  Rank-rank regressions are widely used in economic research to evaluate
phenomena such as intergenerational income persistence or mobility. However,
when covariates are incorporated to capture between-group persistence, the
resulting coefficients can be difficult to interpret as such. We propose the
conditional rank-rank regression, which uses conditional ranks instead of
unconditional ranks, to measure average within-group income persistence. This
property is analogous to that of the unconditional rank-rank regression that
measures the overall income persistence. The difference between conditional and
unconditional rank-rank regression coefficients therefore can measure
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. Families of small
size or with highly educated fathers exhibit greater persistence in passing on
their economic status.
