Decomposing the post-tax Gini coefficient across groups of pre-tax equals reveals the separate contributions to the redistributive effect of an income tax of (1) the effective schedule (the vertical effect), (2) the unequal treatment of equals arising from departures from this effective schedule...

The Gini coefficient has long been thought unsuitable for inequality decomposition analysis because of a troublesome and little-understood residual term that occurs when subgroup income ranges overlap after the between-groups and within-groups contributions to inequality have been separated out....