Proposing indicators to measure achievement and shortfall inequality consistently

In several economic fields, such as those related to health or education, the individuals’ characteristics are measured by bounded variables. Accordingly, these characteristics may be indistinctly represented by achievements or shortfalls. A difficulty arises when inequality needs to be assessed. One may focus either on achievements or on shortfalls, but the respective inequality rankings may lead to contradictory results. In this note, we propose a procedure to define indicators to measure consistently the achievement and shortfall inequality. Specifically, we derive measures which are invariant under ratio-scale or translation transformations, and a decomposable measure also is proposed.