Inference for deprivation profiles in a binary setting

The paper addresses the issue of comparing deprivation distributions, when poverty is measured by a sum of binary variables. To accomplish this task, it provides a graphical device, the Three I's of Deprivation (TID) curve, that summarizes incidence, intensity and inequality aspects of deprivation in a society, and it is the natural counterpart of the TIP curve widely used in income poverty analysis. Uncertainty around the estimated deprivation curves is evaluated through simultaneous confidence bands. An hypothesis test of dominance is presented to facilitate the comparison and the ordering of deprivation curves across groups and over time. An extension of the Sen-Shorrocks poverty index that summarizes the three I's of deprivation is characterized and confidence intervals are developed. As a substantive illustration the evolution of material and social deprivation across European countries over the period of the outbreak of the pandemic is analysed.