Redistribution, Horizontal Inequity, and Reranking

Abstract

The decomposition of the Gini-based index of redistributive effect of an income tax into vertical, horizontal, and reranking contributions according to the model of Aronson, Johnson, and Lambert (AJL) is revisited. When close equals groups are used, rather than the exact equals groups on which the model is predicated, problems arise. A new measurement system is proposed, in which three distinct forms of reranking are disentangled and the vertical and horizontal contributions are redefined. Other approaches to measuring equity in tax systems are set in context. Findings are briefly applied to Croatian data, and recommendations for users of the AJL methodology are given.

On the Aronson-Johnson-Lambert Decomposition of the Redistributive Effect

“…This implies 0 = However, as observed before, this decomposition can be correctly applied provided that each group is composed by observations with the same pre-tax income and taxation does not modify either the ranking among group averages or the within group rankings (van de Ven, Creedy and Lambert, 2001;Urban and Lambert, 2005;Vernizzi, 2006). In the real word taxation W y G is generally different from zero, as only groups with close pre-tax incomes can be considered.…”

“…As Urban and Lambert (2005) moreover it is likely that the former can vanish only if the latter increases, thanks to an enlargement of the bandwidth.…”

“…We focus on the idea that the optimal bandwidth should be individuated by looking not only to the highest vertical contribution to the redistributive effect, but also to the horizontal inequity due to the reranking of the mean post-tax income among groups. In doing so we propose a decomposition of the Atkinson-Plotnick-Kakwani index in three terms, following the decompositions applied in Lambert and Urban (2005). Using this decomposition, the optimal bandwidth can be individuated without leading to misleading results: a bandwidth with which the vertical effect is the highest and there is no reranking of the mean post-tax income among groups can be considered the best one to be adopted.…”

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AbstractRecently 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) decompose the Atkinson-Plotnick-Kakwani index into three terms.

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Distribution of Income and Taxes in Slovenia and Croatia

“…In these circumstances the methodology originally developed falls down in terms of decomposing the redistributive effect. Urban and Lambert (2005) propose a new measurement system in which three distinct forms of reranking are disentangled and the vertical and horizontal contributions are redefined. In this paper we apply this new methodology to obtain measures of vertical, horizontal and reranking effects.…”