Statistical Inferences for Poverty Measures with Relative Poverty Rates

Relative poverty lines such as one-half of median income have been widely used in poverty comparisons. The U.S. government has also been urged to adopt the notion of relative poverty lines. This paper contributes to the literature by developing statistical inferences for testing poverty measures with relative poverty lines. The poverty measures we consider are the decomposable class and the measure proposed by Sen. The poverty lines we specify are percentages of mean income and percentages of quantiles. We show that poverty indices can be consistently estimated and the sample estimates are asymptotically normally distributed. As a consequence, distribution-free statistical inferences can be established in a straightforward manner. We illustrate the inference procedures by comparing poverty across ten countries and over two time periods.