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Is the Pareto–Lévy law a good representation of income distributions?

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  • John Dagsvik

    ()

  • Zhiyang Jia

    ()

  • Bjørn Vatne

    ()

  • Weizhen Zhu

    ()

Abstract

Mandelbrot (Int Econ Rev 1:79–106, 1960 ) proposed using the so-called Pareto–Lévy class of distributions as a framework for representing income distributions. We argue in this article that the Pareto–Lévy distribution is an interesting candidate for representing income distributions because its parameters are easy to interpret and it satisfies a specific invariance-under-aggregation property. We also demonstrate that the Gini coefficient can be expressed as a simple formula of the parameters of the Pareto–Lévy distribution. We subsequently use income data for Norway and seven other OECD countries to fit the Pareto–Lévy distribution as well as the Generalized Beta type II (GB2) distribution. The results show that the Pareto–Lévy distribution fits the data better than the GB2 distribution for most countries, despite the fact that GB2 distribution has four parameters whereas the Pareto–Lévy distribution has only three. Copyright Springer-Verlag 2013

Suggested Citation

  • John Dagsvik & Zhiyang Jia & Bjørn Vatne & Weizhen Zhu, 2013. "Is the Pareto–Lévy law a good representation of income distributions?," Empirical Economics, Springer, vol. 44(2), pages 719-737, April.
  • Handle: RePEc:spr:empeco:v:44:y:2013:i:2:p:719-737
    DOI: 10.1007/s00181-011-0539-z
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    References listed on IDEAS

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    1. Singh, S K & Maddala, G S, 1976. "A Function for Size Distribution of Incomes," Econometrica, Econometric Society, vol. 44(5), pages 963-970, September.
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    6. Esteban, Joan M, 1986. "Income-Share Elasticity and the Size Distribution of Income," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(2), pages 439-444, June.
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    10. van Dijk, Herman K & Kloek, Teun, 1980. "Inferential Procedures in Stable Distributions for Class Frequency Data on Incomes," Econometrica, Econometric Society, vol. 48(5), pages 1139-1148, July.
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    Cited by:

    1. Vladimir Hlasny, 2020. "Parametric Representation of the Top of Income Distributions: Options, Historical Evidence and Model Selection," Working Papers 547, ECINEQ, Society for the Study of Economic Inequality.
    2. Frank A. Cowell & Emmanuel Flachaire, 2014. "Statistical Methods for Distributional Analysis," Working Papers halshs-01115996, HAL.
    3. Frank A. Cowell & Philippe Kerm, 2015. "Wealth Inequality: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 29(4), pages 671-710, September.

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    More about this item

    Keywords

    Stable distributions; Pareto–Lévy distribution; Income distributions; Invariance principles; Generalized Beta type II distributions;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution

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