Modeling of Income and Indicators of Poverty and Social Exclusion Using the Generalized Beta Distribution of the Second Kind

Abstract

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 E uropean U nion S tatistics on I ncome and L iving C onditions ( 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 ( GB 2). 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.