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Pareto-Lognormal Income Distributions:Inequality and Poverty Measures, Estimation and Performance

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  • Gholamreza Hajargasht and William E. Griffiths

Abstract

The (double) Pareto-lognormal is an emerging parametric distribution for income that has a sound underlying generating process, good theoretical properties, and favourable evidence of its fit to data. We extend existing results for this distribution in 3 directions. We derive closed form formula for its moment distribution functions, and for various inequality and poverty measures. We show how it can be estimated from grouped data using the GMM method developed in Hajargasht et al. (2012). Using grouped data from ten countries, we compare its performance with that of another leading 4-parameter income distribution, the generalized beta-2 distribution. The results confirm that both distributions provide a good fit, with the double Pareto-lognormal distribution outperforming the beta distribution in some but not all cases.

Suggested Citation

  • Gholamreza Hajargasht and William E. Griffiths, 2012. "Pareto-Lognormal Income Distributions:Inequality and Poverty Measures, Estimation and Performance," Department of Economics - Working Papers Series 1149, The University of Melbourne.
    • Handle: RePEc:mlb:wpaper:1149
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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. William J. Reed & Fan Wu, 2008. "New Four- and Five-Parameter Models for Income Distributions," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 11, pages 211-223, Springer.
    3. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 69(2), pages 427-428, October.
    4. Duangkamon Chotikapanich (ed.), 2008. "Modeling Income Distributions and Lorenz Curves," Economic Studies in Inequality, Social Exclusion, and Well-Being, Springer, number 978-0-387-72796-7, Fall.
    5. James B. McDonald & Michael Ransom, 2008. "The Generalized Beta Distribution as a Model for the Distribution of Income: Estimation of Related Measures of Inequality," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 8, pages 147-166, Springer.
    6. Jess Benhabib & Shenghao Zhu, 2008. "Age, Luck, and Inheritance," NBER Working Papers 14128, National Bureau of Economic Research, Inc.
    7. Gholamreza Hajargasht & William E. Griffiths & Joseph Brice & D.S. Prasada Rao & Duangkamon Chotikapanich, 2012. "Inference for Income Distributions Using Grouped Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(4), pages 563-575, May.
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    More about this item

    Keywords

    GB2 distribution; GMM; moment distributions; double-Pareto.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution

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