Close equals and calculation of the vertical, horizontal and reranking effects of taxation

This paper examines the Gini-based method of decomposing the redistributive effect of taxation into vertical, horizontal, and reranking components. The consequences of different bandwidth choices, used to identify close-equals groups to estimate the horizontal effect, are discussed. Two opposing forces are identified which militate against choosing a very small or large bandwidth. It is suggested that the best procedure is to use the bandwidth that maximises the estimated vertical component, compute the reranking component exactly as a sample statistic and obtain the horizontal effect by subtraction. The technique is used to analyse the progressivity of tax and transfer payments in Australia.