Sequential procedures for Poverty Gap dominance

Poverty evaluations differ from welfare evaluations in one significant aspect, the existence of a threshold or reference point, the poverty line. It is therefore possible to build up normative evaluation models in which comparisons are made taking distances from this reference point and not only from the origin to be ethically relevant. This is the case in our model of poverty comparisons over heterogeneous populations, which focuses upon poverty gaps and not incomes. When poverty lines differ for the different groups in the population, choosing poverty gaps instead of incomes as the relevant indicator brings in normatively appealing classes of poverty indices not previously accommodated. For these indices poverty comparisons are implemented through sequential poverty gap curves (or poverty gap distributions) dominance. These novel conditions are logically related to those suggested in Atkinson and Bourguignon (1987) [Income distribution and differences in needs. In Arrow and the Foundations of the Theory of Economic Policy, Feiwel (ed.)] for welfare comparisons, and can also be grounded firmly upon those of Bourguignon (1989) [Family size and social utility: income distribution dominance criteria. Journal of Econometrics, 42, 67-80]. The proportion of poor individuals in the society and their average poverty gap play a role in our comparisons, though not in the existing poverty dominance criteria for heterogeneous populations. Various intermediate poverty dominance conditions and a generalization of the poverty gap approach are also investigated.