An extended Gini approach to inequality measurement

Abstract

It is well-known that, when the Lorenz curves do not cross, the ranking of distributions provided by the Gini index is identical to the one implied by the Lorenz criterion. This does not preclude inequality as measured by the Gini index to increase while the Lorenz curves cross. A suitable modification of the Gini coefficient allows the Lorenz quasi-ordering to coincide with the ranking generated by the application of unanimity over the class of extended Gini indices. Recently the Lorenz quasi-ordering and the underlying principle of transfers have come under attack, while new criteria – the differentials, deprivation and satisfaction quasi-orderings – have been proposed for providing unambiguous rankings of distributions. We suggest to weaken the principle of transfers by imposing additional restrictions on the progressive transfers, which take into account the positions on the income scale of the donors and beneficiaries. We identify the subclasses of extended Gini indices that satisfy these weaker versions of the principle of transfers and we show that the application of unanimity among these classes generate rankings of distributions that coincide with those implied by the differentials, deprivation and satisfaction quasi-orderings.