Rank-correlations are not robust to differences in group inequality

Rank-based measures of intergenerational mobility are generally justified by their invariance to changes in inequality. However, I show that whenever the source of inequality is uncorrelated to parent ranks, such as in the cases of gender and birth order, increasing equality leads to a fall in rank mobility as measured by the rank correlation. I develop a method to ex-post quantify the importance of inequality for mobility measurement using cross-sectional income distributions and show that US income mobility could have fallen by as much as 24 percent since 1970 due to increased gender equality. Without specifying a policy objective of interest, it is therefore unclear which conclusions to draw from differences in rank-correlations across societies or from changes over time.