A Unified Approach to Measuring Poverty and Inequality
subgroup consistency have proved to be very important for regional evaluations of poverty and for targeting. They are discussed below. Income Standards Another way of understanding poverty measures makes use of our previous insights from income standards. Like inequality measures, most poverty measures are based on a comparison of two income levels. In this case, however, one of them is the fixed poverty line z, whereas the other is an income standard applied to a modified distribution that focuses on the poor. Two forms of modification are employed, leading to two general forms of poverty measures. The first makes use of a censoring process that ignores the portion of any income lying above the poverty line z. The censored distribution x* for a given distribution x replaces all incomes above z with z itself. Applying an income standard to the censored distribution yields a poor income standard, which reflects the size of the censored distribution and is clearly bounded above by z (the maximum value achieved when no one is poor). Many poverty measures take the form P = (b − a)/b, or some monotonic transformation, where a is some poor income standard and b is the poverty line z. P measures poverty as the shortfall of the poor income standard from the poverty line as a percentage of the poverty line. For example, if a were the mean censored income m(x*), then the resulting poverty measure would be (z − m(x*))/z, which is another way of expressing the poverty gap. Below we will see other poverty measures that share this general structure but employ different income standards. The second form of modification changes the focus from incomes to income gaps. The gap distribution g* is found by replacing the income x*i in x* with the income gap z − x*i. The gap will be 0 for anyone who is nonpoor, and it increases in size as the income of a poor person falls further below z. Applying an income standard to the gap distribution yields a gap standard, which measures the overall departure of incomes in x* from z. Many poverty measures take the form P = a/b, or some monotonic transformation, where a is some gap standard and b is the poverty line z. P measures poverty using a gap standard taken as a percentage of the poverty line. For example, if a were the mean gap m(g*), then the resulting poverty measure would be m(g*)/z, which is another way of defining the poverty gap. Below we will
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