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GMM Estimation of Income Distributions from Grouped Data

Author

Listed:
  • Gholamreza Hajargsht
  • William E. Griffiths
  • Joseph Brice
  • D.S. Prasada Rao
  • Duangkamon Chotikapanich

Abstract

We develop a GMM procedure for estimating income distributions from grouped data with unknown group bounds. The approach enables us to obtain standard errors for the estimated parameters and functions of the parameters, such as inequality and poverty measures, and to test the validity of an assumed distribution using a J-test. Using eight countries/regions for the year 2005, we show how the methodology can be applied to estimate the parameters of the generalized beta distribution of the second kind, and its special-case distributions, the beta-2, Singh-Maddala, Dagum, generalized gamma and lognormal distributions. This work extends earlier work (Chotikapanich et al., 2007, 2012) that did not specify a formal GMM framework, did not provide methodology for obtaining standard errors, and considered only the beta-2 distribution. The results show that generalized beta distribution fits the data well and outperforms other frequently used distributions.

Suggested Citation

  • Gholamreza Hajargsht & William E. Griffiths & Joseph Brice & D.S. Prasada Rao & Duangkamon Chotikapanich, 2011. "GMM Estimation of Income Distributions from Grouped Data," Department of Economics - Working Papers Series 1129, The University of Melbourne.
    • Handle: RePEc:mlb:wpaper:1129
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    References listed on IDEAS

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    1. Branko Milanovic, 2002. "True World Income Distribution, 1988 and 1993: First Calculation Based on Household Surveys Alone," Economic Journal, Royal Economic Society, vol. 112(476), pages 51-92, January.
    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. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-766, May.
    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. 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.
    6. Wu, Ximing & Perloff, Jeffrey M., 2007. "GMM estimation of a maximum entropy distribution with interval data," Journal of Econometrics, Elsevier, vol. 138(2), pages 532-546, June.
    7. Cameron,A. Colin & Trivedi,Pravin K., 2005. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9780521848053, January.
    8. John Creedy & Vance L. Martin (ed.), 1997. "Nonlinear Economic Models," Books, Edward Elgar Publishing, number 1314.
    9. Butler, Richard J. & McDonald, James B., 1989. "Using incomplete moments to measure inequality," Journal of Econometrics, Elsevier, vol. 42(1), pages 109-119, September.
    10. Ximing Wu & Jeffrey M. Perloff, 2005. "China's Income Distribution, 1985-2001," The Review of Economics and Statistics, MIT Press, vol. 87(4), pages 763-775, November.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. McDonald, James B & Ransom, Michael R, 1979. "Functional Forms, Estimation Techniques and the Distribution of Income," Econometrica, Econometric Society, vol. 47(6), pages 1513-1525, November.
    16. 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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    More about this item

    Keywords

    GMM; generalized beta distribution; grouped data; inequality and poverty;
    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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