A Unified Approach to Measuring Poverty and Inequality
quantify the relative impacts of demographic changes and the changes in subgroup poverty on the overall poverty level. • What share of overall poverty can be attributed to a particular population group? We can define a subgroup’s contribution to overall poverty to be the population share of a subgroup times the poverty level of the subgroup divided by the overall poverty level. Some subgroups with low levels of poverty may have large contributions as a result of their population sizes. Others may have smaller population shares, but still have large contribution shares because subgroup poverty levels are high. For decomposable poverty measures, subgroup contributions must sum to one. Dominance and Unanimity The above discussion assumes that it is possible to select a correct poverty line to separate the poor from the nonpoor. Yet it is clear that any cutoff selected is bound to be arbitrary and that alternative poverty lines could be chosen with equal justification. Conclusions obtained at the original poverty line may be reversed at some other reasonable standard. They also could be robust to a change in the poverty line. To help discern which of these possibilities is true—a reversal or unanimity for all poverty lines—we can construct a poverty (value) curve which graphs the poverty measure as a function of the poverty line over the relevant range of poverty lines. If the original comparison continues to hold at all poverty lines in the range, then the comparison is robust. This gives rise to a (variable line) poverty ordering, which ranks one distribution as having less poverty than another when its poverty curve is not above (and is somewhere below) the poverty curve of the other distribution. The range of poverty lines usually begins at 0 and ends at some highest value z*, although it is instructive to consider the case where there is no upper bound. Our discussion begins with the latter case. Although the general approach can be used with any poverty measure, it is standard to focus on the three main measures from the FGT family: the headcount ratio, the poverty gap measure, and the FGT squared gap measure. The headcount ratio for a given poverty line is the share of the population having incomes below the poverty line. Consequently, the poverty
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