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


  • 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))


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.

Suggested Citation

  • Raquel Andres & Samuel Calonge, 2005. "Inference on Income Inequality and Tax Progressivity Indices: U-Statistics and Bootstrap Methods," Working Papers 09, ECINEQ, Society for the Study of Economic Inequality.
  • Handle: RePEc:inq:inqwps:ecineq2005-09

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    References listed on IDEAS

    1. Russell Davidson & Jean-Yves Duclos, 1997. "Statistical Inference for the Measurement of the Incidence of Taxes and Transfers," Econometrica, Econometric Society, vol. 65(6), pages 1453-1466, November.
    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, vol. 16(3), pages 322-330, July.
    3. Mills, Jeffrey A & Zandvakili, Sourushe, 1997. "Statistical Inference via Bootstrapping for Measures of Inequality," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(2), pages 133-150, March-Apr.
    4. Duclos, Jean-Yves, 1997. "The asymptotic distribution of linear indices of inequality, progressivity and redistribution," Economics Letters, Elsevier, vol. 54(1), pages 51-57, January.
    5. Thistle, Paul D, 1990. "Large Sample Properties of Two Inequality Indices," Econometrica, Econometric Society, vol. 58(3), pages 725-728, May.
    6. Quirmbach, Herman C. & Swenson, Charles W. & Vines, Cynthia C., 1996. "An experimental examination of general equilibrium tax incidence," Journal of Public Economics, Elsevier, vol. 61(3), pages 337-358, September.
    7. 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, edition 1, number 201117, December.
    8. Cowell, Frank A., 1989. "Sampling variance and decomposable inequality measures," Journal of Econometrics, Elsevier, vol. 42(1), pages 27-41, September.
    9. Quirmbach, Herman & Swenson, Charles & Vines, Cynthia, 1996. "An Experimental Examination of General Equilibrium Tax Incidence," Staff General Research Papers Archive 5204, Iowa State University, Department of Economics.
    10. Biewen, Martin, 2002. "Bootstrap inference for inequality, mobility and poverty measurement," Journal of Econometrics, Elsevier, vol. 108(2), pages 317-342, June.
    11. Charles M. Beach & Russell Davidson, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," Review of Economic Studies, Oxford University Press, vol. 50(4), pages 723-735.
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    Cited by:

    1. William Horrace & Joseph Marchand & Timothy Smeeding, 2008. "Ranking inequality: Applications of multivariate subset selection," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 6(1), pages 5-32, March.
    2. Abu-Zaineh, Mohammad & Mataria, Awad & Luchini, Stéphane & Moatti, Jean-Paul, 2008. "Equity in health care financing in Palestine: The value-added of the disaggregate approach," Social Science & Medicine, Elsevier, vol. 66(11), pages 2308-2320, June.
    3. Abu-Zaineh, Mohammad & Mataria, Awad & Luchini, Stéphane & Moatti, Jean-Paul, 2009. "Equity in health care finance in Palestine: The triple effects revealed," Journal of Health Economics, Elsevier, vol. 28(6), pages 1071-1080, December.

    More about this item


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

    JEL classification:

    • H00 - Public Economics - - General - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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