GMM Estimation of Mixtures from Grouped Data:
AbstractWe 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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Bibliographic InfoPaper provided by The University of Melbourne in its series Department of Economics - Working Papers Series with number 1148.
Length: 32 pages
Date of creation: 2012
Date of revision:
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Lognormal distribution; Generalized beta distribution; Inequality measures;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-07-23 (All new papers)
- NEP-CIS-2012-07-23 (Confederation of Independent States)
- NEP-ECM-2012-07-23 (Econometrics)
- NEP-SEA-2012-07-23 (South East Asia)
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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Statistics and Econometrics Working Papers
ws030201, Universidad Carlos III, Departamento de Estadística y Econometría.
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