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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.

Suggested Citation

  • Stephen G. Donald & Garry F. Barrett, 2004. "Consistent Nonparametric Tests for Lorenz Dominance," Econometric Society 2004 Australasian Meetings 321, Econometric Society.
  • Handle: RePEc:ecm:ausm04:321
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    References listed on IDEAS

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    1. 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.
    2. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    3. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
    4. Banks, J. & Kapteyn, A. & Smith, J.P. & van Soest, A.H.O., 2004. "International Comparisons of Work Disability," Discussion Paper 2004-36, Tilburg University, Center for Economic Research.
    5. Anthony F. Shorrocks & James E. Foster, 1987. "Transfer Sensitive Inequality Measures," Review of Economic Studies, Oxford University Press, vol. 54(3), pages 485-497.
    6. 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.
    7. 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.
    8. Charles M. Beach & Russell Davidson, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," Review of Economic Studies, Oxford University Press, vol. 50(4), pages 723-735.
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    Citations

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    Cited by:

    1. Firmin Doko Tchatoka & Robert Garrard & Virginie Masson, 2017. "Testing for Stochastic Dominance in Social Networks," School of Economics Working Papers 2017-02, University of Adelaide, School of Economics.
    2. Amy Beech & Rosetta Dollman & Richard Finlay & Gianni La Cava, 2014. "The Distribution of Household Spending in Australia," RBA Bulletin, Reserve Bank of Australia, pages 13-22, March.
    3. Dhongde, Shatakshee, 2017. "Measuring Segregation of the Poor: Evidence from India," World Development, Elsevier, vol. 89(C), pages 111-123.
    4. 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 1-30, February.
    5. 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.
    6. Khaled, Mohamad A. & Makdissi, Paul & Yazbeck, Myra, 2018. "Income-related health transfers principles and orderings of joint distributions of income and health," Journal of Health Economics, Elsevier, vol. 57(C), pages 315-331.
    7. 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.
    8. David Lander & David Gunawan & William Griffiths & Duangkamon Chotikapanich, 2017. "Bayesian assessment of Lorenz and stochastic dominance," Monash Econometrics and Business Statistics Working Papers 15/17, Monash University, Department of Econometrics and Business Statistics.
    9. Frank A. Cowell & Emmanuel Flachaire, 2014. "Statistical Methods for Distributional Analysis," Working Papers halshs-01115996, HAL.
    10. Andrews, Donald W.K. & Shi, Xiaoxia, 2017. "Inference based on many conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 196(2), pages 275-287.
    11. 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.
    12. Nianqing Liu & Yao Luo, 2014. "A Nonparametric Test of Exogenous Participation in First-Price Auctions," Working Papers tecipa-519, University of Toronto, Department of Economics.
    13. Mussa, Richard, 2017. "To Err is Human: Inconsistencies in Food Conversion Factors and Inequality in Malawi," MPRA Paper 75981, University Library of Munich, Germany.
    14. 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.
    15. David Lander & David Gunawan & William E. Griffiths & Duangkamon Chotikapanich, 2016. "Bayesian Assessment of Lorenz and Stochastic Dominance Using a Mixture of Gamma Densities," Department of Economics - Working Papers Series 2023, The University of Melbourne.
    16. David Lander & David Gunawan & William Griffiths & Duangkamon Chotikapanich, 2017. "Bayesian Assessment of Lorenz and Stochastic Dominance," Department of Economics - Working Papers Series 2029, The University of Melbourne.
    17. Barrett, Garry F. & Donald, Stephen G. & Hsu, Yu-Chin, 2016. "Consistent tests for poverty dominance relations," Journal of Econometrics, Elsevier, vol. 191(2), pages 360-373.

    More about this item

    Keywords

    Lorenz dominance; test consistency; simulation.;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution

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