Combining absolute and relative poverty: income poverty measurement with two poverty lines

I study income poverty indices in a framework considering two poverty lines: one absolute line capturing subsistence and one relative line capturing social exclusion. In this framework, a set of basic axioms à la Foster and Shorrocks (Econometrica 59(3): 687–709, 1991) characterizes the class of hierarchical indices. This is a class of additive indices for which the poverty contribution of any individual depends on both her income and the income standard in her society. The key feature of hierarchical indices is to grant some form of precedence to absolutely poor individuals. These indices always consider that an absolutely poor individual is poorer than an individual who is only relatively poor, regardless of the income standard in their respective societies. Classical indices are not hierarchical, except in trivial cases. As a result, they yield debatable poverty comparisons of societies having different income standards.