INEQUALITY DECOMPOSITION: THREE BAD MEASURES

Abstract

One of the most interesting practical applications of inequality measures is the decomposition by population subgroups of overall income inequality. This analysis typically focusses on the ‘contributions to inequality ’ from different subgroups of the population and- explicitly or implicitly- uses a structure of the form 4,,,,,,, = F ( 1, Y 1,... *) where the suffices 1,2,... refer to subgroup inequalities and F also depends on group means and population shares; the cardinalization of I is often chosen such that F is a linear function although this is by no means essential. A number of authors ’ have discussed formally the. class of inequality measures which are suitable for this type of exercise. But perhaps what is less commonly recognized is how awful some widely used inequality measures are in this regard. I shall discuss the following three, each of which is still employed in empirical applications involving decomposition or disaggregation:2 The logarithmic variance

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