A Unified Approach to Measuring Poverty and Inequality
Additive Decomposability and Geographic Targeting A poverty measure of a population subgroup reflects the level of deprivation for that subgroup. A higher value of a population subgroup’s poverty measure reflects a higher level of deprivation. The poverty measures we have discussed in this chapter satisfy population replication invariance to be able to compare the poverty levels of different population sizes, so these measures are invariant to population size. However, a population subgroup with a higher level of poverty does not necessarily imply that the subgroup has a larger contribution to overall poverty. A subgroup’s contribution to overall poverty also depends on the population distribution across subgroups. Therefore, targeting a region or a group based on only a poverty measure may not be completely accurate. We also need to take the population distribution into account. If P is an additively decomposable poverty measure and the income distribution x with total population size N is divided into M subgroups—x1 with population size N1, x2 with population size N2, …, xM with population size NM—then the contribution of group m to total poverty is NmP(xm;z)/NP(x;z), where z is the poverty line. Consider the situation when poverty is assessed by the headcount ratio. A population subgroup’s headcount ratio denotes the population percentage identified as poor. Interpreting a population subgroup’s contribution to overall poverty in terms of the headcount ratio is intuitive. If the total number of poor is q, and qm is the number of poor in subgroup m, then the overall headcount ratio is q/N and that of subgroup m is qm/Nm for all m = 1,…, M. Then subgroup m’s share of overall poverty is Nm[qm/Nm]/N[q/N] = qm/q. Thus, the contribution of the subgroup’s poverty to overall poverty in terms of the headcount ratio is just the share of overall poor in that subgroup. For example, consider table 3.9 in chapter 3, which shows the distribution of the poor across Georgian subnational regions for years 2003 and 2006. Suppose that, in 2003, the headcount ratio of the subnational region Kvemo Kartli is 44.4 percent, which is more than twice the headcount ratio of 20.9 percent in Tbilisi. However, the share of total poor living in Tbilisi is, in fact, slightly larger than that living in Kvemo Kartli, because the population size of Tbilisi is more than twice that of Kvemo Kartli. In 2006, the headcount ratio of Kvemo Kartli decreased to 35.1 percent, which is still 10 percent higher than the headcount ratio of Tbilisi, but the share of the poor living in Tbilisi increased to 20.4 percent alongside only 12.2 percent in Kvemo Kartli. Therefore, the Georgian government needs to understand
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