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Distributions of posterior quantiles via matching

Author

Listed:
  • Kolotilin, Anton

    (School of Economics, UNSW Business School)

  • Wolitzky, Alexander

    (Department of Economics, MIT)

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 ∈ (0,1). We show that a single experiment---the q-quantile matching experiment---implements all implementable distributions of posterior q-quantiles, with different distributions spanned by different selections from the sets of posterior q-quantiles. 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 posterior q-quantiles. The q-quantile matching experiment is the only experiment that simultaneously implements all implementable distributions of posterior q-quantiles.

Suggested Citation

  • Kolotilin, Anton & Wolitzky, Alexander, 2024. "Distributions of posterior quantiles via matching," Theoretical Economics, Econometric Society, vol. 19(4), November.
    • Handle: RePEc:the:publsh:6057
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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.
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    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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