A survey of some recent developments in measures of association

Chatterjee, Sourav

doi:10.48550/arxiv.2211.04702

Cited by 1 publication

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“…Our paper contributes to the general literature on nonparametric rank statistics. Since the literature is large, we provide here only some key references, referring an interested reader, for example, to a recent review Chatterjee (2023). As mentioned above, Hoeffding (1948) derived the asymptotic distribution for Spearman's rank correlation in the case of continuous distributions.…”

Section: Introductionmentioning

confidence: 99%

Inference for rank-rank regressions

2024

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Slope coefficients in rank-rank regressions are popular measures of intergenerational mobility. In this paper, we first point out two important properties of the OLS estimator in such regressions: commonly used variance estimators do not consistently estimate the asymptotic variance of the OLS estimator and, when the underlying distribution is not continuous, the OLS estimator may be highly sensitive to the way in which ties are handled. Motivated by these findings we derive the asymptotic theory for the OLS estimator in a general rank-rank regression specification without making 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 three empirical studies. We find that the confidence intervals based on estimators of the correct variance may sometimes be substantially shorter and sometimes substantially longer than those based on commonly used variance estimators. The differences in confidence intervals concern economically meaningful values of mobility and thus may lead to different conclusions when comparing mobility across different regions or countries.

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Section: Introductionmentioning

confidence: 99%

Inference for rank-rank regressions

2024

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A survey of some recent developments in measures of association

Abstract: In honor of friend and teacher Prof. Rajeeva L. Karandikar on the occasion of his 65 th birthday.

Cited by 1 publication

References 103 publications

Inference for rank-rank regressions

Inference for rank-rank regressions

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