Inequality measurement for bounded variables

Numerous non-pecuniary variables of interest for inequality assessment are bounded and often represented in terms of attainments or shortfalls. Inequality measurement for bounded variables suffers from two key challenges: the consistency problem and the boundary problem. The former occurs when inequality rankings reverse while switching between attainment and shortfall representations. The latter stems from the existence of a predictable functional relationship between mean attainment and maximum feasible inequality hindering inequality comparisons across distributions with different means. Unlike consistency, the boundary problem has not received significant attention in the literature. We propose two novel classes of normalized inequality measures that are immune to both problems. We illustrate the empirical relevance ofour approach with cross-country comparisons of inequality in well-established indicators of education and health. A starkly different picture emerges when traditional inequality indices give way to our normalized inequality indices.