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Improved Nonparametric Bootstrap Tests of Lorenz Dominance

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  • Zhenting Sun
  • Brendan K. Beare

Abstract

One income or wealth distribution is said to Lorenz dominate another when the Lorenz curve for the former is nowhere below that of the latter, indicating a (weakly) more equitable allocation of resources. Existing tests of the null of Lorenz dominance based on pairs of samples of income or wealth achieve the nominal rejection rate asymptotically when the two Lorenz curves are equal, but are conservative at other null configurations. We propose new nonparametric bootstrap tests of Lorenz dominance based on preliminary estimation of a contact set. Our tests achieve the nominal rejection rate asymptotically on the boundary of the null; that is, when Lorenz dominance is satisfied, and the Lorenz curves coincide on some interval. Numerical simulations indicate that our tests enjoy substantially improved power compared to existing procedures at relevant sample sizes. Supplementary materials for this article are available online.

Suggested Citation

  • Zhenting Sun & Brendan K. Beare, 2021. "Improved Nonparametric Bootstrap Tests of Lorenz Dominance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(1), pages 189-199, January.
    • Handle: RePEc:taf:jnlbes:v:39:y:2021:i:1:p:189-199
    DOI: 10.1080/07350015.2019.1647214
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    Citations

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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. Hongyi Jiang & Zhenting Sun & Shiyun Hu, 2023. "A Nonparametric Test of $m$th-degree Inverse Stochastic Dominance," Papers 2306.12271, arXiv.org, revised Jul 2023.
    3. Sun, Zhenting, 2023. "Instrument validity for heterogeneous causal effects," Journal of Econometrics, Elsevier, vol. 237(2).
    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. Hongyi Jiang & Zhenting Sun, 2023. "Testing Partial Instrument Monotonicity," Papers 2308.08390, arXiv.org, revised Aug 2023.
    6. Brendan K. Beare & Jackson D. Clarke, 2022. "Modified Wilcoxon-Mann-Whitney tests of stochastic dominance," Papers 2210.08892, arXiv.org.
    7. Jiang, Hongyi & Sun, Zhenting, 2023. "Testing partial instrument monotonicity," Economics Letters, Elsevier, vol. 233(C).
    8. Amparo Ba'illo & Javier C'arcamo & Carlos Mora-Corral, 2024. "Tests for almost stochastic dominance," Papers 2403.15258, arXiv.org.
    9. Xiaojun Song & Zhenting Sun, 2023. "Almost Dominance: Inference and Application," Papers 2312.02288, arXiv.org.
    10. Zhenting Sun & Kaspar Wuthrich, 2022. "Pairwise Valid Instruments," Papers 2203.08050, arXiv.org, revised Jan 2024.

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