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A nonparametric test of mth-degree inverse stochastic dominance

Author

Listed:
  • Jiang, Hongyi
  • Sun, Zhenting
  • Hu, Shiyun

Abstract

This paper proposes a nonparametric test for mth-degree inverse stochastic dominance which is a powerful tool for ranking distribution functions according to social welfare. We construct the test based on empirical process theory. The test is shown to be asymptotically size controlled and consistent. The good finite sample properties of the test are illustrated via Monte Carlo simulations. We apply our test to the inequality growth in the United Kingdom from 1995 to 2010, and obtain a more complete ranking of the income distributions.

Suggested Citation

  • Jiang, Hongyi & Sun, Zhenting & Hu, Shiyun, 2024. "A nonparametric test of mth-degree inverse stochastic dominance," Economics Letters, Elsevier, vol. 244(C).
    • Handle: RePEc:eee:ecolet:v:244:y:2024:i:c:s0165176524004622
    DOI: 10.1016/j.econlet.2024.111978
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    References listed on IDEAS

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    1. Zhenting Sun, 2020. "Instrument Validity for Heterogeneous Causal Effects," Papers 2009.01995, arXiv.org, revised Oct 2023.
    2. Xingyu Li & Xiaojun Song & Zhenting Sun, 2022. "Unified Inference on Moment Restrictions with Nuisance Parameters," Papers 2202.11031, arXiv.org, revised Dec 2025.
    3. Beare, Brendan K., 2012. "Archimedean Copulas And Temporal Dependence," Econometric Theory, Cambridge University Press, vol. 28(6), pages 1165-1185, December.
    4. Francesco Andreoli, 2018. "Robust Inference for Inverse Stochastic Dominance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 146-159, January.
    5. Zheng Fang & Andres Santos, 2019. "Inference on Directionally Differentiable Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(1), pages 377-412.
    6. Brendan K. Beare, 2010. "Copulas and Temporal Dependence," Econometrica, Econometric Society, vol. 78(1), pages 395-410, January.
    7. Richard Blundell & Ben Etheridge, 2010. "Consumption, Income and Earnings Inequality in Britain," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 13(1), pages 76-102, January.
    8. Sun, Zhenting, 2023. "Instrument validity for heterogeneous causal effects," Journal of Econometrics, Elsevier, vol. 237(2).
    9. Rolf Aaberge & Tarjei Havnes & Magne Mogstad, 2021. "Ranking intersecting distribution functions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(6), pages 639-662, September.
    10. Muliere, Pietro & Scarsini, Marco, 1989. "A note on stochastic dominance and inequality measures," Journal of Economic Theory, Elsevier, vol. 49(2), pages 314-323, December.
    11. Beare, Brendan K. & Shi, Xiaoxia, 2019. "An improved bootstrap test of density ratio ordering," Econometrics and Statistics, Elsevier, vol. 10(C), pages 9-26.
    12. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    13. 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.
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    Full references (including those not matched with items on IDEAS)

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    Keywords

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    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

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