🤖 AI Summary
Conventional inference methods for slope parameters in rank-rank regression fail under distributional discontinuities; OLS estimation and its asymptotic distribution are highly sensitive to rank ties, undermining the reliability of intergenerational mobility analyses.
Method: This paper establishes the first universal asymptotic theory for the OLS estimator in rank-rank regression—applicable to arbitrary distributions, including discrete ones—thereby relaxing the standard continuity assumption. It further extends the framework to multiple classes of rank-based regression models, developing confidence intervals and hypothesis tests via nonstandard asymptotic analysis and robust rank modeling.
Contribution/Results: Empirically, the proposed methods substantially revise prior findings in two prominent intergenerational mobility studies, yielding more statistically valid and robust policy evaluations. The approach enhances inferential reliability in settings with ties, mass points, or mixed discrete-continuous outcomes—common in socioeconomic data—while preserving interpretability through rank-scale parameters.
📝 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.