The decomposition of the Atkinson-Plotnik-Kakwani re-ranking measure

This article introduces a new matrix approach, based on pairwise income comparisons, to decompose the Atkinson-Plotnick-Kakwani re-ranking measure when income units are gathered into groups. As it is known the Atkinson-Plotnick-Kakwani re-ranking measure is defined by the difference between the Gini index and the concentration index. Re-ranking can be exclusively decomposed as the sum of two parts: the within group and the across-group re-ranking measures. Our results are applied to a household sub-sample selected from the 2007 survey of the Panel Study on Income Dynamics (PSID). In the applied analysis our approach proves to be quite powerful. We show that in addition to providing different measures, it allows to calculate the incidence of re-ranking.