Decomposing inequality indices across household groups or income sources is useful in estimating the contribution of each component to total inequality. This can help policy makers draw efficient policies to reduce disparities in the distribution of incomes using targeting tools. Decomposing relative inequality indices, such as the Gini coefficient, is not a simple procedure since, in many cases, the functional form of inequality indices is not additively separable in incomes. More importantly, for some of the indices on which this decomposition can be performed, the interpretation of the decomposition components is often not well founded. In this paper, we use the Shapley value as well as analytical approaches to perform the decomposition of the Gini coefficient and generalize it, in some cases, to the decomposition of other inequality indices. For the analytical approach, our aim is to extend the same interpretation, attributed to the Gini coefficient, to that of the contribution components.
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