GMM Estimation of Income Distributions from Grouped Data

We develop a GMM procedure for estimating income distributions from grouped data with unknown group bounds. The approach enables us to obtain standard errors for the estimated parameters and functions of the parameters, such as inequality and poverty measures, and to test the validity of an assumed distribution using a J-test. 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. This work extends earlier work (Chotikapanich et al., 2007, 2012) that did not specify a formal GMM framework, did not provide methodology for obtaining standard errors, and considered only the beta-2 distribution. The results show that generalized beta distribution fits the data well and outperforms other frequently used distributions.