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Pareto–lognormal distributions: Inequality, poverty, and estimation from grouped income data

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  • Hajargasht, Gholamreza
  • Griffiths, William E.

Abstract

The (double) Pareto–lognormal is an emerging parametric distribution for income that has a sound underlying generating process, good theoretical properties, and some limited favorable evidence of its fit to data. We extend existing results for this distribution in 3 directions. (1) We derive closed form formula for its moment distribution functions, and for various inequality and poverty measures. (2) We show how it can be estimated from grouped data using GMM. (3) 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, when using grouped data, both distributions provide a good fit, with the double Pareto–lognormal distribution outperforming the beta distribution in 4 out of 10 cases.

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  • Hajargasht, Gholamreza & Griffiths, William E., 2013. "Pareto–lognormal distributions: Inequality, poverty, and estimation from grouped income data," Economic Modelling, Elsevier, vol. 33(C), pages 593-604.
    • Handle: RePEc:eee:ecmode:v:33:y:2013:i:c:p:593-604
    DOI: 10.1016/j.econmod.2013.04.046
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    1. Christophe Muller, 2001. "The Properties of the Watts Poverty Index under Lognormality," Economics Bulletin, AccessEcon, vol. 9(1), pages 1-9.
    2. 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.
    3. Reed, William J., 2001. "The Pareto, Zipf and other power laws," Economics Letters, Elsevier, vol. 74(1), pages 15-19, December.
    4. 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.
    5. 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.
    6. Cowell, Frank, 2011. "Measuring Inequality," OUP Catalogue, Oxford University Press, edition 3, number 9780199594047.
    7. Reed, William J., 2003. "The Pareto law of incomes—an explanation and an extension," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 469-486.
    8. 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.
    9. Duangkamon Chotikapanich & William E Griffiths & D.S. Prasada Rao & Vicar Valencia, 2009. "Global Income Distribution and Inequality: 1993 and 2000," Department of Economics - Working Papers Series 1062, The University of Melbourne.
    10. Duangkamon Chotikapanich & William E. Griffiths & D. S. Prasada Rao & Vicar Valencia, 2012. "Global Income Distributions and Inequality, 1993 and 2000: Incorporating Country-Level Inequality Modeled with Beta Distributions," The Review of Economics and Statistics, MIT Press, vol. 94(1), pages 52-73, February.
    11. 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.
    12. 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.
    13. Jess Benhabib & Shenghao Zhu, 2008. "Age, Luck, and Inheritance," NBER Working Papers 14128, National Bureau of Economic Research, Inc.
    14. Stephen P. Jenkins, 2009. "Distributionally‐Sensitive Inequality Indices And The Gb2 Income Distribution," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 55(2), pages 392-398, June.
    15. 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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    Cited by:

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    4. Safari, Muhammad Aslam Mohd & Masseran, Nurulkamal & Ibrahim, Kamarulzaman & AL-Dhurafi, Nasr Ahmed, 2020. "The power-law distribution for the income of poor households," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    5. Michal Fabinger & E. Glen Weyl, 2018. "Functional Forms for Tractable Economic Models and the Cost Structure of International Trade," CIRJE F-Series CIRJE-F-1092, CIRJE, Faculty of Economics, University of Tokyo.
    6. Mathias Silva, 2023. "Parametric estimation of income distributions using grouped data: an Approximate Bayesian Computation approach [Working Papers / Documents de travail]," Working Papers hal-04066544, HAL.
    7. Toda, Alexis Akira, 2017. "A Note On The Size Distribution Of Consumption: More Double Pareto Than Lognormal," Macroeconomic Dynamics, Cambridge University Press, vol. 21(6), pages 1508-1518, September.
    8. Michal Fabinger & E. Glen Weyl, 2016. "The Average-Marginal Relationship and Tractable Equilibrium Forms," CIRJE F-Series CIRJE-F-1028, CIRJE, Faculty of Economics, University of Tokyo.
    9. E. Weyl & Michal Fabinger, 2015. "A Tractable Approach to Pass-Through Patterns," 2015 Meeting Papers 747, Society for Economic Dynamics.
    10. Enrique Calderín-Ojeda & Kevin Fergusson & Xueyuan Wu, 2017. "An EM Algorithm for Double-Pareto-Lognormal Generalized Linear Model Applied to Heavy-Tailed Insurance Claims," Risks, MDPI, vol. 5(4), pages 1-24, November.
    11. Nicholas Rohde, 2016. "J-divergence measurements of economic inequality," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(3), pages 847-870, June.
    12. William Griffiths & Duangkamon Chotikapanich & Gholamreza Hajargasht, 2021. "A Note on Inequality Measures for Mixtures of Double Pareto-Lognormal Distributions," Monash Econometrics and Business Statistics Working Papers 14/21, Monash University, Department of Econometrics and Business Statistics.
    13. Michal Fabinger & E. Glen Weyl, 2016. "Functional Forms for Tractable Economic Models and the Cost Structure of International Trade," Papers 1611.02270, arXiv.org, revised Aug 2018.
    14. Masato Okamoto, 2022. "Lorenz and Polarization Orderings of the Double-Pareto Lognormal Distribution and Other Size Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 548-574, November.
    15. Fernández-Morales, Antonio, 2016. "Measuring poverty with the Foster, Greer and Thorbecke indexes based on the Gamma distribution," MPRA Paper 69648, University Library of Munich, Germany.
    16. D.S. Prasada Rao & Alicia N. Rambald & Gholamreza Hajargasht & William E Griffiths, 2023. "The University of Queensland International Comparison Database, UQICD V3.0: User Guide," CEPA Working Papers Series WP092022, School of Economics, University of Queensland, Australia.
    17. José María Sarabia & Vanesa Jordá & Lorena Remuzgo, 2017. "The Theil Indices in Parametric Families of Income Distributions—A Short Review," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 63(4), pages 867-880, December.
    18. Antinyan, Armenak & Horváth, Gergely & Jia, Mofei, 2019. "Social status competition and the impact of income inequality in evolving social networks: An agent-based model," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 79(C), pages 53-69.
    19. Duangkamon Chotikapanich & William E. Griffiths & Gholamreza Hajargasht & Wasana Karunarathne & D. S. Prasada Rao, 2018. "Using the GB2 Income Distribution," Econometrics, MDPI, vol. 6(2), pages 1-24, April.
    20. Sugasawa, Shonosuke & Kobayashi, Genya & Kawakubo, Yuki, 2020. "Estimation and inference for area-wise spatial income distributions from grouped data," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    21. William Griffiths & Duangkamon Chotikapanich & Gholamreza Hajargasht, 2022. "A note on inequality measures for mixtures of double Pareto–lognormal distributions," Australian Economic Papers, Wiley Blackwell, vol. 61(2), pages 280-290, June.

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    More about this item

    Keywords

    Double-Pareto; GB2 distribution; GMM; Moment distributions;
    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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