Statistical inference and the Sen index of poverty

Statistical inference procedures are developed for Sen's distribution-sensitive index of poverty and each of its components-the headcount ratio, income gap ratio, and the Gini index of the poor. Using results from U-statistics we show that estimates of the index and its components all have a jointly asymptotically normal distribution and the variance-covariance structure can be consistently estimated. The inference tests are illustrated by applying them to the same microeconomic data set used in estimating official U.S. poverty statistics. The application reveals that the Sen index increased significantly in each of the three periods considered.