The Gini Index Decomposition and Overlapping Between Population Subgroups

This chapter illustrates a development of overlapping and Gini index decomposition focused on gender gap analysis, with a case study related to Italian personal income. The evaluation of the differences between two non-overlapping subgroups is quite simple and the subgroups means are the first and most natural candidate. The Gini index has known many different expressions and applications during its over-100 years of life. Also, the decomposition of the Gini index is the object of uncountable studies and researches, which belong to the more general discussion about the decomposition of inequality measures. A significant step forward in the Gini index decomposition was made in 1991 thanks to S. Yitzhaki and R. Lerman, who introduced a decomposition of the Gini index where overlapping is explicitly taken into account. The joint combination of inequality decomposition and overlapping measurement allows many interesting developments.