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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 (call these state beliefs), as well as (b) beliefs over the distribution of beliefs in the population (call these hypothetical beliefs). If these are generated via updating a common prior using a fixed information structure, then the information structure can (generically) be derived by regressing hypothetical beliefs on state beliefs, provided there are at least as many signals as states. In addition, the prior solves an eigenvector equation derived from a matrix determined by the state beliefs and the hypothetical beliefs. Thus, the ex-ante informational environment (i.e., how signals are generated) can be determined using ex-post data (i.e., the beliefs in the population). I discuss implications of this finding, as well as what is identified when there are more states than signals.

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  • Jonathan Libgober, 2021. "Identifying Wisdom (of the Crowd): A Regression Approach," Papers 2105.07097, arXiv.org, revised Apr 2023.
    • Handle: RePEc:arx:papers:2105.07097
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    References listed on IDEAS

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    Cited by:

    1. Smolin, Alex & Doval, Laura, 2021. "Information Payoffs: An Interim Perspective," CEPR Discussion Papers 16543, C.E.P.R. Discussion Papers.
    2. Laura Doval & Alex Smolin, 2021. "Persuasion and Welfare," Papers 2109.03061, arXiv.org, revised Sep 2023.
    3. 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.

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