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.

翻译：秩-秩回归在经济学研究中被广泛用于评估代际收入持续性或流动性等现象。然而，当引入协变量以捕捉组间持续性时，所得系数的解释往往存在困难。为此，我们提出了条件秩-秩回归方法，该方法采用条件秩而非无条件秩，以度量组内平均收入持续性。这一性质类似于度量总体收入持续性的无条件秩-秩回归。因此，条件与无条件秩-秩回归系数之间的差异可用于度量组间持续性。我们基于分布回归发展了一种灵活的估计方法，并建立了大样本推断的理论框架。一项关于瑞士代际收入流动性的实证研究展示了该方法的优势。研究发现，父子间的代际持续性明显强于父女间，其中组内持续性分别解释了儿子总体收入持续性的62%和女儿的52%。家庭规模较小或父亲受教育程度较高的家庭，其经济地位的代际传递表现出更强的持续性。