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Consistent Nonparametric Tests for Lorenz Dominance

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  • 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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Bibliographic Info

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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Keywords: Lorenz dominance; test consistency; simulation.;

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References

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  1. 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.
  2. James Banks & Arie Kapteyn & James P. Smith & Arthur van Soest, 2004. "International Comparisons of Work Disability," Working Papers 155, RAND Corporation Publications Department.
  3. 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.
  4. 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.
  5. Beach, Charles M & Davidson, Russell, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," Review of Economic Studies, Wiley Blackwell, vol. 50(4), pages 723-35, October.
  6. 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.
  7. Shorrocks, Anthony F & Foster, James E, 1987. "Transfer Sensitive Inequality Measures," Review of Economic Studies, Wiley Blackwell, vol. 54(3), pages 485-97, July.
  8. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
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Citations

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Cited by:
  1. Stephen G. Donald & Yu‐Chin Hsu & Garry F. Barrett, 2012. "Incorporating covariates in the measurement of welfare and inequality: methods and applications," Econometrics Journal, Royal Economic Society, vol. 15(1), pages C1-C30, 02.
  2. Sotomayor, Orlando J., 2009. "Changes in the Distribution of Household Income in Brazil: The Role of Male and Female Earnings," World Development, Elsevier, vol. 37(10), pages 1706-1715, October.
  3. Luca Crivelli & Paola Salari, 2012. "Fiscal federalism and income redistribution through healthcare financing: An empirical analysis for the Swiss cantons," CEPRA working paper 1204, USI Università della Svizzera italiana.
  4. Susan Thorp & Hardy Hulley & Rebecca McKibbin & Andreas Pedersen, 2009. "Means-Tested Income Support, Portfolio Choice and Decumulation in Retirement," Research Paper Series 248, Quantitative Finance Research Centre, University of Technology, Sydney.
  5. Duangkamon Chotikapanich & William E. Griffiths, 2006. "Bayesian Assessment of Lorenz and Stochastic Dominance in Income Distributions," Department of Economics - Working Papers Series 960, The University of Melbourne.

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