ABSTRACT
More than twenty-five years ago Shorrocks (1980), analyzing the issue of decomposing inequality by population subgroups when the latter are defined by the age group to which the individuals belong, stressed the fact that ‘one interpretation suggests a comparison of total inequality with the amount which would arise if inequality was zero within each age group, but the difference in mean income between age groups remained the same. . . .’. The second ‘interpretation suggests a comparison of total inequality with the inequality value which would result if the mean incomes of the age groups were made identical, but inequality within each age group remained unchanged.’ Deutsch and Silber (1999) compared these two approaches. Since the inequality index they used was the Gini index and given that the components of the latter (between-and within-groups inequality and overlapping component) can have more than one definition, depending on how the individual incomes are ranked, Deutsch and Silber (1999) came up with a whole series of between-and within-groups components as well as overlapping terms, although they observed a relatively high correlation between the various definitions, at least on the basis of the data they used.
