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Improving the Power of Tests of Stochastic Dominance

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Abstract

We extend Hansen’s (2005) recentering method to a continuum of inequality constraints to construct new Kolmogorov-Smirnov tests for stochastic dominance of any pre-specified order. We show that our tests have correct size asymptotically, are consistent against fixed alternatives and are unbiased against some N−1/2 local alternatives. It is shown that by avoiding the use of the least favorable configuration, our tests are less conservative and more powerful than Barrett and Donald’s (2003) and in some simulation examples we consider, we find that our test can be more powerful than the subsampling test of Linton, Maasoumi and Whang (2005). We apply our method to test stochastic dominance relations between Canadian income distributions in 1978 and 1986 as considered in Barrett and Donald (2003) and find that some of the hypothesis test results are different using the new method.

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  • Stephen G. Donald & Yu-Chin Hsu, 2012. "Improving the Power of Tests of Stochastic Dominance," IEAS Working Paper : academic research 12-A015, Institute of Economics, Academia Sinica, Taipei, Taiwan, revised Jun 2013.
    • Handle: RePEc:sin:wpaper:12-a015
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    File URL: https://www.econ.sinica.edu.tw/~econ/pdfPaper/12-A015.pdf
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    Cited by:

    1. Chang, Chia-Lin & Jimenez-Martin, Juan-Angel & Maasoumi, Esfandiar & McAleer, Michael & Pérez-Amaral, Teodosio, 2019. "Choosing expected shortfall over VaR in Basel III using stochastic dominance," International Review of Economics & Finance, Elsevier, vol. 60(C), pages 95-113.
    2. Yoichi Arai & Yu‐Chin Hsu & Toru Kitagawa & Ismael Mourifié & Yuanyuan Wan, 2022. "Testing identifying assumptions in fuzzy regression discontinuity designs," Quantitative Economics, Econometric Society, vol. 13(1), pages 1-28, January.
    3. Toru Kitagawa & Aleksey Tetenov, 2018. "Who Should Be Treated? Empirical Welfare Maximization Methods for Treatment Choice," Econometrica, Econometric Society, vol. 86(2), pages 591-616, March.
    4. Goldman, Matt & Kaplan, David M., 2018. "Comparing distributions by multiple testing across quantiles or CDF values," Journal of Econometrics, Elsevier, vol. 206(1), pages 143-166.
    5. Chang, Chia-Lin & Jiménez-Martín, Juan-Ángel & Maasoumi, Esfandiar & Pérez-Amaral, Teodosio, 2015. "A stochastic dominance approach to financial risk management strategies," Journal of Econometrics, Elsevier, vol. 187(2), pages 472-485.
    6. Lok, Thomas M. & Tabri, Rami V., 2021. "An improved bootstrap test for restricted stochastic dominance," Journal of Econometrics, Elsevier, vol. 224(2), pages 371-393.
    7. David Lander & David Gunawan & William Griffiths & Duangkamon Chotikapanich, 2020. "Bayesian assessment of Lorenz and stochastic dominance," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 53(2), pages 767-799, May.
    8. 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.
    9. Chia-Lin Chang & Juan-Ángel Jiménez-Martín & Esfandiar Maasoumi & Michael McAleer & Teodosio Pérez-Amaral, 2015. "A Stochastic Dominance Approach to the Basel III Dilemma: Expected Shortfall or VaR?," Documentos de Trabajo del ICAE 2015-16, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    10. Beare, Brendan K. & Shi, Xiaoxia, 2019. "An improved bootstrap test of density ratio ordering," Econometrics and Statistics, Elsevier, vol. 10(C), pages 9-26.
    11. Arvanitis, Stelios & Topaloglou, Nikolas, 2017. "Testing for prospect and Markowitz stochastic dominance efficiency," Journal of Econometrics, Elsevier, vol. 198(2), pages 253-270.
    12. Chung, D. & Linton, O. & Whang Y-J., 2021. "Consistent Testing for an Implication of Supermodular Dominance," Cambridge Working Papers in Economics 2134, Faculty of Economics, University of Cambridge.
    13. Goldman, Matt & Kaplan, David M., 2018. "Comparing distributions by multiple testing across quantiles or CDF values," Journal of Econometrics, Elsevier, vol. 206(1), pages 143-166.
    14. Yu‐Chin Hsu & Shu Shen, 2021. "Testing monotonicity of conditional treatment effects under regression discontinuity designs," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(3), pages 346-366, April.
    15. Hsu, Yu-Chin & Shen, Shu, 2019. "Testing treatment effect heterogeneity in regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 208(2), pages 468-486.
    16. Yu-Chin Hsu & Robert P. Lieli, 2021. "Inference for ROC Curves Based on Estimated Predictive Indices," Papers 2112.01772, arXiv.org.
    17. Brendan K. Beare & Jackson D. Clarke, 2022. "Modified Wilcoxon-Mann-Whitney tests of stochastic dominance," Papers 2210.08892, arXiv.org.
    18. 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.
    19. Yu-Chin Hsu & Martin Huber & Ying-Ying Lee & Chu-An Liu, 2021. "Testing Monotonicity of Mean Potential Outcomes in a Continuous Treatment with High-Dimensional Data," Papers 2106.04237, arXiv.org, revised Aug 2022.
    20. 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.
    21. Toru Kitagawa & Aleksey Tetenov, 2017. "Who should be treated? Empirical welfare maximization methods for treatment choice," CeMMAP working papers 24/17, Institute for Fiscal Studies.
    22. Chuang, O-Chia & Kuan, Chung-Ming & Tzeng, Larry Y., 2017. "Testing for central dominance: Method and application," Journal of Econometrics, Elsevier, vol. 196(2), pages 368-378.
    23. Mariusz Górajski & Zbigniew Kuchta, 2022. "Which hallmarks of optimal monetary policy rules matter in Poland? A stochastic dominance approach," Bank i Kredyt, Narodowy Bank Polski, vol. 53(2), pages 149-182.

    More about this item

    Keywords

    Stochastic dominance; test consistency; simulation; bootstrap; uniform inference;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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