Playing with the Hadamard product in decomposing Gini, concentration, redistribution and re-ranking indexes
Gini and concentration indexes are well known useful tools in analysing redistribution and re-ranking effects of taxes with respect to a population of income earners. Aronson, Johnson and Lambert (1994), Urban and Lambert (2008) decompose Gini and re-ranking indices to analyse potential redistribution effects and the unfairness of a tax systems. Urban and Lambert (2008) consider contiguous income groups which are created by dividing the pre-tax income parade according to the same bandwidth. However, earners may be very often split into groups characterized by social and demographic aspects or by other characteristics: in these circumstances groups can easily overlap. In this paper we consider a more general situation that takes into account overlapping among groups; we obtain matrix compact forms for Gini and concentration indexes, and consequently, for redistribution and re-ranking indexes. In deriving formulae the so called matrix Hadamard product is extensively used. Matrix algebra allows to write indexes aligning incomes in a non decreasing order either with respect to post-tax income or to pre-tax incomes. Moreover, matrix compact formulae allow an original discussion for the signs of the within group, across group, between and transvariation components into which the Atkinson-Plotnick-Kakwany (Plotnick, 1981) re-ranking index can split.
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- Maria Giovanna MONTI, 2007. "A note on the Dagum decomposition of the Gini inequality index," Departmental Working Papers 2007-16, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
- Achille Vernizzi, 2007.
"Una precisazione sulla scomposizione dell'indice di redistribuzione RE di Aronson-Johnson-Lambert e una proposta di estensione dell'indice di Plotnick,"
FrancoAngeli Editore, vol. 2007(1-2), pages 145-154.
- Achille VERNIZZI, 2006. "Una precisazione sulla scomposizione dell’indice di redistribuzione RE di Aronson-Johnson-Lambert e una proposta di estensione dell’indice di Plotnick," Departmental Working Papers 2006-28, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
- Dagum, Camilo, 1997. "A New Approach to the Decomposition of the Gini Income Inequality Ratio," Empirical Economics, Springer, vol. 22(4), pages 515-531.
- Aronson, J Richard & Johnson, Paul & Lambert, Peter J, 1994. "Redistributive Effects and Unequal Income Tax Treatment," Economic Journal, Royal Economic Society, vol. 104(423), pages 262-270, March.
- Lambert, Peter J & Aronson, J Richard, 1993. "Inequality Decomposition Analysis and the Gini Coefficient Revisited," Economic Journal, Royal Economic Society, vol. 103(420), pages 1221-1227, September.
- Ivica Urban & Peter J. Lambert, 2008. "Redistribution, Horizontal Inequity, and Reranking: How to Measure Them Properly," Public Finance Review, , vol. 36(5), pages 563-587, September.
- Ivica Urban & Peter J. Lambert, 2005. "Redistribution, horizontal inequity and reranking: how to measure them properly," University of Oregon Economics Department Working Papers 2005-12, University of Oregon Economics Department.
- Plotnick, Robert, 1981. "A Measure of Horizontal Inequity," The Review of Economics and Statistics, MIT Press, vol. 63(2), pages 283-288, May.
- Aronson, J. Richard & Lambert, Peter J., 1994. "Decomposing the Gini Coefficient to Reveal the Vertical, Horizontal, and Reranking Effects of Income Taxation," National Tax Journal, National Tax Association, vol. 47(2), pages 273-294, June.
- Maria Giovanna MONTI & Alessandro SANTORO, 2009. "The Gini decomposition: an alternative formulation with an application to tax reform," Departmental Working Papers 2009-30, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
- Aronson, J. Richard & Lambert, Peter J., 1994. "Decomposing the Gini Coefficient to Reveal the Vertical, Horizontal, and Reranking Effects of Income Taxation," National Tax Journal, National Tax Association, vol. 47(2), pages 273-94, June. Full references (including those not matched with items on IDEAS)
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