Conditional Rank-Rank Regression

TL;DR

This paper introduces conditional rank-rank regression, a new method to measure within-group association accounting for covariates, with theoretical foundations and an empirical application to intergenerational income mobility in Switzerland.

Contribution

It proposes the conditional rank-rank regression approach, providing a natural measure of within-group association and a flexible estimation method with large sample inference.

Findings

Stronger intergenerational income persistence between fathers and sons than with daughters.

Within-group persistence explains 62% of income persistence for sons and 52% for daughters.

Smaller families and higher paternal education are associated with greater income persistence.

Abstract

Rank-rank regression is commonly employed in economic research as a way of capturing the relationship between two economic variables. The slope of this regression is the Spearman rank correlation, a classical measure of association. However, in many applications it is common practice to include covariates to account for differences in association levels between groups as defined by the values of these covariates. This is either done by including the covariates or by modeling the residuals obtained after partialing out the impact of the covariates. In each of these instances the resulting rank-rank regression coefficients can be difficult to interpret. We propose the conditional rank-rank regression, which uses conditional ranks instead of unconditional ranks, to measure average within-group persistence. The coefficient of this new regression corresponds to the average Spearman rank correlation conditional on the covariates, a natural summary measure of within-group association. We develop a flexible estimation approach using distribution regression and establish a theoretical framework for large sample inference. An empirical study on intergenerational income mobility in Switzerland demonstrates the advantages of this approach. The study reveals stronger intergenerational persistence between fathers and sons compared to fathers and daughters, with the within-group persistence explaining 62% of the overall income persistence for sons and 52% for daughters. Smaller families and those with highly educated fathers exhibit greater persistence in economic status.