Intergenerational mobility quantifies the transmission of socio-economic outcomes from parents to children. While rank-rank regression (RRR) is standard, adding covariates directly (RRRX) often yields parameters with unclear interpretation. Conditional rank-rank regression (CRRR) resolves this by using covariate-adjusted (conditional) ranks to measure within-group mobility. We improve and extend CRRR by estimating conditional ranks with a deep conditional transformation model (DCTM) and cross-fitting, enabling end-to-end conditional distribution learning with structural constraints and strong performance under nonlinearity, high-order interactions, and discrete ordered outcomes where the distributional regression used in traditional CRRR may be cumbersome or prone to misconfiguration. We further extend CRRR to discrete outcomes via an $ω$-indexed conditional-rank definition and study sensitivity to $ω$. For continuous outcomes, we establish an asymptotic theory for the proposed estimators and verify the validity of exchangeable bootstrap inference. Simulations across simple/complex continuous and discrete ordered designs show clear accuracy gains in challenging settings. Finally, we apply our method to two empirical studies, revealing substantial within-group persistence in U.S. income and pronounced gender differences in educational mobility in India.

翻译：代际流动性量化了社会经济结果从父母到子女的传递。虽然秩-秩回归（RRR）是标准方法，但直接添加协变量（RRRX）通常会产生解释不明确的参数。条件秩-秩回归（CRRR）通过使用协变量调整（条件）秩来测量组内流动性，从而解决了这一问题。我们通过使用深度条件转换模型（DCTM）和交叉拟合来估计条件秩，从而改进和扩展了CRRR，实现了具有结构约束的端到端条件分布学习，并在非线性、高阶交互作用以及离散有序结果的情况下表现出强大性能，而传统CRRR中使用的分布回归在这些情况下可能繁琐或容易配置错误。我们进一步通过$ω$索引的条件秩定义将CRRR扩展到离散结果，并研究其对$ω$的敏感性。对于连续结果，我们为所提出的估计量建立了渐近理论，并验证了可交换自助法推断的有效性。在简单/复杂的连续和离散有序设计下的模拟显示，在具有挑战性的设置中准确性有明显提升。最后，我们将我们的方法应用于两项实证研究，揭示了美国收入中显著的组内持续性以及印度教育流动性中明显的性别差异。