Estimation of Standard Errors of Selected Income Concentration Measures

            Measures of concentration are often used in the analysis of income and wage size distributions.  They are basic tools in the investigations concerning  poverty and  social welfare issues. They can also be helpful to analyze the efficiency of a tax policy or to measure the level of social stratification and polarization.  Among many income inequality measures the Gini and Zenga coefficients  are of the greatest importance. Unfortunately the standard errors of these measures, being actually sample statistics,  are rarely reported in practice.

       Estimators of many concentration coefficients are nonlinear thus their standard errors cannot  be obtained easily . The methods of variance estimation that can solve this problem include: various replication techniques, Taylor expansion and some parametric procedures based on income distribution models.

       In the paper some variance estimation methods for Gini and Zenga concentration measures are presented together with their application to the analysis of income distributions in Poland by socio-economic groups and by regions. The basis for the calculations was individual data coming from the Household Budget Survey conducted by Central Statistical Office. The variance estimates were obtained by means of the bootstrap and the parametric approach based on the Dagum model.