On determining "Close equals groups" in decomposing redistributive and reranking effects.

Recently van De Van, Creedy and Lambert (2001) and Lambert and Urban (2005) have reconsidered the original Aronson, Johnson and Lambert (1994) decomposition of the redistributive effect in order to properly evaluate personal income tax reforms when sequential income groups do not concern exact equals. Lambert and Urban (2005) discuss a set of further possible decompositions of the redistributive effect together with a decomposition of the Atkinson-Plotnick-Kakwani index into three terms. If the issue is to chose the optimal income bandwidth which splits the pre-tax income parade into contiguous sets, we suggest combining the information given by the latter decomposition with those concerning the highest vertical contributions to the redistributive effect. We show that the horizontal inequity due to the reranking of the mean post-tax income among groups plays a crucial role in choosing the optimal bandwidth either within the van De Van, Creedy and Lambert (2001) methodology or in pursuing coherent measures for the potential redistributive effect.