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Testing for restricted stochastic dominance: some further results

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  • Russell Davidson

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique, CIREQ - Centre interuniversitaire de recherche en économie quantitative, Department of Economics [Montréal] - McGill University = Université McGill [Montréal, Canada])

Abstract

Extensions are presented to the results of Davidson and Duclos (2007), whereby the null hypothesis of restricted stochastic non dominance can be tested by both asymptotic and bootstrap tests, the latter having considerably better properties as regards both size and power. In this paper, the methodology is extended to tests of higherorder stochastic dominance. It is seen that, unlike the first-order case, a numerical nonlinear optimisation problem has to be solved in order to construct the bootstrap DGP. Conditions are provided for a solution to exist for this problem, and efficient numerical algorithms are laid out. The empirically important case in which the samples to be compared are correlated is also treated, both for first-order and for higher-order dominance. For all of these extensions, the bootstrap algorithm is presented. Simulation experiments show that the bootstrap tests perform considerably better than asymptotic tests, and yield reliable inference in moderately sized samples.

Suggested Citation

  • Russell Davidson, 2009. "Testing for restricted stochastic dominance: some further results," Working Papers halshs-00443556, HAL.
    • Handle: RePEc:hal:wpaper:halshs-00443556
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00443556
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    Cited by:

    1. Frank A. Cowell & Emmanuel Flachaire, 2014. "Statistical Methods for Distributional Analysis," Working Papers halshs-01115996, HAL.
    2. Russell Davidson & Jean-Yves Duclos, 2013. "Testing for Restricted Stochastic Dominance," Econometric Reviews, Taylor & Francis Journals, vol. 32(1), pages 84-125, January.
    3. Dirk Van de gaer & Joost Vandenbossche & José Luis Figueroa, 2014. "Children's Health Opportunities and Project Evaluation: Mexico's Oportunidades Program," The World Bank Economic Review, World Bank, vol. 28(2), pages 282-310.
    4. Branko Milanovic & Mauricio Apablaza & Florent Bresson & Gaston Yalonetzky, 2016. "When More Does Not Necessarily Mean Better: Health-Related Illfare Comparisons with Non-Monotone Well-Being Relationships," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 62, pages 145-178, August.
    5. Russell Davidson, 2010. "Innis Lecture: Inference on income distributions," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 43(4), pages 1122-1148, November.
    6. Stengos, Thanasis & Thompson, Brennan S., 2012. "Testing for bivariate stochastic dominance using inequality restrictions," Economics Letters, Elsevier, vol. 115(1), pages 60-62.
    7. Yélé Maweki Batana & Jean-Yves Duclos, 2010. "Comparing Multidimensional Poverty with Qualitative Indicators of Well-Being," Cahiers de recherche 1004, CIRPEE.
    8. George M. Constantinides & Michal Czerwonko & Stylianos Perrakis, 2020. "Mispriced index option portfolios," Financial Management, Financial Management Association International, vol. 49(2), pages 297-330, June.
    9. Arvanitis, Stelios & Post, Thierry & Potì, Valerio & Karabati, Selcuk, 2021. "Nonparametric tests for Optimal Predictive Ability," International Journal of Forecasting, Elsevier, vol. 37(2), pages 881-898.
    10. Kolokolova, Olga & Le Courtois, Olivier & Xu, Xia, 2022. "Is the index efficient? A worldwide tour with stochastic dominance," Journal of Financial Markets, Elsevier, vol. 59(PB).
    11. James E. Hodder & Jens Carsten Jackwerth & Olga Kolokolova, 2015. "Improved Portfolio Choice Using Second-Order Stochastic Dominance," Review of Finance, European Finance Association, vol. 19(4), pages 1623-1647.
    12. Hsu, Justine & Majdzadeh, Reza & Mills, Anne & Hanson, Kara, 2021. "A dominance approach to analyze the incidence of catastrophic health expenditures in Iran," Social Science & Medicine, Elsevier, vol. 285(C).
    13. Nguyen, Duc Khuong & Topaloglou, Nikolas & Walther, Thomas, 2020. "Asset Classes and Portfolio Diversification: Evidence from a Stochastic Spanning Approach," MPRA Paper 103870, University Library of Munich, Germany.
    14. Barrera-Osorio, Felipe & Raju, Dhushyanth, 2010. "Short-run learning dynamics under a test-based accountability system : evidence from Pakistan," Policy Research Working Paper Series 5465, The World Bank.
    15. Thierry Post & Iňaki Rodríguez Longarela, 2021. "Risk Arbitrage Opportunities for Stock Index Options," Operations Research, INFORMS, vol. 69(1), pages 100-113, January.
    16. George M. Constantinides & Michal Czerwonko & Jens Carsten Jackwerth & Stylianos Perrakis, 2011. "Are Options on Index Futures Profitable for Risk‐Averse Investors? Empirical Evidence," Journal of Finance, American Finance Association, vol. 66(4), pages 1407-1437, August.
    17. Liesiö, Juuso & Xu, Peng & Kuosmanen, Timo, 2020. "Portfolio diversification based on stochastic dominance under incomplete probability information," European Journal of Operational Research, Elsevier, vol. 286(2), pages 755-768.
    18. Brendan K. Beare & Juwon Seo & Zhongxi Zheng, 2022. "Stochastic arbitrage with market index options," Papers 2207.00949, arXiv.org, revised May 2024.
    19. Kolokolova, Olga & Xu, Xia, 2024. "Enhancing betting against beta with stochastic dominance," Journal of Empirical Finance, Elsevier, vol. 76(C).

    More about this item

    Keywords

    Higher-order stochastic dominance; empirical likelihood; bootstrap test; correlated samples;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • I32 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Measurement and Analysis of Poverty

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