An implementation of the Gini concentration ratio decomposition by sources

Kakwani suggested a decomposition of Gini concentration ratio by components in which the concentration ratio of the whole variable is a linear combination of the concentration ratios of the components, the weights being the products of the shares of the same components and some correlation coefficients. In this note we show that in the case of some null observations of the component, which is very common in applications, each of the three factors of the decomposition can be split in two parts, one due to positive observations and another due to null observations. This paper gives a more complete interpretation of the results of the applications of Kakwani decomposition.