ON COMPARING DISTRIBUTIONS OF POVERTY GAPS

Abstract

we provide sufficient conditions based on crossings of absolute or generalized Lorenz curves and on crossings of cumulative distribution functions. Necessary and sufficient conditions based on crossings of rotated absolute Lorenz curves are also provided. The conditions are related to but not equivalent to those used for checking whether income distribution is more unequal in one population than another. When populations cannot be ordered by uniform hardship, their rankings cannot be made without the introduction of social judgements. An altternative to using poverty indexes to impose judgements is to report two (or more) numbers that summarize all of the information needed for choosing a ranking. One of the numbers represents social judgments, and the other represents the rankings of the populations according to that particular set of social judgements. Two variants on this approach, including one developed by Atkinson, are discussed.