DISCUSSION PAPERS IN STATISTICS AND ECONOMETRICS SEMINAR OF ECONOMIC AND SOCIAL STATISTICS UNIVERSITY OF COLOGNE No. 3/00 Statistical Inference for Tail Behaviour of Lorenz Curves

The appeal of the Lorenz dominance criterion is undermined by the fact that many sample Lorenz curves intersect in the tails. Tests for Lorenz dominance which ignore tails (such as those considering only deciles) are therefore invalidated. Moreover, the usual inferential methods, based on central limit theorem arguments, do not apply to the tails of the Lorenz curve since the tails contain too few observations. By contrast, we have proposed a test procedure, based on a domain of attraction assumption, which fully takes into account the tail behaviour of Lorenz curves. Our experiments and empirical examples demonstrate the success and usefulness of the proposed test: in many cases we are able to infer that despite sample tail crossings the population Lorenz curves do, in fact, exhibit Lorenz dominance.