, revised Dec 2021.
    13. Fudenberg, Drew & Gao, Ying & Pei, Harry, 2022. "A reputation for honesty," Journal of Economic Theory, Elsevier, vol. 204(C).
    14. Simon Board & Moritz Meyer‐ter‐Vehn, 2021. "Learning Dynamics in Social Networks," Econometrica, Econometric Society, vol. 89(6), pages 2601-2635, November.
    15. Cuimin Ba, 2021. "Robust Misspecified Models and Paradigm Shifts," Papers 2106.12727, arXiv.org, revised Aug 2023.
    16. Gagnon-Bartsch, Tristan & Rosato, Antonio, 2022. "Quality is in the eye of the beholder: taste projection in markets with observational learning," MPRA Paper 115426, University Library of Munich, Germany.
    17. Mira Frick & Ryota Iijima & Yuhta Ishii, 2020. "Belief Convergence under Misspecified Learning: A Martingale Approach," Cowles Foundation Discussion Papers 2235R3, Cowles Foundation for Research in Economics, Yale University, revised Apr 2022.
    18. Tanvir Ahmed Khan, 2023. "Can Unbiased Predictive AI Amplify Bias?," Working Paper 1510, Economics Department, Queen's University.
    19. Le Yaouanq, Yves, 2023. "A model of voting with motivated beliefs," Journal of Economic Behavior & Organization, Elsevier, vol. 213(C), pages 394-408.
    20. Fudenberg, Drew & Lanzani, Giacomo, 2023. "Which misspecifications persist?," Theoretical Economics, Econometric Society, vol. 18(3), July.
    21. 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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