Inference for deprivation profiles in a binary setting

The paper addresses the issue of comparing deprivation distributions when the severity of deprivation is measured by a sum of (weighted) binary variables. To accomplish this task, it provides a graphical tool, the Three I’s of Deprivation (TID) curve, which summarises the incidence, intensity and inequality aspects of deprivation in a society and is the natural counterpart to the TIP curve widely used in income poverty analysis. Uncertainty around the estimated deprivation curves is assessed by simultaneous confidence bands. A dominance hypothesis test is presented to facilitate the comparison and ordering of TID curves across groups and over time. A rank-dependent multi-deprivation index consistent with the TID ordering is calculated and confidence intervals are developed. As a substantive illustration, the evolution of material and social deprivation across European countries over the period of the pandemic outbreak is analysed.