Poverty Orderings with Asymmetric Attributes

We provide a theorem that lists the necessary and sufficient dominance conditions for the poverty comparisons of the bivariate distributions function when considering an asymmetric treatment of attributes. The normative justification for an asymmetric treatment is based on the compensation principle proposed by Muller and Trannoy (2012), under which it makes sense to use one attribute to compensate another. The formulation results in a generalization of the needs approach in poverty analysis proposed by Atkinson (1992). The dominance conditions we found lie between those obtained by Bourguignon and Chakravarty (2002) and Duclos, Sahn, and Younger (2006a) when attributes are symmetric and those obtained within the needs framework by Atkinson (1992) and Jenkins and Lambert (1993) when attributes are asymmetric, but one is of discrete nature.

Poverty orderings and intra-household inequality: The Lost Axiom

We investigate under which conditions it is possible to infer the evolution of poverty at the individual level from the knowledge of poverty among households. Poverty measurement is approached by the poverty orderings introduced by Foster and Shorrocks (1988). The analysis is based on a reduced form of household bargaining (Peluso and Trannoy, 2007) and provides results in terms of preservation of poverty orderings. We point out the main analogies and differences between inequality and poverty assessment, expressing them in terms of empirically testable conditions. In particular, knowing the change in poverty at the household level is not sufficient to deduce a similar change in poverty at the individual level. We need to know the change in the household income distributions far beyond their poverty line. The focus axiom does not hold in this context.