Can we Measure Inequalities without Measuring Equalities?

The purpose of this article is to show that the Gini index of equality is decomposable: (i) both by subgroup and income source and (ii) into a parametric configuration permitting statistical inference on equality components. We demonstrate that the Gini index of equality decompositions imply those of the Gini index of inequality. These results suggest that the use of the Gini index of equality decompositions yields the contribution of each income source to the within-group equality and to the between-group equality. The interpretation of the decomposed inequalities must be done with respect to those of equalities and vice versa.