Income stratification and between-group inequality

- I generalize a result on the decomposition of the Gini index to more than two groups.
- It is shown explicitly how overlapping of groups impacts between-group inequality.
- An overall index of income stratification is identified for the population.
- I tabulate the pairwise contributions of regions to global income stratification.

The paper shows explicitly how the overlapping of groups impacts between-group inequality by generalizing a result on the group-wise decomposition of the Gini index to more than two groups. It is demonstrated that the ratio of Yitzhaki's measure of between-group inequality to the conventional measure is in general equal to one minus twice the weighted average probability that a random member of a richer (on average) group is poorer than a random member of a poorer (on average) group, and may therefore be interpreted as an overall index of income stratification in the population. The results are used to tabulate the contribution of each pair of regions in the world to the overall level of global income stratification.