Note: This research was conducted at the Swiss Federal Statistical Office and was partly funded by the FP7-SSH-2007-217322 AMELI Research Project.
Modeling of Income and Indicators of Poverty and Social Exclusion Using the Generalized Beta Distribution of the Second Kind
Version of Record online: 15 APR 2013
© 2013 International Association for Research in Income and Wealth
Review of Income and Wealth
Volume 60, Issue 4, pages 821–842, December 2014
How to Cite
Graf, M. and Nedyalkova, D. (2014), Modeling of Income and Indicators of Poverty and Social Exclusion Using the Generalized Beta Distribution of the Second Kind. Review of Income and Wealth, 60: 821–842. doi: 10.1111/roiw.12031
- Issue online: 9 NOV 2014
- Version of Record online: 15 APR 2013
- AMELI Research Project. Grant Number: FP7-SSH-2007-217322
- income distribution;
- maximum pseudo-likelihood estimation;
- monetary indicators;
- sandwich variance estimator
There are three reasons why estimation of parametric income distributions may be useful when empirical data and estimators are available: to stabilize estimation; to gain insight into the relationships between the characteristics of the theoretical distribution and a set of indicators, e.g. by sensitivity plots; and to deduce the whole distribution from known empirical indicators, when the raw data are not available. The European Union Statistics on Income and Living Conditions (EU-SILC) survey is used to address these issues. In order to model the income distribution, we consider the generalized beta distribution of the second kind (GB2). A pseudo-likelihood approach for fitting the distribution is considered, which takes into account the design features of the EU-SILC survey. An ad-hoc procedure for robustification of the sampling weights, which improves estimation, is presented. This method is compared to a non-linear fit from the indicators. Variance estimation within a complex survey setting of the maximum pseudo-likelihood estimates is done by linearization (a sandwich variance estimator), and a simplified formula for the sandwich variance, which accounts for clustering, is given. Performance of the fit and estimated indicators is evaluated graphically and numerically.