Asymptotically Distribution-Free Statistical Test for Generalized Lorenz Curves: An Alternative Approach

  • Kuan Xu


A generalized Lorenz (GL) curve differs from a Lorenz curve in that the former is a rescaled version of the latter. A GL curve represents the relationship between the average income computed from a cumulative percentage of the populations and the corresponding cumulative percentage. GL dominance is a useful criterion for ranking GL curves either for an economy over time or for a number of economies at one point in time. Relative to a dominated GL curve, a dominating GL curve indicates both that total income for the population is higher and that it is more equally distributed. Hence, it is obviously more desirable in a certain social sense. While sound statistical tests are essential for making statistical inference about GL dominance from sample GL curve estimates, the lack of suitable joint test procedure for GL dominance is an unsolved problem in income distribution literature. This paper aims at solving this problem and provides an illustrative empirical example to show how to apply this test procedure in empirical research.