Chapter 1: Introduction
standard that is closely linked to an inequality measure. For the SST index, it is the Gini coefficient. For the CHUC indices, the Atkinson measures are used. For the Watts index, the mean log deviation is the inequality measure. In each case, the inequality measure is applied to the censored distribution x* with greater censored inequality being reflected in a higher level of poverty (for a given poverty gap level). The FGT measures (for a > 1) use generalized entropy measures applied to the gap distribution g* with greater gap inequality leading to a higher level of poverty (for a given level of the poverty gap). The focused inequality measures underlying these distribution-sensitive poverty indices ignore variations in incomes above the poverty line. Trends in focused inequality may well be very different from trends in overall inequality. Certain income standards can be viewed as welfare functions, and this link can provide yet another lens for interpreting poverty measures. The Sen mean underlying the SST index and the general means for a ≤ 1 that are behind the CHUC indices can be interpreted as welfare functions. In each case, the welfare function is applied to the censored distribution to obtain the poor income standard a, which is now seen to be a censored welfare function that takes into account the incomes of the poor and only part of the incomes of the nonpoor (up to the poverty line). For these measures, poverty and censored welfare are inversely related. Every increase in poverty is seen as a decrease in censored welfare. Of course, the trends in censored welfare may be very different from the trends in overall welfare, as the latter take into account the actual incomes of the nonpoor. We will see below another link between welfare and poverty when we consider poverty comparisons over a range of lines. Applications A poverty methodology can be used to identify the poor (through its identification step) and to evaluate the extent of poverty (through the aggregation step). The first step by itself allows many interesting analyses to be conducted, given appropriately rich data. Consider, for example, the following questions: • Who are the poor and how do they differ from the nonpoor? A range of characteristics can be examined—including location, household size, ethnicity, education indicators, health indicators, housing, and
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