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Inference for Rank-Rank Regressions

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  • Denis Chetverikov
  • Daniel Wilhelm

Abstract

The slope coefficient in a rank-rank regression is a popular measure of intergenerational mobility. In this article, we first show that commonly used inference methods for this slope parameter are invalid. Second, when the underlying distribution is not continuous, the OLS estimator and its distribution may be sensitive to how ties in the ranks are handled. Motivated by these findings we derive the asymptotic distribution of the OLS estimator and provide valid inference methods for a general class of rank-rank regression specifications.

Suggested Citation

  • Denis Chetverikov & Daniel Wilhelm, 2023. "Inference for Rank-Rank Regressions," Papers 2310.15512, arXiv.org, revised Aug 2026.
    • Handle: RePEc:arx:papers:2310.15512
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    References listed on IDEAS

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    1. Martin Klein & Tommy Wright & Jerzy Wieczorek, 2020. "A joint confidence region for an overall ranking of populations," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(3), pages 589-606, June.
    2. Pedro Carneiro & Yyannu Cruz-Aguayo & Francesca Salvati & Norbert Schady, 2025. "The Effect of Classroom Rank on Learning throughout Elementary School: Experimental Evidence from Ecuador," Journal of Labor Economics, University of Chicago Press, vol. 43(2), pages 433-466.
    3. Petra Ornstein & Johan Lyhagen, 2016. "Asymptotic Properties of Spearman’s Rank Correlation for Variables with Finite Support," PLOS ONE, Public Library of Science, vol. 11(1), pages 1-7, January.
    4. Borkowf, Craig B., 2002. "Computing the nonnull asymptotic variance and the asymptotic relative efficiency of Spearman's rank correlation," Computational Statistics & Data Analysis, Elsevier, vol. 39(3), pages 271-286, May.
    5. Raj Chetty & Nathaniel Hendren & Patrick Kline & Emmanuel Saez, 2014. "Where is the land of Opportunity? The Geography of Intergenerational Mobility in the United States," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(4), pages 1553-1623.
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    Cited by:

    1. Marc-Oliver Pohle & Jan-Lukas Wermuth & Christian H. Wei{ss}, 2025. "Asymptotic Inference for Rank Correlations," Papers 2512.14609, arXiv.org, revised Feb 2026.

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