A matrix approach to the Gini index decomposition by subgroup and by income source

The literature offers two main ways of decomposing the Gini index: decomposition by population subgroup and by income source. This article proposes merging the two decomposition dimensions by suggesting a matrix formula for the Gini index which permits the simultaneous decomposition by subgroup and by income source. Using this multi‐decomposition, one can investigate the role of the interaction between the subgroup and the source components in determining the overall inequality. We apply the methodology to sample data on Italian household incomes collected in 2008.