Personal gini coefficients

The Gini coefficient is based on the sum of pairwise income differences, which can be decomposed into separate sums for individuals. Differences vis-à-vis poorer people represent an individual's advantage, while those with respect to richer people constitute deprivation. Weighting deprivation and advantage differently produces a family of personal Gini coefficients whose population averages each equal the overall Gini coefficient. Properties of the personal indexes explain why the Gini coefficient is most sensitive to changes in the middle of typical income distributions. Behavior of the personal indexes also throws light on the inequality impacts of secular changes in income distribution. In a simple Kuznetstype process, the Gini coefficient first rises and then falls but, throughout, a personal Gini coefficient will be rising for people in the traditional sector, while it is falling for those in the modern sector. In a leading case, the population shifts associated with polarization in labor markets in advanced economies also reduce personal inequality at the top and increase it at the bottom. The shift of population toward the two extremes unambiguously raises personal inequality for those in the middle. The wage changes accompanying polarization can, however, reverse these results, particularly at the top, as illustrated by calculations for U.S. polarization between 1980 and 2005.