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Distributions of Posterior Quantiles and Economic Applications

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Abstract

We characterize the distributions of posterior quantiles under a given prior. Unlike the distributions of posterior means, which are known to be mean-preserving contractions of the prior, the distributions of posterior quantiles coincide with a first-order stochastic dominance interval bounded by an upper and a lower truncation of the prior. We apply this characterization to several environments, ranging across political economy, Bayesian persuasion, industrial organization, econometrics, finance, and accounting.

Suggested Citation

  • Kai Hao Yang & Alexander K. Zentefis, 2022. "Distributions of Posterior Quantiles and Economic Applications," Cowles Foundation Discussion Papers 2328R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2022.
    • Handle: RePEc:cwl:cwldpp:2328r
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d23/d2328-ra.pdf
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    References listed on IDEAS

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    1. Elliot Lipnowski & Doron Ravid, 2020. "Cheap Talk With Transparent Motives," Econometrica, Econometric Society, vol. 88(4), pages 1631-1660, July.
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    More about this item

    Keywords

    Posterior quantiles; stochastic dominance; gerrymandering; Bayesian persuasion; two-sided markets; quantile regression;
    All these keywords.

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation
    • L12 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Monopoly; Monopolization Strategies
    • M41 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Accounting - - - Accounting

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