Consistent Nonparametric Tests for Lorenz Dominance

Stephen G. Donald and Garry F. Barrett

No 321, Econometric Society 2004 Australasian Meetings from Econometric Society

Abstract: This paper proposes a test for Lorenz dominance. Given independent samples of income or other welfare related variable, we propose a test of the null hypothesis that the Lorenz curve for one population is dominated by the Lorenz curve for a second population. The test statistic is based on the standardized largest difference between the empirical Lorenz curves for the two samples. The test is nonparametric in the sense that no distributional assumptions are made and the test is consistent because it compares the Lorenz curves at all quantiles. We derive the asymptotic distribution of the test statistic under the null hypothesis. Since the limiting distribution of the test statistic is nonstandard, being dependent on the underlying Lorenz curves, we propose the use of two computer based procedures for conducting inference. The first is a simulation method that simulates p-values from an approximation to the underlying limiting distribution of the statistic while the second is based on the nonparametric bootstrap. We examine the performance of the methods in a Monte Carlo study and with a comparison of the income based Lorenz curves for the US and Canada.

Keywords: Lorenz dominance; test consistency; simulation. (search for similar items in EconPapers)
JEL-codes: C12 C14 D31 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2004-08-11
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