A Unified Approach to Measuring Poverty and Inequality
One way of examining the robustness of poverty comparisons is by calculating the vector of poverty levels of different measures for a fixed poverty line. For instance, the headcount ratio, the poverty gap measure, the squared gap measure, the Watts index, and the SST index can be depicted in a five-dimensional vector. If there are two distributions x and x', then the five-dimensional vector of x for poverty line z is (PH(x; z), PG(x; z), PSG(x ;z), PW(x ;z), PSST(x ;z)), and the five-dimensional vector of x' for poverty line z is (PH(x'; z), PG(x'; z), PSG(x'; z), PW(x'; z), PSST(x'; z)). Vector dominance between these two vectors would then be interpreted as a variable measure poverty ordering that ranks distributions when all five measures unanimously agree. If each element in the vector x is greater than each corresponding element in the vector x', then distribution x has unanimously more poverty than distribution x' for poverty line z.
Sensitivity Analysis with Respect to the Poverty Line The dominance analysis discussed earlier helps us understand whether one distribution has more or less poverty than another distribution. It is not concerned about the level of poverty, which is often of particular policy interest. The number of poor people in a country or the fact that many poor people have been moved out of poverty over a particular time period are always matters of great concern. These data, of course, depend on the particular poverty line chosen. As discussed in the introductory chapter, there are three different types of poverty lines: • An absolute poverty line may be adjusted with the rate of inflation over time, but it is not adjusted with income growth over time. • A relative poverty line is not fixed over time, and it changes with income growth. For example, if a poverty line is set at 50 percent of the median income, then the poverty line changes as the median income changes over time. Or the poverty line may be set at 50 percent of mean income. In this case, the growth rate of the poverty line over time is the same as the growth rate of per capita income over time. • A hybrid poverty line is created by taking a weighted average of an absolute poverty line and a relative poverty line.
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