GMM Estimation of Mixtures from Grouped Data:
We show how the generalized method of moments (GMM) framework developed in Hajargasht et al. (2012) for estimating income distributions from grouped data can be adapted for estimating mixtures. This approach can be used to estimate a mixture of any distributions where the moments and moment distribution functions of the mixture components can be expressed in terms of the parameters of those components. The required expressions for mixtures of lognormal and gamma densities are provided; in our empirical work we focus on estimation of mixtures of lognormal distributions. Two- and three-component lognormal mixtures are estimated for the income distributions of China rural, China urban, India rural, India urban, Pakistan, Russia, South Africa, Brazil and Indonesia. Their performance, in terms of goodness-of-fit and validity of moment conditions, is compared with that of a generalized beta (GB2) distribution. We find that the three-component lognormal mixture always outperforms the GB2 distribution, but the two-component mixture does not. For Brazil and Indonesia we have single observations, making it possible to compare maximum likelihood estimation of the mixtures from a complete set of single observations with GMM estimates obtained after grouping the data. Estimates from both procedures are found to be comparable, lending support to the usefulness of the GMM approach.
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- 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.
- 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.
- 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.
- Russell Davidson, 2009.
"Reliable inference for the GINI Index,"
- Hasegawa, Hikaru & Kozumi, Hideo, 2003. "Estimation of Lorenz curves: a Bayesian nonparametric approach," Journal of Econometrics, Elsevier, vol. 115(2), pages 277-291, August.
- Branko Milanovic, 2002.
"True World Income Distribution, 1988 and 1993: First Calculation Based on Household Surveys Alone,"
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.
- Duangkamon Chotikapanich & William E. Griffiths & D. S. Prasada Rao & Vicar Valencia, 2012. "Global Income Distributions and Inequality, 1993 and 2000: Incorporating Country-Level Inequality Modeled with Beta Distributions," The Review of Economics and Statistics, MIT Press, vol. 94(1), pages 52-73, February.
- Emmanuel Flachaire & Olivier Nunez, 2007.
"Estimation of income distribution and detection of subpopulations: an explanatory model,"
Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers)
- Emmanuel Flachaire & Olivier G. Núñez, 2003. "Estimation Of Income Distribution And Detection Of Subpopulations: An Explanatory Model," Statistics and Econometrics Working Papers ws030201, Universidad Carlos III, Departamento de Estadística y Econometría.
- Gholamreza Hajargsht, William E. Griffiths, Joseph Brice, D.S. Prasada Rao, Duangkamon Chotikapanich, 2012.
"Inference for Income Distributions Using Grouped Data,"
Department of Economics - Working Papers Series
1140, The University of Melbourne.
- 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, Taylor & Francis Journals, vol. 30(4), pages 563-575, May.
- Michel Lubrano & Abdoul Aziz Junior Ndoye, 2011. "Inequality decomposition using the Gibbs output of a Mixture of lognormal distributions," Working Papers halshs-00585248, HAL.
- 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.
- Flachaire, Emmanuel & Nunez, Olivier, 2007. "Estimation of the income distribution and detection of subpopulations: An explanatory model," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3368-3380, April.
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