Asymptotic and Bootstrap Inference for the Generalized Gini Indices

The Gini index represents a special case of the generalized Gini indices, which permit to choose a level of inequality aversion and to stress the different proportions of the income distribution. In order to apply these indices to income sample data, it is necessary to use reliable inferential procedures. In fact, also if often in income studies we have large samples for which the precision of estimates is not of primary interest, it has been noticed that, however, the standard errors are very high. Strengthened by these reasons, in this paper inferential procedures for generalized Gini indices are studied, specifically for Sand E-Gini indices, defined by means of the asymptotic distribution of their estimators and by the bootstrap method. To do this, the level of coverage of confidence intervals of the indices has been validated using Monte Carlo simulations, assuming as a model for the size distribution of incomes the generalized beta of the second kind, which is very flexible, with the ability to take a wide variety of shapes depending on particular values of its parameters.