On the decomposition of the Schutz coefficient: an exact approach with an application

Decomposing inequality indices across household groups are useful in estimating the contribution of each component to total inequality. Decomposing relative inequality index for the Schutz coefficient (S-coefficient) is not simple since the functional form of inequality indices is not additively separable in incomes. In this article, the decomposition of Schultz coefficient across sub-groups is derived where it has a general form of decomposition as between-groups term, within-groups term and error term. Moreover, the error analysis is used to obtain the exact decomposition for the Schutz coefficient by dividing the error term to within-groups and between-groups terms. The final two main component types that we obtained are the exclusive within-groups and between-groups terms. Several examples are given that illustrate the benefits of the proposed method