A Nonparametric Index of Stratification

The author presents a nonparametric approach to measuring stratification that highlights the distinction between stratification and inequality. Using pairwise comparison of ranks, the author develops an index of stratification that gauges the overall degree to which population subgroups occupy distinct strata with respect to a hierarchical outcome. This new index possesses a number of desirable properties that are not satisfied by existing measures of stratification. The overall index can be decomposed as a weighted average of pair-specific indices of stratification, which capture the extent of separation between any two particular groups. Besides, this index can be easily extended to measure conditional stratification through control of a third variable. In addition, the author builds a parallel between stratification and inequality in their measurement by developing a general formula of which the index of stratification and the Gini index of inequality can be considered as two special cases. Finally, this new approach is applied to depict the temporal trends of wage stratification by gender, race, and educational attainment over the past three decades in the United States.