Source decomposition of changes in income inequality: the integral-based approach and its approximation by the chained Shapley-value approach

This paper proposes source decomposition of the change in income inequality between two time points using the integral-based approach (IBA) and the (chained) Shapley-value approach as its approximation. In comparison to static Shapley-value decompositions and traditional decompositions for the square of the coefficient of variation and the Gini index, the new dynamic Shapley-value approach is intuitively appealing as a decomposition procedure for changes in inequality. It is expected to yield relatively small differences among various inequality measures, essentially maintaining consistency with income source classification. Path dependency, a possible drawback of the new decompositions, is not expected to be a particular problem in the usual cases. The properties are illustrated for application to the increase in US family income inequality during 1979–1996. In this empirical study, the new decompositions showed a tendency that was clearly different from those of the existing decompositions, indicating that the proposed procedures shed new light on analysis of the causes of inequality changes. An extension to incorporate other factors such as family structure is also successful without loss of the desirable properties.