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Estimating Income Distributions Using a Mixture of Gamma Densities

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  • Duangkamon Chotikapanich
  • William E Griffiths

Abstract

The estimation of income distributions is important for assessing income inequality and poverty and for making comparisons of inequality and poverty over time, countries and regions, as well as before and after changes in taxation and transfer policies. Distributions have been estimated both parametrically and nonparametrically. Parametric estimation is convenient because it facilitates subsequent inferences about inequality and poverty measures and lends itself to further analysis such as the combining of regional distributions into a national distribution. Nonparametric estimation makes inferences more difficult, but it does not place what are sometimes unreasonable restrictions on the nature of the distribution. By estimating a mixture of gamma distributions, in this paper we attempt to benefit from the advantages of parametric estimation without suffering the disadvantage of inflexibility. Using a sample of Canadian income data, we use Bayesian inference to estimate gamma mixtures with two and three components. We describe how to obtain a predictive density and distribution function for income and illustrate the flexibility of the mixture. Posterior densities for Lorenz curve ordinates and the Gini coefficient are obtained

Suggested Citation

  • Duangkamon Chotikapanich & William E Griffiths, 2008. "Estimating Income Distributions Using a Mixture of Gamma Densities," Department of Economics - Working Papers Series 1034, The University of Melbourne.
  • Handle: RePEc:mlb:wpaper:1034
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    File URL: http://fbe.unimelb.edu.au/__data/assets/pdf_file/0006/802725/1034.pdf
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    References listed on IDEAS

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    1. 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.
    2. Frank A Cowell, 1996. "Estimation of Inequality Indices," STICERD - Distributional Analysis Research Programme Papers 25, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. Duangkamon Chotikapanich & William E. Griffiths, 2006. "Bayesian Assessment of Lorenz and Stochastic Dominance in Income Distributions," Department of Economics - Working Papers Series 960, The University of Melbourne.
    4. Hasegawa, Hikaru & Kozumi, Hideo, 2003. "Estimation of Lorenz curves: a Bayesian nonparametric approach," Journal of Econometrics, Elsevier, vol. 115(2), pages 277-291, August.
    5. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
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    Cited by:

    1. William E. Griffiths and Gholamreza Hajargasht, 2012. "GMM Estimation of Mixtures from Grouped Data:," Department of Economics - Working Papers Series 1148, The University of Melbourne.
    2. García-Fernández, Rosa María & Gottlieb, Daniel & Palacios-González, Frederico, 2013. "Polarization, growth and social policy in the case of Israel, 1997-2008," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy (IfW), vol. 7, pages 1-40.
    3. 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.
    4. Stanislaw Maciej Kot, 2016. "Estimates Of The World Distribution Of Personal Incomes Based On Country Sample Clones," GUT FME Working Paper Series A 41, Faculty of Management and Economics, Gdansk University of Technology.
    5. David Warner & Prasada Rao & William E. Griffiths & Duangkamon Chotikapanich, 2011. "Global Inequality: Levels and Trends, 1993-2005," Discussion Papers Series 436, School of Economics, University of Queensland, Australia.
    6. Iead Rezek, 2011. "Constrained Mixture Models for Asset Returns Modelling," Papers 1103.2670, arXiv.org.
    7. Lubrano, Michel & Ndoye, Abdoul Aziz Junior, 2016. "Income inequality decomposition using a finite mixture of log-normal distributions: A Bayesian approach," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 830-846.
    8. Chang, Andrew C. & Li, Phillip & Martin, Shawn M., 2017. "Comparing Cross-Country Estimates of Lorenz Curves Using a Dirichlet Distribution Across Estimators and Datasets," Finance and Economics Discussion Series 2017-062, Board of Governors of the Federal Reserve System (U.S.).

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