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Information Validates the Prior: A Theorem on Bayesian Updating and Applications

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  • Navin Kartik
  • Frances Xu Lee
  • Wing Suen

Abstract

We develop a result on expected posteriors for Bayesians with heterogenous priors, dubbed information validates the prior (IVP). Under familiar ordering requirements, Anne expects a (Blackwell) more informative experiment to bring Bob's posterior mean closer to Anne's prior mean. We apply the result in two contexts of games of asymmetric information: voluntary testing or certification, and costly signaling or falsification. IVP can be used to determine how an agent's behavior responds to additional exogenous or endogenous information. We discuss economic implications.

Suggested Citation

  • Navin Kartik & Frances Xu Lee & Wing Suen, 2021. "Information Validates the Prior: A Theorem on Bayesian Updating and Applications," American Economic Review: Insights, American Economic Association, vol. 3(2), pages 165-182, June.
    • Handle: RePEc:aea:aerins:v:3:y:2021:i:2:p:165-82
    DOI: 10.1257/aeri.20200284
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    References listed on IDEAS

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    1. Weiss, Andrew, 1983. "A Sorting-cum-Learning Model of Education," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 420-442, June.
    2. Alonso, Ricardo & Câmara, Odilon, 2016. "Bayesian persuasion with heterogeneous priors," Journal of Economic Theory, Elsevier, vol. 165(C), pages 672-706.
    3. Kreps, David M. & Francetich, Alejandro, 2014. "Bayesian Inference Does Not Lead You Astray . . . On Average," Research Papers 3059, Stanford University, Graduate School of Business.
    4. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn.
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    Cited by:

    1. Vladimir Novak & Andrei Matveenko & Silvio Ravaioli, 2021. "The Status Quo and Belief Polarization of Inattentive Agents: Theory and Experiment," Working Papers 674, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    2. Onuchic, Paula & Ray, Debraj, 2023. "Conveying value via categories," Theoretical Economics, Econometric Society, vol. 18(4), November.
    3. Chang, Dongkyu & Vong, Allen, 2021. "Perverse Ethical Concerns: Online Platforms and Offline Conflicts," MPRA Paper 110507, University Library of Munich, Germany.
    4. Giampaolo Bonomi, 2023. "The Disagreement Dividend," Papers 2308.06607, arXiv.org, revised Jan 2024.

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    More about this item

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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