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Behavioral Foundations of Model Misspecification

Author

Listed:
  • J. Aislinn Bohren

    (University of Pennsylvania)

  • Daniel N. Hauser

    (Aalto University and Helsinki GSE)

Abstract

We link two approaches to biased belief formation: non-Bayesian updating rules and model misspecification. Each approach has advantages: updating rules transparently capture the underlying bias and are identifiable from belief data; misspecified models are `complete' and amenable to general analysis. We show that misspecified models can be decomposed into an updating rule and forecast of anticipated future beliefs. We derive necessary and sufficient conditions for an updating rule and forecast to have a misspecified model representation, show the representation is unique, and construct it. This highlights the belief restrictions implicit in the misspecified model approach. Finally, we explore two ways to elect forecasts introspection-proof and naive consistent and derive when a representation of each exists.

Suggested Citation

  • 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.
    • Handle: RePEc:pen:papers:23-007
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    References listed on IDEAS

    as
    1. Joshua Schwartzstein, 2014. "Selective Attention And Learning," Journal of the European Economic Association, European Economic Association, vol. 12(6), pages 1423-1452, December.
    2. Ignacio Esponda & Demian Pouzo, 2016. "Berk–Nash Equilibrium: A Framework for Modeling Agents With Misspecified Models," Econometrica, Econometric Society, vol. 84, pages 1093-1130, May.
    3. Gilat Levy & Ronny Razin & Alwyn Young, 2022. "Misspecified Politics and the Recurrence of Populism," American Economic Review, American Economic Association, vol. 112(3), pages 928-962, March.
    4. J. Aislinn Bohren & Kareem Haggag & Alex Imas & Devin G. Pope, 2019. "Inaccurate Statistical Discrimination: An Identification Problem," PIER Working Paper Archive 19-010, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 17 Jul 2020.
    5. Daniel J. Benjamin & Matthew Rabin & Collin Raymond, 2016. "A Model of Nonbelief in the Law of Large Numbers," Journal of the European Economic Association, European Economic Association, vol. 14(2), pages 515-544.
    6. 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.
    7. Matthew Rabin & Ted O'Donoghue, 1999. "Doing It Now or Later," American Economic Review, American Economic Association, vol. 89(1), pages 103-124, March.
    8. Eran Shmaya & Leeat Yariv, 2016. "Experiments on Decisions under Uncertainty: A Theoretical Framework," American Economic Review, American Economic Association, vol. 106(7), pages 1775-1801, July.
    9. Nyarko, Yaw, 1991. "Learning in mis-specified models and the possibility of cycles," Journal of Economic Theory, Elsevier, vol. 55(2), pages 416-427, December.
    10. Jonathan Libgober, 2021. "Identifying Wisdom (of the Crowd): A Regression Approach," Papers 2105.07097, arXiv.org, revised Apr 2023.
    11. Jehiel, Philippe, 2005. "Analogy-based expectation equilibrium," Journal of Economic Theory, Elsevier, vol. 123(2), pages 81-104, August.
    12. Andrew Caplin & Mark Dean & John Leahy, 2022. "Rationally Inattentive Behavior: Characterizing and Generalizing Shannon Entropy," Journal of Political Economy, University of Chicago Press, vol. 130(6), pages 1676-1715.
    13. He, Xue Dong & Xiao, Di, 2017. "Processing consistency in non-Bayesian inference," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 90-104.
    14. David M. Grether, 1980. "Bayes Rule as a Descriptive Model: The Representativeness Heuristic," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 95(3), pages 537-557.
    15. 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.
    16. Paul Heidhues & Botond Kőszegi & Philipp Strack, 2018. "Unrealistic Expectations and Misguided Learning," Econometrica, Econometric Society, vol. 86(4), pages 1159-1214, July.
    17. Manski, Charles F. & Neri, Claudia, 2013. "First- and second-order subjective expectations in strategic decision-making: Experimental evidence," Games and Economic Behavior, Elsevier, vol. 81(C), pages 232-254.
    18. Ran Spiegler, 2016. "Bayesian Networks and Boundedly Rational Expectations," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(3), pages 1243-1290.
    19. Edi Karni, 2020. "A mechanism for the elicitation of second-order belief and subjective information structure," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(1), pages 217-232, February.
    20. Pooya Molavi, 2019. "Macroeconomics with Learning and Misspecification: A General Theory and Applications," 2019 Meeting Papers 1584, Society for Economic Dynamics.
    21. Alonso, Ricardo & Câmara, Odilon, 2016. "Bayesian persuasion with heterogeneous priors," Journal of Economic Theory, Elsevier, vol. 165(C), pages 672-706.
    22. , G. & , & ,, 2008. "Non-Bayesian updating: A theoretical framework," Theoretical Economics, Econometric Society, vol. 3(2), June.
    23. Michael Woodford, 2020. "Modeling Imprecision in Perception, Valuation, and Choice," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 579-601, August.
    24. Dražen Prelec & H. Sebastian Seung & John McCoy, 2017. "A solution to the single-question crowd wisdom problem," Nature, Nature, vol. 541(7638), pages 532-535, January.
    25. Epstein Larry G & Noor Jawwad & Sandroni Alvaro, 2010. "Non-Bayesian Learning," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-20, January.
    26. Ignacio Esponda, 2008. "Behavioral Equilibrium in Economies with Adverse Selection," American Economic Review, American Economic Association, vol. 98(4), pages 1269-1291, September.
    27. Fudenberg, Drew & Romanyuk, Gleb & Strack, Philipp, 2017. "Active learning with a misspecified prior," Theoretical Economics, Econometric Society, vol. 12(3), September.
    28. 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.
    29. Lee, Yong-Ju & Lim, Wooyoung & Zhao, Chen, 2023. "Cheap talk with prior-biased inferences," Games and Economic Behavior, Elsevier, vol. 138(C), pages 254-280.
    30. Cuimin Ba, 2021. "Robust Misspecified Models and Paradigm Shifts," Papers 2106.12727, arXiv.org, revised Aug 2023.
    31. Christopher P. Chambers & Nicolas S. Lambert, 2021. "Dynamic Belief Elicitation," Econometrica, Econometric Society, vol. 89(1), pages 375-414, January.
    32. Esponda, Ignacio & Pouzo, Demian & Yamamoto, Yuichi, 2021. "Asymptotic behavior of Bayesian learners with misspecified models," Journal of Economic Theory, Elsevier, vol. 195(C).
    33. Alexander Frankel & Emir Kamenica, 2019. "Quantifying Information and Uncertainty," American Economic Review, American Economic Association, vol. 109(10), pages 3650-3680, October.
    34. Emir Kamenica, 2019. "Bayesian Persuasion and Information Design," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 249-272, August.
    35. 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.
    36. David Danz & Lise Vesterlund & Alistair J. Wilson, 2022. "Belief Elicitation and Behavioral Incentive Compatibility," American Economic Review, American Economic Association, vol. 112(9), pages 2851-2883, September.
    37. Zhao, Chen, 2022. "Pseudo-Bayesian updating," Theoretical Economics, Econometric Society, vol. 17(1), January.
    38. 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.
    39. Drew Fudenberg & Giacomo Lanzani & Philipp Strack, 2021. "Limit Points of Endogenous Misspecified Learning," Econometrica, Econometric Society, vol. 89(3), pages 1065-1098, May.
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    Keywords

    Model misspeci cation; belief formation; learning; non-Bayesian updating; heuristics;
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