A Unified Approach to Measuring Poverty and Inequality
Other measures evaluate poverty by the average gap or depth of poverty: • The normalized gap vector is constructed by replacing income of each poor individual with the normalized gap (or the gap between the poverty line and the income expressed as a share of the poverty line) and income of every nonpoor individual with 0. The poverty gap measure is the mean of the normalized gap vector. It is sensitive to both the prevalence of poverty in a society and the extent to which the poor fall below the poverty line. • Another measure is based on the squared gap vector, which uses the square of the normalized gap for each poor person. The squaring process emphasizes the larger gaps relative to the smaller gaps. The squared gap or Foster-Greer-Thorbecke (FGT) measure index is the mean of the squared gap vector. It is sensitive to the prevalence of the poor, the extent to which their incomes fall below the poverty line, and the distribution of their incomes or shortfalls. All of those measures are members of a parametric family of indices: the FGT family of poverty indices is derived by taking the mean of an a-gap vector, which is obtained by raising each positive entry in the normalized gap vector by a power of a ≥ 0. There are two main ways of interpreting what a poverty measure is actually measuring. One way is by examining the properties that the measure satisfies. The other makes use of income standards in interpreting the measure. We begin with the axiomatic approach. Poverty Measure Properties There are six basic properties for poverty measures: • The first two are the symmetry and population invariance properties given above for income standards and inequality measures. They are important for ensuring that the measure is based on the anonymous distribution and not on the income recipients’ names or the population size. • The third basic property is the focus axiom, which requires the poverty measure to ignore changes in the distribution involving nonpoor incomes. This approach ensures that the measure focuses on poor incomes in evaluating poverty.
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