Inference for Rank-Rank Regressions

TL;DR

This paper reveals the limitations of existing inference methods for rank-rank regressions in measuring intergenerational mobility and introduces a new, robust asymptotic theory that handles ties and distribution discontinuities.

Contribution

It develops a novel asymptotic framework for rank-rank regressions that does not rely on distribution continuity assumptions, improving inference accuracy.

Findings

Common inference methods are invalid for rank-rank regressions.

The new theory handles ties and distribution discontinuities effectively.

Empirical applications demonstrate practical implications of the new methods.

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.