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Distributions of Posterior Quantiles via Matching

Author

Listed:
  • Anton Kolotilin

    (School of Economics, UNSW)

  • Alexander Wolitzky

    (Department of Economics, MIT)

Abstract

We offer a simple analysis of the problem of choosing a statistical exper- iment to optimize the induced distribution of posterior medians, or more generally q-quantiles for any q ∈ (0, 1). We show that all implementable distributions of the posterior q-quantile are implemented by a single experiment, the q-quantile matching experiment, which pools pairs of states across the q-quantile of the prior in a positively assortative manner, with weight q on the lower state in each pair. A dense subset of implementable distributions of posterior q-quantiles can be uniquely implemented by perturbing the q-quantile matching experiment. A linear functional is optimized over distributions of posterior q-quantiles by taking the optimal selection from each set of q-quantiles induced by the q-quantile matching experiment. The q-quantile matching experiment is the only experiment that simultaneously implements all implementable distributions of the posterior q-quantile.

Suggested Citation

  • Anton Kolotilin & Alexander Wolitzky, 2024. "Distributions of Posterior Quantiles via Matching," Discussion Papers 2024-01, School of Economics, The University of New South Wales.
    • Handle: RePEc:swe:wpaper:2024-01
    as

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    File URL: http://research.economics.unsw.edu.au/RePEc/papers/2024-01.pdf
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    References listed on IDEAS

    as
    1. Kremer, M & Maskin, E, 1996. "Wage Inequality and Segregation by Skill," Working papers 96-23, Massachusetts Institute of Technology (MIT), Department of Economics.
    2. Andreas Kleiner & Benny Moldovanu & Philipp Strack, 2021. "Extreme Points and Majorization: Economic Applications," Econometrica, Econometric Society, vol. 89(4), pages 1557-1593, July.
    3. Patrick Legros & Andrew F. Newman, 2002. "Monotone Matching in Perfect and Imperfect Worlds," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(4), pages 925-942.
    4. Kolotilin, Anton, 2018. "Optimal information disclosure: a linear programming approach," Theoretical Economics, Econometric Society, vol. 13(2), May.
    5. John N. Friedman & Richard T. Holden, 2008. "Optimal Gerrymandering: Sometimes Pack, but Never Crack," American Economic Review, American Economic Association, vol. 98(1), pages 113-144, March.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    quantiles; statistical experiments; overconfidence; gerrymandering; persuasion;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • 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

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