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Keywords:

  • C13;
  • C46;
  • D63
  • income distribution;
  • inequality;
  • 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.