Asymptotic and bootstrap inference for the generalized Gini indices

摘要

The Gini index represents a special case of the generalized Gini indices, which allow 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, even 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 standard errors are very high. Motivated by these reasons, in this paper inferential procedures for generalized Gini indices are studied, specifically for S- and E-Gini indices, defined by means of the asymptotic distribution of their estimators and using bootstrap technique. 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.