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|
Phone: +61 3 8344 8560
Fax: +61 3 8344 6899
Web page: http://fbe.unimelb.edu.au/economics
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- D.S. Prasada Rao & Duangkamon Chotikapanich & William E. Griffiths, 2004. "Estimating and Combining National Income Distributions using Limited Data," Econometric Society 2004 Australasian Meetings 213, Econometric Society.
- 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.
- 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.
- 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.
- Wu, Ximing & Perloff, Jeffrey M., 2005. "China's Income Distribution, 1985-2001," Institute for Research on Labor and Employment, Working Paper Series qt0zd6m0sf, Institute of Industrial Relations, UC Berkeley.
- 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.
- Milanovic, Branko, 1999. "True world income distribution, 1988 and 1993 - first calculations, based on household surveys alone," Policy Research Working Paper Series 2244, The World Bank.
- Branko milanovic, 2003. "True world income distribution, 1988 and 1993: First calculation based on household surveys alo," HEW 0305002, EconWPA.
- McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-663, May.
- 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.
- 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.
- Cameron,A. Colin & Trivedi,Pravin K., 2008. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9787111235767.
- 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.
- 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.
- Cameron,A. Colin & Trivedi,Pravin K., 2005. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9780521848053.
- Butler, Richard J. & McDonald, James B., 1989. "Using incomplete moments to measure inequality," Journal of Econometrics, Elsevier, vol. 42(1), pages 109-119, September. Full references (including those not matched with items on IDEAS)