Inference for Income Distributions Using Grouped Data
AbstractWe 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.
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Bibliographic InfoPaper provided by The University of Melbourne in its series Department of Economics - Working Papers Series with number 1140.
Length: 43 pages
Date of creation: 2012
Date of revision:
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Postal: Department of Economics, The University of Melbourne, 5th Floor, Economics and Commerce Building, Victoria, 3010, Australia
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Web page: http://www.economics.unimelb.edu.au
More information through EDIRC
GMM; Generalized beta distribution; Inequality and poverty.;
Other versions of this item:
- Gholamreza Hajargasht & William E. Griffiths & Joseph Brice & D.S. Prasada Rao & Duangkamon Chotikapanich, 2012. "Inference for Income Distributions Using Grouped Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 30(4), pages 563-575, May.
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.:
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- 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.
- Duangkamon Chotikapanich, William Griffiths, Wasana Karunarathne, D.S. Prasada Rao, 2012. "Calculating Poverty Measures from the Generalized Beta Income Distribution," Department of Economics - Working Papers Series 1154, The University of Melbourne.
- Gholamreza Hajargasht and William E. Griffiths, 2012. "Pareto-Lognormal Income Distributions:Inequality and Poverty Measures, Estimation and Performance," Department of Economics - Working Papers Series 1149, The University of Melbourne.
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