On the Interaction Between Focus and Distributional Properties in Multidimensional Poverty Measurement

In the multidimensional poverty measurement literature, most measures satisfy the deprivation focus property, which means that they disregard any improvement in non-deprived achievements. Such measures cannot satisfy strong distributional properties as traditionally defined, because the distributional transformations among the poor are allowed to take place among their non-deprived achievements. We formally address this incompatibility and propose a set of alternative definitions of distributional properties that restrict distributional transformations to take place only among deprived achievements. This alternative definition allows discerning within the set of measures that satisfy the deprivation focus property, those that are strongly sensitive to distributional transformations from those that are not. With this new lens, we review some of the most prominent multidimensional poverty measures proposed in the literature and illustrate how measures within the same class as well as measures across different classes can be discerned from each other based on the alternative definitions.