Redistribution, horizontal inequity and reranking: how to measure them properly

The decomposition of the redistributive effect of an income tax into vertical, horizontal and reranking contributions according to the model of Aronson, Johnson and Lambert (1994), henceforth AJL, is revisited. When close equals groups are used, rather than the exact equals groups upon 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 applied to Croatian data, and recommendations for users of the AJL methodology are given.