On the alleged sensitivity of the Gini index to differences in the center of the income distribution

One commonly cited flaw of the Gini index is its alleged excessive sensitivity to changes in the middle of the income distribution. However, in most scenarios, a transfer from a rich household to a low-income household has a greater impact than a transfer to a middle-income household. In this context, the changes are directly associated with the concept of redistributing income among individuals through transfers. While changes primarily denotes income transfers, it can also refer to adjacent income differences in a sorted distribution. We show that the Gini index is invariant to any reasonable weighting of adjacent income differences, so such differences cannot substantiate claims of special sensitivity to the middle of the distribution. In practice, relying solely on this index to assess distributional dynamics or policy effects leads to information loss. For more information on the distribution, and depending on their project, researchers should therefore complement it with position sensitive measures – such as the Theil index, or the Atkinson index – to capture structural reallocations of national income with accuracy. Yet, because of its well-established merits, the Gini index continues to function as the leading instrument through which governmental and international agencies evaluate overall inequality.