Nonparametric and Semiparametric Estimation of Upward Rank Mobility Curves

We introduce the upward rank mobility curve as a new measure of intergenerational mobility that captures upward movements across the entire parental income distribution. Our approach extends Bhattacharya and Mazumder (2011) by conditioning on a single parental income rank, thereby eliminating aggregation bias. We show that the measure can be characterized solely by the copula of parent and child income, and we propose a nonparametric copula-based estimator with better properties than kernel-based alternatives. For a conditional version of the measure without such a representation, we develop a two-step semiparametric estimator based on distribution regression and establish its asymptotic properties. An application to U.S. data reveals that whites exhibit significant upward mobility dominance over blacks among lower-middle-income families.