Measuring Intergenerational Mobility in Population Subgroups
Using φ-Divergences

This paper introduces a measure of intergenerational social mobility based on φ-divergences. The measure can be decomposed to study mobility in population subgroups of interest and  can be used to describe mobility of multiple outcome variables across an arbitrary number of generations, unlike most indicators in the literature. The measure also fully controls for marginal distributions, meaning it is not affected by income growth or changes in income inequality. I propose two estimators for the measure: a non-parametric estimator and an estimator based on the mobility matrix. I provide conditions under which these estimators are √n-consistent and asymptotically normal. With a specific φ-divergence, the Hellinger distance, I measure multidimensional social mobility in the USA and Germany using the PSID, the SOEP, and US administrative tax data. The measure reveals lower income and health mobility in the USA than Germany, but the opposite for educational mobility. It also shows income mobility for both countries is lowest in the tails of the parental income distribution and greatest in the center. This inverted U-pattern is more pronounced in the USA. Most of these empirical findings for population subgroups are hidden to the existing indicators in the literature.