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Identifying Wisdom (of the Crowd): A Regression Approach

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  • Jonathan Libgober

Abstract

Experts in a population hold (a) beliefs over a state and (b) beliefs over the population’s belief distribution. If these are generated via Bayesian updating from a common prior using signal observations from a fixed information structure, a linear regression using the experts’ beliefs identifies the information structure, provided there are no more states than signals. Furthermore, an eigenvector equation derived from the experts’ beliefs identifies the prior. Thus, the ex ante informational environment (i.e., how signals are generated) can be determined using ex post data (i.e., the experts’ beliefs). I interpret these findings and also discuss identification when states outnumber signals.

Suggested Citation

  • Jonathan Libgober, 2025. "Identifying Wisdom (of the Crowd): A Regression Approach," Journal of Political Economy Microeconomics, University of Chicago Press, vol. 3(4), pages 798-826.
    • Handle: RePEc:ucp:jpemic:doi:10.1086/733781
    DOI: 10.1086/733781
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    Cited by:

    1. 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.
    2. Peker, Cem & Wilkening, Tom, 2025. "Robust recalibration of aggregate probability forecasts using meta-beliefs," International Journal of Forecasting, Elsevier, vol. 41(2), pages 613-630.
    3. Smolin, Alex & Doval, Laura, 2021. "Information Payoffs: An Interim Perspective," CEPR Discussion Papers 16543, C.E.P.R. Discussion Papers.
    4. Laura Doval & Alex Smolin, 2024. "Persuasion and Welfare," Journal of Political Economy, University of Chicago Press, vol. 132(7), pages 2451-2487.

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