A Unified Approach to Measuring Poverty and Inequality
nonpoor. In this example, society X has two poor people and two nonpoor people. We summarize the incomes of the poor in vector x by the vector xq. Poverty analysis is concerned only with the poor or the distribution’s base, which should be the group targeted for public assistance. It naturally ignores the incomes of nonpoor people in a society. In this way, the identification step allows us to construct a censored distribution or censored vector of incomes for society X, which we denote by x* = (x*1,x*2, …,x*N) such that x*n = xn if income xn is less than the poverty line z and xn* = z if income xn is greater than or equal to the poverty line z. For the four-person income vector x = ($1k, $2k, $50k, $70k) in the previous example, the censored vector is denoted by x* = ($1k, $2k, $10k, $10k). Notice that incomes of the two nonpoor people are replaced by the poverty line, and portions of their income above the poverty line are ignored. A policy maker’s objective should be to include poor people at or above the poverty line. Including all poor people at or above the poverty line results in a nonpoverty censored distribution of income. We denote the nonpoverty censored distribution of society X corresponding to poverty line z by x– z* such that x– z* = (z,z,…,z). The second step for constructing a poverty measure is aggregation. In this step, incomes of individuals who are identified as poor using the poverty line in the identification stage are aggregated to obtain a poverty measure. Therefore, a poverty measure depends on both the incomes of the poor and the criterion that is used for identifying the poor—that is, the poverty line. In fact, it turns out that any poverty measure is obtained by aggregating elements in the censored distribution x∗. In this section, we denote a poverty measure by P, where specific indices are denoted using corresponding subscripts. We denote the poverty measure of distribution x for poverty line z by P(x; z). Alternatively, it may be denoted by P(x∗). There are two different ways to understand a poverty measure: one is based on the properties it satisfies and the other is through its link with income standards. First, we discuss the properties that a poverty measure should satisfy. Desirable Properties A useful poverty measure should satisfy some desirable properties. Like income standards and inequality measures, poverty measure properties can fall into two categories:
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