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Almost Lorenz dominance

Author

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  • Buhong Zheng

    (University of Colorado Denver)

Abstract

This paper extends Leshno and Levy’s (Manag Sci 48:1074–1085, 2002) approach of “almost stochastic dominance” to inequality orderings. We define and characterize the notion of “almost Lorenz dominance” (ALD) and illustrate it with the US income data. An income distribution is said to “almost” Lorenz dominate another distribution when its Lorenz curve lies almost everywhere but not entirely above the other Lorenz curve. We show that this condition is equivalent to requiring that “almost” all Gini-type inequality measures rank the former distribution to have less inequality than the latter distribution; the condition on the Gini-type inequality measures has a clear interpretation and is easy to apply. We further define an almost composite transfer (ACT) and show that ALD amounts to a sequential application of such transfers. The empirical illustration with the US income data (1967–1986) demonstrates the utility of this generalized notion of inequality ordering.

Suggested Citation

  • Buhong Zheng, 2018. "Almost Lorenz dominance," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(1), pages 51-63, June.
    • Handle: RePEc:spr:sochwe:v:51:y:2018:i:1:d:10.1007_s00355-017-1106-0
    DOI: 10.1007/s00355-017-1106-0
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    References listed on IDEAS

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    Cited by:

    1. Yang Wei & Zhouping Li & Yunqiu Dai, 2022. "Unified smoothed jackknife empirical likelihood tests for comparing income inequality indices," Statistical Papers, Springer, vol. 63(5), pages 1415-1475, October.
    2. Louis Chauvel, 2023. "Isograph and LaSiPiKa Distribution: The Comparative Morphology of Income Inequalities and Intelligible Parameters of 53 LIS Countries 1967-2020," LIS Working papers 852, LIS Cross-National Data Center in Luxembourg.
    3. Buhong Zheng, 2021. "Stochastic dominance and decomposable measures of inequality and poverty," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(2), pages 228-247, April.
    4. Amparo Ba'illo & Javier C'arcamo & Carlos Mora-Corral, 2021. "Extremal points of Lorenz curves and applications to inequality analysis," Papers 2103.03286, arXiv.org.
    5. Tzu-Ying Chen & Yi-Hsin Elsa Hsu & Rachel J. Huang & Larry Y. Tzeng, 2021. "Making socioeconomic health inequality comparisons when health concentration curves intersect," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(4), pages 875-899, November.
    6. John A. Bishop & Haiyong Liu & Lester A. Zeager & Yizhen Zhao, 2020. "Revisiting macroeconomic activity and income distribution in the USA," Empirical Economics, Springer, vol. 59(3), pages 1107-1125, September.
    7. Amparo Ba'illo & Javier C'arcamo & Carlos Mora-Corral, 2024. "Tests for almost stochastic dominance," Papers 2403.15258, arXiv.org.
    8. Xiaojun Song & Zhenting Sun, 2023. "Almost Dominance: Inference and Application," Papers 2312.02288, arXiv.org.

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