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Inference on Income Inequality and Tax Progressivity Indices: U-Statistics and Bootstrap Methods

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  • Raquel Andres

    (Centre for the Study of Wealth and Inequality, Columbia University and Centre of Research on Welfare Economics (CREB))

  • Samuel Calonge

    ()
    (Department of Econometrics, Statistics and Spanish Economy, University of Barcelona and Centre of Research on Welfare Economics (CREB))

Abstract

This paper discusses asymptotic and bootstrap inference methods for a set of inequality and progressivity indices. The application of non-degenerate U-statistics theory is described, particularly through the derivation of the Suits-progressivity index distribution. We have also provided formulae for the “plug-in” estimator of the index variances, which are less onerous than the U-statistic version (this is especially relevant for those indices whose asymptotic variances contain kernels of degree 3). As far as inference issues are concerned, there are arguments in favour of applying bootstrap methods. By using an accurate database on income and taxes of the Spanish households (statistical matching EPF90-IRPF90), our results show that bootstrap methods perform better (considering their sample precision), particularly those methods yielding asymmetric CI. We also show that the bootstrap method is a useful technique for Lorenz dominance analysis. An illustration of such application has been made for the Spanish tax and welfare system. We distinguish clear dominance of cashbenefits on income redistribution. Public health and state school education also have significant redistributive effects.

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File URL: http://www.ecineq.org/milano/WP/ECINEQ2005-09.pdf
File Function: First version, 2005
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Bibliographic Info

Paper provided by ECINEQ, Society for the Study of Economic Inequality in its series Working Papers with number 09.

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Length: 44 pages
Date of creation: Nov 2005
Date of revision:
Handle: RePEc:inq:inqwps:ecineq2005-09

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Keywords: Income Inequality; Tax Progressivity; Statistical Inference; U-statistics; Bootstrap method.;

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  1. Beach, Charles M & Davidson, Russell, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 50(4), pages 723-35, October.
  2. Bishop, John A & Formby, John P & Zheng, Buhong, 1998. "Inference Tests for Gini-Based Tax Progressivity Indexes," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 16(3), pages 322-30, July.
  3. Davidson, R. & Duclos, J.Y., 1995. "Statistical Inference for the Measurement of the Incidence of Taxes and Transfers," Papers, Laval - Recherche en Politique Economique 9521, Laval - Recherche en Politique Economique.
  4. Mills, Jeffrey A & Zandvakili, Sourushe, 1997. "Statistical Inference via Bootstrapping for Measures of Inequality," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 12(2), pages 133-50, March-Apr.
  5. Thistle, Paul D, 1990. "Large Sample Properties of Two Inequality Indices," Econometrica, Econometric Society, Econometric Society, vol. 58(3), pages 725-28, May.
  6. Cowell, Frank A., 1989. "Sampling variance and decomposable inequality measures," Journal of Econometrics, Elsevier, Elsevier, vol. 42(1), pages 27-41, September.
  7. Quirmbach, Herman C. & Swenson, Charles W. & Vines, Cynthia C., 1996. "An experimental examination of general equilibrium tax incidence," Journal of Public Economics, Elsevier, Elsevier, vol. 61(3), pages 337-358, September.
  8. Calonge Ramírez Samuel & Manresa Sánchez Antonio, 2001. "Incidencia fiscal y del gasto público social sobre la distribución de la renta en España y sus CC. AA," Books, Fundacion BBVA / BBVA Foundation, Fundacion BBVA / BBVA Foundation, edition 1, number 201117.
  9. Biewen, Martin, 2002. "Bootstrap inference for inequality, mobility and poverty measurement," Journal of Econometrics, Elsevier, Elsevier, vol. 108(2), pages 317-342, June.
  10. Quirmbach, Herman & Swenson, Charles & Vines, Cynthia, 1996. "An Experimental Examination of General Equilibrium Tax Incidence," Staff General Research Papers, Iowa State University, Department of Economics 5204, Iowa State University, Department of Economics.
  11. Duclos, Jean-Yves, 1997. "The asymptotic distribution of linear indices of inequality, progressivity and redistribution," Economics Letters, Elsevier, Elsevier, vol. 54(1), pages 51-57, January.
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Cited by:
  1. William C. Horrace & Joseph T. Marchand & Timothy M. Smeeding, 2005. "Ranking Inequality: Applications of Multivariate Subset Selection," Center for Policy Research Working Papers, Center for Policy Research, Maxwell School, Syracuse University 70, Center for Policy Research, Maxwell School, Syracuse University.

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