Consistent Nonparametric Tests for Lorenz Dominance

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Consistent Nonparametric Tests for Lorenz Dominance

Author Info

Stephen G. Donald
Garry F. Barrett

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.

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Paper provided by Econometric Society in its series Econometric Society 2004 Australasian Meetings with number 321.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:ausm04:321

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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution

This paper has been announced in the following NEP Reports:

NEP-ALL-2004-10-30 (All new papers)
NEP-ECM-2004-10-30 (Econometrics)

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Ryu, Hang K. & Slottje, Daniel J., 1996. "Two flexible functional form approaches for approximating the Lorenz curve," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 251-274. [Downloadable!] (restricted)
Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-30, March. [Downloadable!] (restricted)
Other versions:
- Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
Shorrocks, Anthony F & Foster, James E, 1987. "Transfer Sensitive Inequality Measures," Review of Economic Studies, Blackwell Publishing, vol. 54(3), pages 485-97, July. [Downloadable!] (restricted)
Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January. [Downloadable!] (restricted)
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 461-77, November. [Downloadable!] (restricted)
Beach, Charles M & Davidson, Russell, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," Review of Economic Studies, Blackwell Publishing, vol. 50(4), pages 723-35, October. [Downloadable!] (restricted)

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