Maximum Entropy Estimation of Income Distributions from Bonferroni Indices

Abstract

This paper presents an information efficient technique to determine the functional forms of income distributions subject to the given side conditions such as the Bonferroni index (BI) and the Gini coefficient (GINI). The original GINI is insensitive to the income share changes of the lower income groups and greater weight is attached to those group shares when the BI was defined. To compare the performance of the BI with those of the GINI and the Theil entropy measure (THEIL) the income deciles of 113 countries were introduced using The UNU/WIDER World Income Inequality Database WIID (2005). The information efficient technique provided guidelines on which income inequality measure performs better for certain countries. The BI performed better for the Czech Republic (GINI=0.26) and the U.S.A. (GINI=0.40), but poorly for Brazil (GINI=0.63). The GINI coefficient performed better for Brazil, but not for the Czech Republic and the U.S.A. The BI is a better index in describing the relative income changes of very evenly distributed country like the Czech Republic or for moderately distributed country like the U.S.A. The GINI is good for an extremely uneven society like Brazil. Based on regression R squared values of 113 countries, the THEIL showed ability in describing the income share changes of upper income groups, the GINI was productive in describing the middle income group shares, and the BI was capable in describing the lower income group shares.