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Social Learning with Model Misspeciification: A Framework and a Robustness Result

Author

Listed:
  • Aislinn Bohren

    () (Department of Economics, University of Pennsylvania)

  • Daniel Hauser

    () (Department of Economics, Aalto University)

Abstract

We explore how model misspecification affects long-run learning in a sequential social learning setting. Individuals learn from diverse sources, including private signals, public signals and the actions and outcomes of others. An agent's type specifies her model of the world. Misspecified types have incorrect beliefs about the signal distribution, how other agents draw inference and/or others' preferences. Our main result is a simple criterion to characterize long-run learning outcomes that is straightforward to derive from the primitives of the misspecification. Depending on the nature of the misspecification, we show that learning may be correct, incorrect or beliefs may not converge. Multiple degenerate limit beliefs may arise and agents may asymptotically disagree, despite observing the same sequence of information. We also establish that the correctly specified model is robust - agents with approximately correct models almost surely learn the true state. We close with a demonstration of how our framework can capture three broad categories of model misspecification: strategic misspecification, such as level-k and cognitive hierarchy, signal misspecification, such as partisan bias, and preference misspecification from social perception biases, such as the false consensus effect and pluralistic ignorance. For each case, we illustrate how to calculate the set of asymptotic learning outcomes and derive comparative statics for how this set changes with the parameters of the misspecification.

Suggested Citation

  • Aislinn Bohren & Daniel Hauser, 2018. "Social Learning with Model Misspeciification: A Framework and a Robustness Result," PIER Working Paper Archive 18-017, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Jul 2018.
  • Handle: RePEc:pen:papers:18-017
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    References listed on IDEAS

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    Cited by:

    1. Aislinn Bohren & Alex Imas & Michael Rosenberg, 2017. "The Dynamics of Discrimination: Theory and Evidence," PIER Working Paper Archive 17-021, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 18 Nov 2017.
    2. Ignacio Esponda & Demian Pouzo, 2019. "Asymptotic Behavior of Bayesian Learners with Misspecified Models," Papers 1904.08551, arXiv.org.
    3. Mira Frick & Ryota Iijima & Yuhta Ishii, 2018. "Dispersed Behavior and Perceptions in Assortative Societies," Cowles Foundation Discussion Papers 2128R, Cowles Foundation for Research in Economics, Yale University, revised Mar 2019.
    4. Mira Frick & Ryota Iijima & Yuhta Ishii, 2019. "Misinterpreting Others and the Fragility of Social Learning," Cowles Foundation Discussion Papers 2160, Cowles Foundation for Research in Economics, Yale University.

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    Keywords

    Social learning; model misspecification; bounded rationality;

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