On factor decomposition of cross-country income inequality: some extensions and qualifications

In a recent paper in this journal Duro and Esteban [Econom. Lett. 60 (1998) 269] have proposed a factor decomposition of the Theil [Economics and Information Theory, Amsterdam, North-Holland, 1967] index of inequality over per capita incomes into the (unweighted) sum of the inequality indexes of the factors in order to measure the contribution of each individual factor to the overall inequality. The purpose of this little note is to extend and qualify the meaning of such a decomposition, to show that the decomposition also holds for another Theil [Economics and Information Theory, Amsterdam, North-Holland, 1967], index of inequality and that both decompositions offer qualitatively the same general results about the contribution of the factors to aggregate inequality when applied to a particular data set, the OECD countries, although quantitative results differ