Inference for Income Distributions Using Grouped Data
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. Generic moment conditions and an optimal weight matrix that can be used for GMM estimation of any parametric income distribution are derived. 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, that incorporates information on class means as well as population proportions, is more efficient than maximum likelihood estimation of the multinomial distribution that uses only population proportions. In contrast to the earlier work of Chotikapanich et al. (2007, 2012), that 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, 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.
|Date of creation:||2012|
|Contact details of provider:|| Postal: Department of Economics, The University of Melbourne, 4th Floor, FBE Building, Level 4, 111 Barry Street. Victoria, 3010, Australia|
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Web page: http://fbe.unimelb.edu.au/economics
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- Branko Milanovic, 2002.
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- Duangkamon Chotikapanich & William E. Griffiths & D.S. Prasada Rao, 2005.
"Estimating and Combining National Income Distributions using Limited Data,"
Department of Economics - Working Papers Series
926, The University of Melbourne.
- 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.
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- 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.
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- 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.
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