The decomposition of the redistributive effect and the issue of close equals identification

Urban and Lambert (2005, 2008) present an exhaustive summary and an in-depth discussion of the literature contributions about the decomposition of the redistributive effect of a tax (RE). The authors discuss the indexes available in the literature for the potential vertical effect (V), the loss due to horizontal fairness violations (H) and that due to re-rankings (R); they also introduce new indexes specifically conceived to take into account problems arising when groups of exact equals are substituted by groups of close equals. Close equals groups are generally obtained by splitting the pre-tax income distribution into contiguous intervals having the same bandwidth, so that the problem of the bandwidth choice arises. van de Van, Creedy and Lambert (2001) suggest choosing the bandwidth that maximizes the potential vertical effect V. Even looking for V maximization, we discuss a new criterion that yields a compromise between the contrasting needs of minimizing the effects of pre-tax within groups inequalities and the minimization of group average re-rankings. The criterion is then applied to evaluate the components of two decompositions: the former is the one suggested by Urban and Lambert (2005, 2008) as preferable, the latter is suggested by us on the basis of Urban and Lambert’s paving discussion. According to our simulation results, when comparing different income tax systems for a same population as well as adopting the “optimal” bandwidth, the new criterion seems to introduce lower approximation errors than the maximization of V