A Unified Approach to Measuring Poverty and Inequality
There are four basic properties for inequality measures: • The first two are symmetry and population invariance properties, which are analogous to those defined for income standards. They ensure that inequality depends entirely on income distribution and not on names or numbers of income recipients. • The third is scale invariance (or homogeneity of degree zero), which requires the inequality measure to be unchanged if all incomes are scaled up or down by a common factor. This ensures that the inequality being measured is a purely relative concept and is independent of the distribution size. In contrast, doubling all incomes will double distribution size as measured by any income standard, thereby reflecting its respective property of linear homogeneity. • The final property is the weak transfer principle, which in this context requires income transfer from one person to another who is richer (or equally rich) to raise inequality or leave it unchanged. In other words, a regressive transfer cannot decrease inequality. This is an intuitive property for inequality measures. It is often presented in a stronger form, known as the transfer principle, which requires a regressive transfer to (strictly) increase inequality. The Gini coefficient and the Kuznets ratio satisfy all four basic properties for inequality measures. The 90/10 ratio satisfies the first three but violates the weak transfer principle: a regressive transfer between people at the 5th percentile and the 10th percentile can raise the 10th percentile income, thus lowering inequality as measured by the 90/10 ratio. Although this result does not rule out the use of the intuitive 90/10 ratio as an inequality measure, it does suggest that conclusions obtained with this measure should be scrutinized. The four basic properties define the general requirements for inequality measures. Additional properties help to discern between acceptable measures. For example, decomposability and subgroup consistency (discussed in a later section) are helpful in certain applications. Transfer sensitivity ensures that an inequality measure is more sensitive to changes in the income distribution at the lower end of the distribution. A second way of understanding inequality measures relies on an intuitive link between inequality measures and pairs of income standards. The basic structure is perhaps easiest to see in the extreme case where there are only two people and, hence, only two incomes. Letting a denote the smaller
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