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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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    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. Parker, Simon C, 1999. "The Beta as a Model for the Distribution of Earnings," Bulletin of Economic Research, Wiley Blackwell, vol. 51(3), pages 243-251, July.
    3. Benoit Mandelbrot, 1962. "Paretian Distributions and Income Maximization," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 76(1), pages 57-85.
    4. Majumder, Amita & Chakravarty, Satya Ranjan, 1990. "Distribution of Personal Income: Development of a New Model and Its Application to U.S. Income Data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 189-196, April-Jun.
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    6. Benoit Mandelbrot, 1963. "New Methods in Statistical Economics," Journal of Political Economy, University of Chicago Press, vol. 71(5), pages 421-421.
    7. Ripsy Bandourian & Robert Turley & James McDonald, 2002. "A Comparison of Parametric Models of Income Distribution across Countries and over Time," LIS Working papers 305, LIS Cross-National Data Center in Luxembourg.
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    14. 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.
    15. Parker, Simon C., 1999. "The generalised beta as a model for the distribution of earnings," Economics Letters, Elsevier, vol. 62(2), pages 197-200, February.
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    Cited by:

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    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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