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Distributions of Posterior Quantiles via Matching

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  • Anton Kolotilin
  • Alexander Wolitzky

Abstract

We offer a simple analysis of the problem of choosing a statistical experiment to optimize the induced distribution of posterior medians, or more generally $q$-quantiles for any $q \in (0,1)$. 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," Papers 2402.17142, arXiv.org.
    • Handle: RePEc:arx:papers:2402.17142
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    References listed on IDEAS

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    1. 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.
    2. Kremer, M & Maskin, E, 1996. "Wage Inequality and Segregation by Skill," Working papers 96-23, Massachusetts Institute of Technology (MIT), Department of Economics.
    3. Kolotilin, Anton, 2018. "Optimal information disclosure: a linear programming approach," Theoretical Economics, Econometric Society, vol. 13(2), May.
    4. Andreas Kleiner & Benny Moldovanu & Philipp Strack, 2021. "Extreme Points and Majorization: Economic Applications," Econometrica, Econometric Society, vol. 89(4), pages 1557-1593, July.
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    More about this item

    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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