Uses of Parametric Modelling of Income and Direct Estimates of Aggregate Income Indicators from EU-SILC Data and the Derived Synthetic Dataset AMELIA with Focus on the Generalized Beta Distribution of the Second Kind (GB2). Derivation of Design-Based Estimation
Monique Graf, Desislava Nedyalkova
Statistical Methods Unit, Swiss Federal Statistical Office, Neuchâtel, Switzerland

The reason why parametric estimation may be useful, when empirical data and estimators are available is threefold: 1. to stabilize estimation; 2. to get insight into the relationships between the characteristics of the theoretical distribution and a set of indicators, e.g. by sensitivity plots; 3. to deduce the whole distribution from known empirical indicators, when the raw data are not available. The talk will address these points and convey the experiences done within the AMELI project on the parametric estimation of the EU-SILC monetary indicators.

Special emphasis will be laid on the Generalized Beta distribution of the second kind (GB2), derived by McDonald (1984). Apart from the scale parameter, this distribution has three shape parameters: the first governing the overall shape, the second the lower tail and the third the upper tail of the distribution. These characteristics give to the GB2 a large flexibility for fitting a wide range of empirical distributions and it has been established that it outperforms other four-parameter distributions for income data (Kleiber and Kotz, 2003). We have studied different types of estimation methods, taking into account the design features of the EU-SILC surveys. Pseudo-maximum likelihood estimation of the parameters is compared with a nonlinear fit from the indicators. Variance estimation is done by linearization and different types of simplified formulas for the variance proposed in the litterature are evaluated by simulation. The computations are made on the synthetic universe AMELIA constructed from the EU-SILC data (Muennich et al., 2010) and the simulation is done with the R package SimFrame (Templ et al., 2010). Both AMELIA and SimFrame are developped in the context of the AMELI project. The parametric methods we have developped are made available in the R package GB2, which is part of the output of the AMELI project.

Keywords: Income data; Monetary indicators; Parametric distribution; generalized beta distribution of the second kind; Design-based variance estimation

Biography: Monique Graf leads a group of experts in statistical methods at the Swiss Federal Statistical Office. The group is part of the Statistical methods unit and is involved in the statistical consulting for the Office, as well as for other offices at the federal and regional level. Research and development are also duties of the statistical methods unit. Monique is responsible for several Work packages in the FP7 AMELI project and will speak about the research conducted by the statistical methods team.