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Inference on Consensus Ranking of Distributions

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Abstract
Instead of testing for unanimous agreement, I propose learning how broad of a consensus favors one distribution over another (of earnings, productivity, asset returns, test scores, etc.). Specifically, given a sample from each of two distributions, I propose statistical inference methods to learn about the set of utility functions for which the first distribution has higher expected utility than the second distribution. With high probability, an "inner" confidence set is contained within this true set, while an "outer" confidence set contains the true set. Such confidence sets can be formed by inverting a proposed multiple testing procedure that controls the familywise error rate. Theoretical justification comes from empirical process results, given that very large classes of utility functions are generally Donsker (subject to finite moments). The theory additionally justifies a uniform (over utility functions) confidence band of expected utility differences, as well as tests with a utility-based "restricted stochastic dominance" as either the null or alternative hypothesis. Simulated and empirical examples illustrate the methodology.

Suggested Citation

  • David M. Kaplan, 2022. "Inference on Consensus Ranking of Distributions," Working Papers 2205, Department of Economics, University of Missouri.
    • Handle: RePEc:umc:wpaper:2205
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    References listed on IDEAS

    as
    1. Magne Mogstad & Joseph P Romano & Azeem M Shaikh & Daniel Wilhelm, 2024. "Inference for Ranks with Applications to Mobility across Neighbourhoods and Academic Achievement across Countries," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 91(1), pages 476-518.
    2. Alberto Abadie & Joshua Angrist & Guido Imbens, 2002. "Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings," Econometrica, Econometric Society, vol. 70(1), pages 91-117, January.
    3. David M. Kaplan, 2019. "distcomp: Comparing distributions," Stata Journal, StataCorp LP, vol. 19(4), pages 832-848, December.
    4. Goldman, Matt & Kaplan, David M., 2018. "Comparing distributions by multiple testing across quantiles or CDF values," Journal of Econometrics, Elsevier, vol. 206(1), pages 143-166.
    5. Joseph P. Romano & Azeem M. Shaikh, 2010. "Inference for the Identified Set in Partially Identified Econometric Models," Econometrica, Econometric Society, vol. 78(1), pages 169-211, January.
    6. Kaplan, David M. & Sun, Yixiao, 2017. "Smoothed Estimating Equations For Instrumental Variables Quantile Regression," Econometric Theory, Cambridge University Press, vol. 33(1), pages 105-157, February.
    7. Goldman, Matt & Kaplan, David M., 2018. "Comparing distributions by multiple testing across quantiles or CDF values," Journal of Econometrics, Elsevier, vol. 206(1), pages 143-166.
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    Cited by:

    1. Wei Zhao & David M. Kaplan, 2024. "Conditions for extrapolating differences in consumption to differences in welfare," Economic Inquiry, Western Economic Association International, vol. 62(3), pages 1090-1104, July.

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    More about this item

    Keywords

    confidence set; Donsker; expected utility; familywise error rate; multiple testing; stochastic dominance;
    All these keywords.

    JEL classification:

    • C29 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Other

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