Partial Horizontal Inequity Orderings: A non-parametric Approach

We provide a partial ordering view of horizontal inequity (henceforth HI), based on the Lorenz criterion, associated with different post-tax income distributions and a (bistochastic) nonparametric estimated benchmark distribution. As a consequence, several measures consistent with the Lorenz criterion can be rationalized. In addition, we establish the so-called horizontal inequity transfer principle, which imposes a normative minimum requirement that any HI measure must satisfy. Our proposed HI ordering is consistent with this principle. Moreover, we adopt a cardinal view to decompose the total effect of a tax system into a welfare gain due to HI-free income redistribution and a welfare loss due to HI, without any additive decomposable restriction on the indices. Hence, more robust tests can be applied. Other decompositions in the literature are seen as particular cases.