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Skewness and Kurtosis Properties of Income Distribution Models

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  • James McDonald
  • Patrick A. Turley
  • Jeff Sorensen

Abstract

This paper explores the ability of some popular income distributions to model observed skewness and kurtosis. We present the generalized beta type 1 (GB1) and type 2 (GB2) distributions’ skewness-kurtosis spaces and clarify and expand on previously known results on other distributions’ skewness-kurtosis spaces. Data from the Luxembourg Income Study are used to estimate sample moments and explore the ability of the generalized gamma, Dagum, Singh-Maddala, beta of the first kind, beta of the second kind, GB1, and GB2 distributions to accommodate the skewness and kurtosis values. The GB2 has the flexibility to accurately describe the observed skewness and kurtosis.

Suggested Citation

  • James McDonald & Patrick A. Turley & Jeff Sorensen, 2011. "Skewness and Kurtosis Properties of Income Distribution Models," LIS Working papers 569, LIS Cross-National Data Center in Luxembourg.
    • Handle: RePEc:lis:liswps:569
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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. Erich Battistin & Richard Blundell & Arthur Lewbel, 2009. "Why Is Consumption More Log Normal than Income? Gibrat's Law Revisited," Journal of Political Economy, University of Chicago Press, vol. 117(6), pages 1140-1154, December.
    3. 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.
    4. Thurow, Lester C, 1970. "Analyzing the American Income Distribution," American Economic Review, American Economic Association, vol. 60(2), pages 261-269, May.
    5. Gastwirth, Joseph L, 1972. "The Estimation of the Lorenz Curve and Gini Index," The Review of Economics and Statistics, MIT Press, vol. 54(3), pages 306-316, August.
    6. Singh, S K & Maddala, G S, 1976. "A Function for Size Distribution of Incomes," Econometrica, Econometric Society, vol. 44(5), pages 963-970, September.
    7. McDonald, James B. & Ransom, Michael R., 1981. "An analysis of the bounds for the Gini coefficient," Journal of Econometrics, Elsevier, vol. 17(2), pages 177-188, November.
    8. 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.
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    2. David Mauler & James McDonald, 2015. "Option Pricing and Distribution Characteristics," Computational Economics, Springer;Society for Computational Economics, vol. 45(4), pages 579-595, April.
    3. Andrew M. Jones & James Lomas & Nigel Rice, 2015. "Healthcare Cost Regressions: Going Beyond the Mean to Estimate the Full Distribution," Health Economics, John Wiley & Sons, Ltd., vol. 24(9), pages 1192-1212, September.
    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. Michael McAleer & Hang K. Ryu & Daniel J. Slottje, 2019. "A New Inequality Measure that is Sensitive to Extreme Values and Asymmetries," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(1), pages 31-61, March.
    6. Jones, A. & Lomas, J. & Rice, N., 2014. "Going Beyond the Mean in Healthcare Cost Regressions: a Comparison of Methods for Estimating the Full Conditional Distribution," Health, Econometrics and Data Group (HEDG) Working Papers 14/26, HEDG, c/o Department of Economics, University of York.
    7. Vladimir Hlasny, 2021. "Parametric representation of the top of income distributions: Options, historical evidence, and model selection," Journal of Economic Surveys, Wiley Blackwell, vol. 35(4), pages 1217-1256, September.
    8. Wang, Frank Xuyan, 2021. "Shape factor asymptotic analysis II," MPRA Paper 110827, University Library of Munich, Germany.
    9. Wang, Frank Xuyan, 2019. "Shape Factor Asymptotic Analysis I," MPRA Paper 93357, University Library of Munich, Germany.
    10. Sriubaite, I. & Harris, A. & Jones, A.M. & Gabbe, B., 2020. "Economic Consequences of Road Traffic Injuries. Application of the Super Learner algorithm," Health, Econometrics and Data Group (HEDG) Working Papers 20/20, HEDG, c/o Department of Economics, University of York.
    11. Jingjing Bai & Wei Gu & Xiaodong Yuan & Qun Li & Feng Xue & Xuchong Wang, 2015. "Power Quality Prediction, Early Warning, and Control for Points of Common Coupling with Wind Farms," Energies, MDPI, vol. 8(9), pages 1-18, August.
    12. Tomson Ogwang, 2022. "The Foster–Greer–Thorbecke Poverty Measures Reveal More," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 164(3), pages 1481-1503, December.
    13. Higbee, Joshua D. & Jensen, Jonathan E. & McDonald, James B., 2019. "The asymmetric log-Laplace distribution as a limiting case of the generalized beta distribution," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 73-78.
    14. Marco Bee & Julien Hambuckers & Flavio Santi & Luca Trapin, 2021. "Testing a parameter restriction on the boundary for the g-and-h distribution: a simulated approach," Computational Statistics, Springer, vol. 36(3), pages 2177-2200, September.
    15. Enrico Fabrizi & Maria Rosaria Ferrante & Carlo Trivisano, 2020. "A functional approach to small area estimation of the relative median poverty gap," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 1273-1291, June.
    16. Andrew M. Jones & James Lomas & Peter T. Moore & Nigel Rice, 2016. "A quasi-Monte-Carlo comparison of parametric and semiparametric regression methods for heavy-tailed and non-normal data: an application to healthcare costs," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(4), pages 951-974, October.
    17. 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.
    18. McDonald, James B. & Sorensen, Jeff, 2017. "Academic salary compression across disciplines and over time," Economics of Education Review, Elsevier, vol. 59(C), pages 87-104.

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    More about this item

    Keywords

    skewness; kurtosis; generalized beta type 2 distribution; generalized gamma distribution;
    All these keywords.

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • E25 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Aggregate Factor Income Distribution

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