Proposing indicators for a consistent measurement of the inequality among the poor and the inequality of bounded distributions

Abstract

In chapter I, we identify a decomposition for the FGT family in the three terms of poverty. The third component could refer to income or to gap inequality indistinctly. However, the choice is not innocuous and different choices may lead to contradictory results. In chapter II we will focus on this problem with the purpose of reinterpreting the inequality term using indicators that measure income inequality and gap inequality equally. This difficulty also arises with bounded distributions. Accordingly, one may focus either on achievements or on shortfalls. Chapter III provides inequality indicators which measures equally the achievement and the shortfall inequality. Nevertheless, the results depend on the upper bound. Hence, chapter III is also devoted to obtaining inequality indicators that lead to the same orderings regardless of the bounds.