Chapter 1: Introduction
Subgroup Consistency and Decomposability Many programs designed to address the needs of the poor are implemented at the local level. Suppose we are evaluating such a program in a country with two equal-sized regions. We find that poverty has fallen significantly in each region, yet when poverty is measured at the country level, it has increased. This possibility could present significant challenges to the analyst and could prove rather difficult to explain to policy makers. It turns out that the inconsistency between regional and national poverty outcomes may be due entirely to the way poverty is measured. To ensure that this possibility does not arise, one can require the poverty measure to satisfy subgroup consistency. This property requires that if poverty falls in one subgroup and is unchanged in another and both have fixed population sizes, then the overall poverty level must likewise fall. The SST index is not subgroup consistent because of its use of the Sen mean. The FGT and CHUC measures, which depend on general means, are subgroup consistent and thus would not be subject to the regional-national dilemma. Subgroup consistency requires overall poverty to move in the same direction as an unambiguous change in subgroup poverty levels. A stronger property provides an explicit formula that makes the link between overall and subgroup poverty. A poverty measure is said to be (additively) decomposable if overall poverty is a population-share weighted average of subgroup poverty levels. Unlike the case of inequality measures, there is no betweengroup term in this decomposition. The reason is that the standard against which subgroup poverty is evaluated is a fixed poverty line. In contrast, an inequality measure typically evaluates subgroup inequality relative to subgroup means, then takes the variation of subgroup means into account as another source of inequality. Additively decomposable poverty measures transparently link subgroup poverty to overall poverty. This approach can be particularly useful in generating a coherent poverty profile in which a broad array of population subgroups and their poverty levels can be broken down or reassembled as needed. Consider these questions: • Is a given change in overall poverty caused by changes in subgroup poverty levels, by population shifts across subgroups, or by a combination of the two effects? A counterfactual approach, which constructs an artificial intermediate distribution to separate the two, can help
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