Statistical Inference for the Measurement of the Incidences of Taxes and Transfers

We establish the asymptotic sampling distribution of general functions of quantile-based estimators computed from samples that are not necessarily independent. The results provide the statistical framework within which to assess the progressivity of taxes and benefits, their horizontal inequity, and the change in the inequality of income which they cause. By the same token, these findings characterise the sampling distribution of a number of popular indices of progressivity, horizontal inequity, and redistribution. They can also be used to assess welfare and inequality changes using panel data, and to assess poverty when it depends on estimated population quantiles. We illustrate these results using micro data on the incidence of taxes and benefits in Canada.