Inference on Income Inequality and Tax Progressivity Indices: U-Statistics and Bootstrap Methods

This paper discusses asymptotic and bootstrap inference methods for a set of inequality and progressivity indices. The application of non-degenerate U-statistics theory is described, particularly through the derivation of the Suits-progressivity index distribution. We have also provided formulae for the “plug-in” estimator of the index variances, which are less onerous than the U-statistic version (this is especially relevant for those indices whose asymptotic variances contain kernels of degree 3). As far as inference issues are concerned, there are arguments in favour of applying bootstrap methods. By using an accurate database on income and taxes of the Spanish households (statistical matching EPF90-IRPF90), our results show that bootstrap methods perform better (considering their sample precision), particularly those methods yielding asymmetric CI. We also show that the bootstrap method is a useful technique for Lorenz dominance analysis. An illustration of such application has been made for the Spanish tax and welfare system. We distinguish clear dominance of cashbenefits on income redistribution. Public health and state school education also have significant redistributive effects.