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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 asymptotic distribution may be highly sensitive to how ties in the ranks are handled. Motivated by these findings we develop a new asymptotic theory for the OLS estimator in a general class of rank-rank regression specifications without imposing any assumptions about the continuity of the underlying distribution. We then extend the asymptotic theory to other regressions involving ranks that have been used in empirical work. Finally, we apply our new inference methods to two empirical studies on intergenerational mobility, highlighting the practical implications of our theoretical findings.

Suggested Citation

  • Denis Chetverikov & Daniel Wilhelm, 2023. "Inference for Rank-Rank Regressions," Papers 2310.15512, arXiv.org, revised Jul 2024.
  • Handle: RePEc:arx:papers:2310.15512
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    References listed on IDEAS

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    1. Carneiro, Pedro & Cruz Aguayo, Yyannu & Salvati, Francesca & Schady, Norbert, 2023. "The Effect of Classroom Rank on Learning throughout Elementary School: Experimental Evidence from Ecuador," IZA Discussion Papers 16384, Institute of Labor Economics (IZA).
    2. 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.
    3. 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.
    4. 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.
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