When Ranks Fail: New Evidence on Intergenerational Educational Mobility

Many recent studies on intergenerational educational mobility adopted the rank-rank model popularized by the work of Chetty et al. (2014, QJE) on income mobility, under the assumption that the approach remains valid for discrete variables. However, conversion of discrete data such as years of schooling into percentile ranks fails to make the empirical rank distribution uniform, unlike continuous variables such as income. Thus, the estimates of relative educational mobility from rank-rank regressions are not margin-free, and capture a fundamentally different concept of mobility compared to the rank-rank slope in income mobility analysis. Taking advantage of recent advances on discrete copulas, we introduce a margin-free measure of relative educational mobility, Yule’s coefficient, which is the analogue of the rank-rank slope in income mobility. Yule’s coefficient was proposed by Geenens (2020) as a summary measure of the margin-free dependence structure between two discrete variables such as children’s and parents’ schooling. The margin-free dependence structure is estimated by an iterative matrix re-scaling procedure applied to the joint probability mass function of the bivariate discrete distribution. We report estimates of Yule’s coefficient for 6 countries: the USA, Bangladesh, India, Indonesia, Chile, and Mexico. The evidence suggests that, in many cases, the rank-rank slope estimates for schooling overestimate the margin-free relative educational mobility (positional mobility). For example, the estimates for the USA (PSID data) are: rank-rank slope=0.441 and Yule’s coefficient=0.534. The extent of overestimation in the national estimates varies considerably across countries: 3.09%−48.31%. The cross-country rankings and evolution of educational mobility across cohorts are substantially different when we use the margin-free Yule’s coefficient instead of the rank-based measures.