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Consistent Nonparametric Tests for Lorenz Dominance

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  • Garry F. Barrett
  • Stephen G. Donald
  • Debopam Bhattacharya

Abstract

This article proposes consistent nonparametric methods for testing the null hypothesis of Lorenz dominance. The methods are based on a class of statistical functionals defined over the difference between the Lorenz curves for two samples of welfare-related variables. We present two specific test statistics belonging to the general class and derive their asymptotic properties. As the limiting distributions of the test statistics are nonstandard, we propose and justify bootstrap methods of inference. We provide methods appropriate for case where the two samples are independent as well as the case where the two samples represent different measures of welfare for one set of individuals. The small sample performance of the two tests is examined and compared in the context of a Monte Carlo study and an empirical analysis of income and consumption inequality.

Suggested Citation

  • Garry F. Barrett & Stephen G. Donald & Debopam Bhattacharya, 2014. "Consistent Nonparametric Tests for Lorenz Dominance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(1), pages 1-13, January.
  • Handle: RePEc:taf:jnlbes:v:32:y:2014:i:1:p:1-13
    DOI: 10.1080/07350015.2013.834262
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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. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
    3. 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.
    4. Anthony F. Shorrocks & James E. Foster, 1987. "Transfer Sensitive Inequality Measures," Review of Economic Studies, Oxford University Press, vol. 54(3), pages 485-497.
    5. 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.
    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. 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.
    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. 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.
    2. Mohamed Khaled & Paul Makdissi & Myra Yazbeck, 2016. "Income-Related Health Transfers Principles and Orderings of Joint Distributions of Income and Health," Discussion Papers Series 574, School of Economics, University of Queensland, Australia.
    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. Frank A. Cowell & Emmanuel Flachaire, 2014. "Statistical Methods for Distributional Analysis," Working Papers halshs-01115996, HAL.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Dhongde, Shatakshee, 2017. "Measuring Segregation of the Poor: Evidence from India," World Development, Elsevier, vol. 89(C), pages 111-123.
    11. 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.
    12. 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.
    13. 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.
    14. Andrews, Donald W.K. & Shi, Xiaoxia, 2017. "Inference based on many conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 196(2), pages 275-287.
    15. 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.
    16. Mussa, Richard, 2017. "To Err is Human: Inconsistencies in Food Conversion Factors and Inequality in Malawi," MPRA Paper 75981, University Library of Munich, Germany.
    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

    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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