A Class of Decomposable Poverty Measures

Abstract

SEVERALRECENT STUDIES OF POVERTY have demonstrated the usefulness of breaking down a population into subgroups defined along ethnic, geographical, or other lines [e.g. 1, 201. Such an approach to poverty analysis places requirements on the poverty measure in addition to those proposed by Sen [IS, 161. In particular, the question of how the measure relates subgroup poverty to total poverty is crucial to its applicability in this form of analysis. At the very least, one would expect that a decrease in the poverty level of one subgroup ceterisparibus should lead to less poverty for the population as a whole. At best, one might hope to obtain a quantitative estimate of the effect of a change in subgroup poverty on total poverty, or to give a subgroup's contribution to total poverty. One way to satisfy the above criteria is to use a poverty measure that is additively decomposable in the sense that total poverty is a weighted average of the subgroup poverty levels.* However, the existing decomposable poverty measures are inadequate in that they violate one or more of the basic properties proposed by Sen.3 Stated another way, of all the measures [I, 3, 10, 191 that are acceptable by the Sen criteria, none is decomposable. In fact, the Sen measure and its variants that rely on rank-order weighting fail to satisfy the basic condition that an increase in subgroup poverty must increase total poverty (see footnote 6). This note is a first step towards resolving these inadequacies. In what follows we present a simple, new poverty measure4 that (i) is additively decomposable with population-share weights, (ii) satisfies the basic properties proposed by Sen, and (iii) is justified by a relative deprivation concept of poverty. The inequality measure associated with our poverty measure is shown to be the squared coefficient of variation and indeed the poverty measure may be expressed as a combination of this inequality measure, the headcount ratio, and the income-gap ratio in a fashion similar to Sen [IS]. We generalize the new poverty measure to a parametric family of measures where the parameter can be interpreted as an indicator of "aversion to poverty." A brief empirical application demonstrates the usefulness of the decomposability property.