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Using the GB2 Income Distribution: A Review

Author

Listed:
  • Duangkamon Chotikapanich

    (Monash University)

  • William E. Griffiths

    (Department of Economics, University of Melbourne)

  • Gholamreza Hajargasht

    (Swinburne University)

  • Wasana Karunarathne

    (Department of Economics, University of Melbourne)

  • D.S. Prasada Rao

    (University of Queensland)

Abstract

To use the GB2 distribution for the analysis of income and other positively-skewed distributions, knowledge of estimation methods and the ability to compute quantities of interest from the estimated parameters are required. We review estimation methodology that has appeared in the literature, and summarise expressions for inequality, poverty, and propoor growth that can be used to compute these measures from GB2 parameter estimates. An application to data from China and Indonesia is provided.

Suggested Citation

  • Duangkamon Chotikapanich & William E. Griffiths & Gholamreza Hajargasht & Wasana Karunarathne & D.S. Prasada Rao, 2018. "Using the GB2 Income Distribution: A Review," Department of Economics - Working Papers Series 2036, The University of Melbourne.
    • Handle: RePEc:mlb:wpaper:2036
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    References listed on IDEAS

    as
    1. Cummins, J. David & Dionne, Georges & McDonald, James B. & Pritchett, B. Michael, 1990. "Applications of the GB2 family of distributions in modeling insurance loss processes," Insurance: Mathematics and Economics, Elsevier, vol. 9(4), pages 257-272, December.
    2. Andrew M. Jones & James Lomas & Nigel Rice, 2014. "Applying Beta‐Type Size Distributions To Healthcare Cost Regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(4), pages 649-670, June.
    3. 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.
    4. Chotikapanich, Duangkamon & Griffiths, William E. & Rao, D. S. Prasada, 2007. "Estimating and Combining National Income Distributions Using Limited Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 97-109, January.
    5. Duangkamon Chotikapanich & William Griffiths & Wasana Karunarathne & D.S. Prasada Rao, 2013. "Calculating Poverty Measures from the Generalised Beta Income Distribution," The Economic Record, The Economic Society of Australia, vol. 89, pages 48-66, June.
    6. 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.
    7. Feng, Shuaizhang & Burkhauser, Richard V. & Butler, J.S., 2006. "Levels and Long-Term Trends in Earnings Inequality: Overcoming Current Population Survey Censoring Problems Using the GB2 Distribution," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 57-62, January.
    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, 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.
    10. 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, July.
    11. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-231, March.
    12. 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.
    13. Audrey Chouchane & Jean-Yves Duclos, 2010. "Working Paper 115 - Analyzing Pro-Poor Growth in Southern Africa: Lessons from Mauritius and South Africa," Working Paper Series 253, African Development Bank.
    14. Robert F. Bordley & James B. McDonald & Anand Mantrala, 1997. "Something New, Something Old: Parametric Models for the Size of Distribution of Income," Journal of Income Distribution, Ad libros publications inc., vol. 6(1), pages 5-5, 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.
    16. Monique Graf & Desislava Nedyalkova, 2014. "Modeling of Income and Indicators of Poverty and Social Exclusion Using the Generalized Beta Distribution of the Second Kind," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 60(4), pages 821-842, December.
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    Cited by:

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    2. 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.
    3. 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.
    4. 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.
    5. Vanesa Jorda & José María Sarabia & Markus Jäntti, 2021. "Inequality measurement with grouped data: Parametric and non‐parametric methods," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(3), pages 964-984, July.
    6. Walter Bossert & Conchita D’Ambrosio & Kohei Kamaga, 2021. "Extreme Values, Means, and Inequality Measurement," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 67(3), pages 564-590, September.
    7. Jiong Liu & R. A. Serota, 2023. "Rethinking Generalized Beta family of distributions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(2), pages 1-14, February.
    8. Mathias Silva, 2023. "Parametric models of income distributions integrating misreporting and non-response mechanisms," AMSE Working Papers 2311, Aix-Marseille School of Economics, France.
    9. Betti, Gianni & Molini, Vasco & Mori, Lorenzo, 2024. "An attempt to correct the underestimation of inequality measures in cross-survey imputation through generalized additive models for location, scale and shape," Socio-Economic Planning Sciences, Elsevier, vol. 91(C).
    10. Tsvetana Spasova, 2024. "Estimating Income Distributions From Grouped Data: A Minimum Quantile Distance Approach," Computational Economics, Springer;Society for Computational Economics, vol. 64(4), pages 2079-2096, October.
    11. Jordá, Vanesa & Niño-Zarazúa, Miguel, 2019. "Global inequality: How large is the effect of top incomes?," World Development, Elsevier, vol. 123(C), pages 1-1.
    12. Stanislaw Maciej Kot & Piotr Paradowski, 2024. "The Equally Distributed Equivalent Income as the Upper Limit of Poverty Lines," LIS Working papers 885, LIS Cross-National Data Center in Luxembourg.
    13. Jiong Liu & R. A. Serota, 2022. "Rethinking Generalized Beta Family of Distributions," Papers 2209.05225, arXiv.org.
    14. Jiong Liu & Hamed Farahani & R. A. Serota, 2023. "Exploring Distributions of House Prices and House Price Indices," Papers 2312.14325, arXiv.org.
    15. Dashti Moghaddam, M. & Mills, Jeffrey & Serota, R.A., 2020. "From a stochastic model of economic exchange to measures of inequality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    16. Jiong Liu & Hamed Farahani & R. A. Serota, 2024. "Exploring Distributions of House Prices and House Price Indices," Economies, MDPI, vol. 12(2), pages 1-16, February.
    17. Amparo Ba'illo & Javier C'arcamo & Carlos Mora-Corral, 2021. "Extremal points of Lorenz curves and applications to inequality analysis," Papers 2103.03286, arXiv.org.

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    More about this item

    JEL classification:

    • I32 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Measurement and Analysis of Poverty
    • O15 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Economic Development: Human Resources; Human Development; Income Distribution; Migration
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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