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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: (i) the effective schedule (we call this the ‘vertical effect'), (ii) the unequal treatment of equals arising from departures from this effective schedule (the ‘horizontal effect') and (iii) the reranking of unequals as a result of such departures (the ‘reranking effect'). The methodology is applied to UK microdata. Throughout the period 1978-1991, reranking understates the (negative) contribution to redistributive effect of unequal tax treatment by about one third, and is far outweighed by the vertical effect.
Aronson et al. (Tue,) studied this question.