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Asymptotic behavior of Bayesian learners with misspecified models

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  • Esponda, Ignacio
  • Pouzo, Demian
  • Yamamoto, Yuichi

Abstract

We consider an agent who represents uncertainty about the environment via a possibly misspecified model. Each period, the agent takes an action, observes a consequence, and uses Bayes' rule to update her belief about the environment. This framework has become increasingly popular in economics to study behavior driven by incorrect or biased beliefs. By first showing that the key element to predict the agent's behavior is the frequency of her past actions, we are able to characterize asymptotic behavior in general settings in terms of the solutions of a differential inclusion that describes the evolution of the frequency of actions. We then present a series of implications that can be readily applied to economic applications, thus providing off-the-shelf tools that can be used to characterize behavior under misspecified learning.

Suggested Citation

  • Esponda, Ignacio & Pouzo, Demian & Yamamoto, Yuichi, 2021. "Asymptotic behavior of Bayesian learners with misspecified models," Journal of Economic Theory, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:jetheo:v:195:y:2021:i:c:s0022053121000776
    DOI: 10.1016/j.jet.2021.105260
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    9. Jehiel, Philippe & Mohlin, Erik, 2021. "Cycling and Categorical Learning in Decentralized Adverse Selection Economies," Working Papers 2021:11, Lund University, Department of Economics.
    10. Junnan He & Lin Hu & Matthew Kovach & Anqi Li, 2023. "Learning Source Biases: Multisource Misspecifications and Their Impact on Predictions," Papers 2309.08740, arXiv.org, revised Sep 2024.
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    12. In-Koo Cho & Jonathan Libgober, 2022. "Learning Underspecified Models," Papers 2207.10140, arXiv.org.
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    More about this item

    Keywords

    Bayesian learning; Misspecified models; Asymptotic behavior; Differential inclusion; Berk-Nash equilibrium;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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