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Inequality and the GB2 income distribution

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  • Stephen P. Jenkins

    (ISER, University of Essex)

Abstract

The generalized entropy class of inequality indices is derived for Generalized Beta of the Second Kind (GB2) income distributions, thereby providing a full range of topsensitive and bottom-sensitive measures. An examination of British income inequality in 1994/95 and 2004/05 illustrates the analysis.

Suggested Citation

  • Stephen P. Jenkins, 2007. "Inequality and the GB2 income distribution," Working Papers 73, ECINEQ, Society for the Study of Economic Inequality.
    • Handle: RePEc:inq:inqwps:ecineq2007-73
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    File URL: http://www.ecineq.org/milano/WP/ECINEQ2007-73.pdf
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    References listed on IDEAS

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    1. Frank A. Cowell, 1980. "On the Structure of Additive Inequality Measures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(3), pages 521-531.
    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. 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.
    4. Cowell, Frank A. & Flachaire, Emmanuel, 2007. "Income distribution and inequality measurement: The problem of extreme values," Journal of Econometrics, Elsevier, vol. 141(2), pages 1044-1072, December.
    5. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-1385, November.
    6. Butler, Richard J. & McDonald, James B., 1989. "Using incomplete moments to measure inequality," Journal of Econometrics, Elsevier, vol. 42(1), pages 109-119, September.
    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. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    10. Stephen P. Jenkins, 2007. "GB2FIT: Stata module to fit Generalized Beta of the Second Kind distribution by maximum likelihood," Statistical Software Components S456823, Boston College Department of Economics, revised 17 Jul 2012.
    11. Frank A. Cowell, 2008. "Income Distribution and Inequality," Chapters, in: John B. Davis & Wilfred Dolfsma (ed.), The Elgar Companion to Social Economics, chapter 13, Edward Elgar Publishing.
    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. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
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    Cited by:

    1. Christian Kleiber, 2008. "A Guide to the Dagum Distributions," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 6, pages 97-117, Springer.
    2. Vladimir Hlasny, 2019. "Redistributive Impacts of Fiscal Policies in Mexico: Corrections for Top Income Measurement Problems," LIS Working papers 765, LIS Cross-National Data Center in Luxembourg.
    3. Alexander Sohn & Nadja Klein & Thomas Kneib, 2014. "A New Semiparametric Approach to Analysing Conditional Income Distributions," SOEPpapers on Multidisciplinary Panel Data Research 676, DIW Berlin, The German Socio-Economic Panel (SOEP).
    4. 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.
    5. Sohn, Alexander & Klein, Nadja & Kneib, Thomas, 2014. "A new semiparamtetric approach to analysing Conditional Income Distributions," VfS Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100630, Verein für Socialpolitik / German Economic Association.
    6. Vladimir Hlasny & Paolo Verme, 2018. "Top Incomes and Inequality Measurement: A Comparative Analysis of Correction Methods Using the EU SILC Data," Econometrics, MDPI, vol. 6(2), pages 1-21, June.
    7. Masato Okamoto, 2013. "Extension of the κ-generalized distribution: new four-parameter models for the size distribution of income and consumption," LIS Working papers 600, LIS Cross-National Data Center in Luxembourg.
    8. Maxim Pinkovskiy & Xavier Sala-i-Martin, 2009. "Parametric Estimations of the World Distribution of Income," NBER Working Papers 15433, National Bureau of Economic Research, Inc.

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    More about this item

    Keywords

    inequality; generalized entropy indices; generalized Beta of the second kind distribution; GB2 distribution; Singh-Maddala distribution; Dagum distribution;
    All these keywords.

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution

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