Conditional rank-rank regression

Rank-rank regression is commonly employed in economic research as a way of capturing the relationship between two economic variables. It frequently features in studies of intergenerational mobility as the resulting coefficient, capturing the rank correlation between the variables, is easy to interpret and measures overall persistence. However, in many applications it is common practice to include other covariates to account for differences in persistence levels between groups defined by the values of these covariates. In these instances the resulting 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 income persistence. The difference between conditional and unconditional rank-rank regression coefficients can then be interpreted as a measure of between-group persistence. 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.