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Modelling Lorenz Curves: Robust and Semi-parametric Issues

In: Modeling Income Distributions and Lorenz Curves

Author

Listed:
  • Frank A. Cowell

    (London School of Economics and Political Science)

  • Maria-Pia Victoria-Feser

    (University of Geneva)

Abstract

Modelling Lorenz curves (LC) for stochastic dominance comparisons is central to the analysis of income distributions. It is conventional to use non-parametric statistics based on empirical income cumulants which are used in the construction of LC and other related second-order dominance criteria. However, although attractive because of its simplicity and its apparent flexibility, this approach suffers from important drawbacks. While no assumptions need to be made regarding the data-generating process (income distribution model), the empirical LC can be very sensitive to data particularities, especially in the upper tail of the distribution. This robustness problem can lead in practice to “wrong” interpretation of dominance orders. A possible remedy for this problem is the use of parametric or semi-parametric models for the data-generating process and robust estimators to obtain parameter estimates. In this paper, we focus on the robust estimation of semi-parametric LC and investigate issues such as sensitivity of LC estimators to data contamination (Cowell and Victoria-Feser, 2002), trimmed LC (Cowell and Victoria-Feser, 2006), and inference for trimmed LC (Cowell and Victoria-Feser, 2003), robust semi-parametric estimation for LC (Cowell and Victoria-Feser, 2007), selection of optimal thresholds for (robust) semi-parametric modelling (Dupuis and Victoria-Feser, 2006), and use both simulations and real data to illustrate these points.

Suggested Citation

  • Frank A. Cowell & Maria-Pia Victoria-Feser, 2008. "Modelling Lorenz Curves: Robust and Semi-parametric Issues," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 13, pages 241-253, Springer.
    • Handle: RePEc:spr:esichp:978-0-387-72796-7_13
    DOI: 10.1007/978-0-387-72796-7_13
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    References listed on IDEAS

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    1. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
    2. Frank A. Cowell & Maria-Pia Victoria-Feser, 2002. "Welfare Rankings in the Presence of Contaminated Data," Econometrica, Econometric Society, vol. 70(3), pages 1221-1233, May.
    3. Kopczuk, Wojciech & Saez, Emmanuel, 2004. "Top Wealth Shares in the United States, 1916-2000: Evidence From Estate Tax Returns," National Tax Journal, National Tax Association;National Tax Journal, vol. 57(2), pages 445-487, June.
    4. Emmanuel Saez & Michael R. Veall, 2005. "The Evolution of High Incomes in Northern America: Lessons from Canadian Evidence," American Economic Review, American Economic Association, vol. 95(3), pages 831-849, June.
    5. Cowell, Frank A. & Victoria-Feser, Maria-Pia, 2006. "Distributional Dominance With Trimmed Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 291-300, July.
    6. Chiaki Moriguchi & Emmanuel Saez, 2006. "The Evolution of Income Concentration in Japan, 1886-2002: Evidence from Income Tax Statistics," NBER Working Papers 12558, National Bureau of Economic Research, Inc.
    7. A. B. Atkinson, 2004. "Income Tax and Top Incomes over the Twentieth Century," Hacienda Pública Española / Review of Public Economics, IEF, vol. 168(1), pages 123-141, march.
    8. Frank Cowell & Maria-Pia Victoria-Feser, 2003. "Distribution-Free Inference for Welfare Indices under Complete and Incomplete Information," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 1(3), pages 191-219, December.
    9. Frank Cowell & Maria-Pia Victoria-Feser, 2007. "Robust stochastic dominance: A semi-parametric approach," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(1), pages 21-37, April.
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    Cited by:

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    More about this item

    Keywords

    Income Distribution; Maximum Likelihood Estimator; Stochastic Dominance; Lorenz Curve; Robust Estimator;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics

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