Modeling of income and indicators of poverty and social exclusion using the Generalized Beta Distribution of the Second Kind
Date issued
December 2, 2014
In
Review of Income and Wealth
Vol
4
No
60
From page
821
To page
842
Reviewed by peer
1
Subjects
income distribution inequality maximum pseudo-likelihood estimation monetary indicators sandwich variance estimator
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 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.
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.
Publication type
journal article