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.