A Note on a Troublesome Axiom for Poverty Indices

Recent axiomatic approaches to the measurement of poverty have not been altogether satisfactory. Studies, such as those by Clark, Hemming, and Ulph (CHU), have tried to design an index that considers the distribution of income among the poor. They have been thwarted, however, by persistent problems with the transfer axiom. The violation can occur if the recipient of a transfer crosses the poverty line. These shortcomings stem from an unwarranted belief that the concavity properties of the group social welfare function are a sufficient condition for the transfer axiom to be satisfied. The second poverty index proposed by CHU is somewhat more acceptable, though. It introduces relative sensitivity to transfers at different levels of income under the shape of Atkinson's index of income distribution among the poor. This inclusion of sensitivity is skillfully done and keeps income considerations separate.