Consistent Nonparametric Tests for Lorenz Dominance
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.
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2004-36, Tilburg University, Center for Economic Research.
- Banks, James & Kapteyn, Arie & Smith, James P. & van Soest, Arthur, 2004. "International Comparisons of Work Disability," IZA Discussion Papers 1118, Institute for the Study of Labor (IZA).
- James Banks & Arie Kapteyn & James P. Smith & Arthur van Soest, 2004. "International Comparisons of Work Disability," Working Papers 155, RAND Corporation.
- Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
- Barrett, Garry F. & Donald, Stephen G., 2009. "Statistical Inference with Generalized Gini Indices of Inequality, Poverty, and Welfare," Journal of Business & Economic Statistics, American Statistical Association, vol. 27, pages 1-17.
- Bishop, John A & Formby, John P & Smith, W James, 1991. "International Comparisons of Income Inequality: Tests for Lorenz Dominance across Nine Countries," Economica, London School of Economics and Political Science, vol. 58(232), pages 461-477, November.
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