Inference Methods on Income Inequality and Tax Progressivity Indices: An empirical application to Spanish data

This paper applies asymptotic and bootstrap inference methods for a set of non-linear inequality and progressivity indices. The non-degenerate U-statistic theory is applied to indices which are functions of several U-statistics. Generally, U-statistic variance estimators are difficult to compute. Formulae for a straightforward plug-in estimator of index variances have been derived. This is especially relevant for those indices whose asymptotic variances contain functionals with kernels of degree >=2. As far as inference issues are concerned, bootstrap methods appear to be favourable. Our results show that bootstrap-t performs more accurately, but an analytical estimation of the index variance is still necessary for this method to be practical. An empirical application has been made for the Spanish Tax and Welfare System. We distinguish clear dominance of cash-benefits on income redistribution. Public health and State school education also have significant redistributive effects.