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Horizontal inequity comparisons

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  • Valentino Dardanoni
  • Peter Lambert

Abstract

When an income tax or tax-benefit system is applied to the distribution of personal incomes, three effects on the distribution of peoples' living standards can be discerned. First, people with equal pre-tax living standard may not receive the same or comparable tax treatment, and in consequence may end up with different post-tax living standards; this would be in violation of classical horizontal equity (HE). Second, is the effect of the tax system as between people with different pre-tax living standards; this is the concern for vertical equity. Finally, the tax system may disturb the rank ordering of people by their living standards from poorest to richest; if this happens, it is in violation of the no-reranking command, often seen in recent literature as an alternative equity criterion to that of classical HE. In this paper, we argue for a new concept of 'purity' in the measurement of horizontal inequity (HI), that renders it independent of the metric for living standards and also of tax system's vertical performance. Specifically, we argue that HI is a property of the taxation process which can be captured as lack of perfect association between pre- and post-tax living standards, and we expound the idea that the HI in different tax systems be compared by transplanting the HI from one tax system into the other, as a mapping between its pre- and post-tax living standard distributions, and then comparing the extent of association. Two appropriate axioms act, in combination, to ensure that HI can indeed be 'transplanted' from one scenario to another. We go on to propose a partial HE ordering, reflecting the desire of a social decision maker that pre- and post-tax living standards should be positively associated, and the more so the better. It quickly emerges that, although Axioms 1 and 2 were introduced for comparability purposes, and are in part classically inspired, in concert they force us into a concern solely for positions (ranks). An implementable procedure based on the 'copula' is derived, which averts the need for transplantation and can be applied to any pair of tax or tax and benefit systems. Statistical inference procedures are discussed, and illustrative empirical exercises are undertaken for the UK, Canadian and Israeli tax and benefit systems. The methodology can be used to compare HI in taxes with that in benefits, and for international, inter-regional and intertemporal comparisons.

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Bibliographic Info

Paper provided by Institute for Fiscal Studies in its series IFS Working Papers with number W98/07.

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Date of creation: Oct 1998
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Handle: RePEc:ifs:ifsewp:98/07

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Cited by:
  1. Casey Quinn, 2005. "Generalisable regression methods for costeffectiveness using copulas," Health, Econometrics and Data Group (HEDG) Working Papers 05/13, HEDG, c/o Department of Economics, University of York.
  2. Dardanoni, Valentino & Lambert, Peter J., 2002. "Progressivity comparisons," Journal of Public Economics, Elsevier, vol. 86(1), pages 99-122, October.
  3. Harvey, James, 2005. "A note on the 'natural rate of subjective inequality' hypothesis and the approximate relationship between the Gini coefficient and the Atkinson index," Journal of Public Economics, Elsevier, vol. 89(5-6), pages 1021-1025, June.
  4. Peter J. Lambert & Thor O. Thoresen, 2011. "The inequality effects of a dual income tax system," Discussion Papers 663, Research Department of Statistics Norway.
  5. Erlend Bø & Peter Lambert & Thor Thoresen, 2012. "Horizontal inequity under a dual income tax system: principles and measurement," International Tax and Public Finance, Springer, vol. 19(5), pages 625-640, October.
  6. Peter Lambert & Thor Thoresen, 2009. "Base independence in the analysis of tax policy effects: with an application to Norway 1992–2004," International Tax and Public Finance, Springer, vol. 16(2), pages 219-252, April.
  7. Decancq K, 2009. "Copula-based Measurement of Dependence Between Dimensions of Well-being," Health, Econometrics and Data Group (HEDG) Working Papers 09/32, HEDG, c/o Department of Economics, University of York.
  8. Ivica Urban, 2013. "Implementation Issues in the Duclos–Jalbert–Araar Decomposition of Redistributive Effect," Public Finance Review, , vol. 41(1), pages 121-143, January.
  9. Diana, Tony, 2011. "Improving schedule reliability based on copulas: An application to five of the most congested US airports," Journal of Air Transport Management, Elsevier, vol. 17(5), pages 284-287.
  10. Duclos, Jean-Yves & Jalbert, Vincent & Araar, Abdelkrim, 2003. "Classical Horizontal Inequity and Reranking: an Integrating Approach," Cahiers de recherche 0306, CIRPEE.
  11. Ivica Urban, 2014. "Contributions of taxes and benefits to vertical and horizontal effects," Social Choice and Welfare, Springer, vol. 42(3), pages 619-645, March.
  12. James Harvey, . "A note on the 'Natural Rate of Subjective Inequality' hypothesis and the approximate relationship between the Gini coefficient and the Atkinson index," Discussion Papers 03/12, Department of Economics, University of York.
  13. Valentino Dardoni & Peter J. Lambert, 2000. "Progressivity comparisons," IFS Working Papers W00/18, Institute for Fiscal Studies.
  14. Sergio Rey, 2014. "Fast algorithms for a space-time concordance measure," Computational Statistics, Springer, vol. 29(3), pages 799-811, June.
  15. Ivica Urban, 2009. "Kakwani decomposition of redistributive effect: Origins, critics and upgrades," Working Papers 148, ECINEQ, Society for the Study of Economic Inequality.
  16. Murray D Smith, 2004. "Stochastic Frontier Models With Correlated Error Components," Econometric Society 2004 Australasian Meetings 121, Econometric Society.

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