Generalized Poverty-gap Orderings

Abstract

This paper provides a characterization of a new class of ordinal poverty measures that are defined by means of the aggregate generalized poverty gap. To be precise, we propose to use the sum of the differences between the transformed fixed poverty line and the transformed level of income of each person below the line as our measure. If the transformation is strictly concave, the resulting measure is strictly inequality averse with respect to the incomes of the poor. In analogy to some existing results on inequality measurement, we show that the only relative (scale-invariant) members of our class are based on strictly concave power functions or the natural logarithm. Moreover, we show that our measures allow for a useful decomposition that is akin to those examined in some earlier contributions. In an empirical analysis, we compare the logarithmic variant of our index to two well-established alternative orderings. Unlike numerous indices that appear in the earlier literature, ours do not explicitly depend on the number of poor or on the total population size, thereby ruling out any direct influence of the head-count ratio on poverty comparisons.