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...

The concentrated poverty index, i.e. the proportion of a metro area's poor population living in extreme-poverty neighborhoods, is widely adopted as a policy-relevant measure of urban poverty. We challenge this view and develop a family of new indices of urban poverty that, differently from...