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Inference for Income Distributions Using Grouped Data

  • Gholamreza Hajargasht
  • William E. Griffiths
  • Joseph Brice
  • D.S. Prasada Rao
  • Duangkamon Chotikapanich

We develop a general approach to estimation and inference for income distributions using grouped or aggregate data that are typically available in the form of population shares and class mean incomes, with unknown group bounds. We derive generic moment conditions and an optimal weight matrix that can be used for generalized method-of-moments (GMM) estimation of any parametric income distribution. Our derivation of the weight matrix and its inverse allows us to express the seemingly complex GMM objective function in a relatively simple form that facilitates estimation. We show that our proposed approach, which incorporates information on class means as well as population proportions, is more efficient than maximum likelihood estimation of the multinomial distribution, which uses only population proportions. In contrast to the earlier work of Chotikapanich, Griffiths, and Rao, and Chotikapanich, Griffiths, Rao, and Valencia, which did not specify a formal GMM framework, did not provide methodology for obtaining standard errors, and restricted the analysis to the beta-2 distribution, we provide standard errors for estimated parameters and relevant functions of them, such as inequality and poverty measures, and we provide methodology for all distributions. A test statistic for testing the adequacy of a distribution is proposed. 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 (GB2), and its special-case distributions, the beta-2, Singh--Maddala, Dagum, generalized gamma, and lognormal distributions. We test the adequacy of each distribution and compare predicted and actual income shares, where the number of groups used for prediction can differ from the number used in estimation. Estimates and standard errors for inequality and poverty measures are provided. Supplementary materials for this article are available online.

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Article provided by Taylor & Francis Journals in its journal Journal of Business & Economic Statistics.

Volume (Year): 30 (2012)
Issue (Month): 4 (May)
Pages: 563-575

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Handle: RePEc:taf:jnlbes:v:30:y:2012:i:4:p:563-575
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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. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-63, May.
  3. repec:cup:cbooks:9780521848053 is not listed on IDEAS
  4. 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.
  5. McDonald, James B & Ransom, Michael R, 1979. "Functional Forms, Estimation Techniques and the Distribution of Income," Econometrica, Econometric Society, vol. 47(6), pages 1513-25, November.
  6. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 133-152.
  7. 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.
  8. 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.
  9. 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.
  10. Butler, Richard J. & McDonald, James B., 1989. "Using incomplete moments to measure inequality," Journal of Econometrics, Elsevier, vol. 42(1), pages 109-119, September.
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