This paper suggest that the decomposition of the redistributive effect of taxation into vertical, horizontal, and re-ranking components is best achieved in terms of the welfare premium from progression, using hte abbreviated social welfare function defined in terms of the Gini measure of inequality. This contrasts with the decomposition given in Aronson et al. (1994) in which the estimate of the horizontal effect is shown here to be contaminated. Estimation of the horizontal effect for small sample populations is achieved by using near-equals to proxy exact-equals, where groups of near-equals are defined using a band-width of pre-tax incomes, following Aronson et al. (1994). It is shown that the horizontal effect is best estimated by selecting a band-width to maximise the estimated vertical effect. The estimate of the horizontal effect is then obtained by subtraction, having computed the re-ranking component exactly as a sample statistic.
