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Stochastic Dominance with Ordinal Variables: Conditions and a Test

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  • Gaston Yalonetzky

Abstract

A re-emerging literature on robustness in multidimensional welfare and poverty comparisons has revived interest in multidimensional stochastic dominance. Considering the widespread use of ordinal variables in wellbeing measurement, and particularly in composite indices, I derive multivariate stochastic dominance conditions for ordinal variables. These are the analogues of the conditions for continuous variables (e.g., Bawa, 1975, and Atkinson and Bourguignon, 1982). The article also derives mixed-order-of-dominance conditions for any type of variable. Then I propose an extension of Anderson's nonparametric test in order to test these conditions for ordinal variables. In addition, I propose the use of vectors and matrices of positions in order to handle multivariate, multinomial distributions. An empirical application to multidimensional wellbeing in Peru illustrates these tests.

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  • Gaston Yalonetzky, 2013. "Stochastic Dominance with Ordinal Variables: Conditions and a Test," Econometric Reviews, Taylor & Francis Journals, vol. 32(1), pages 126-163, January.
    • Handle: RePEc:taf:emetrv:v:32:y:2013:i:1:p:126-163
    DOI: 10.1080/07474938.2012.690653
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    References listed on IDEAS

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    1. Sen, Amartya, 2001. "Development as Freedom," OUP Catalogue, Oxford University Press, number 9780192893307.
    2. Bram Thuysbaert & Ricardas Zitikis, 2005. "Consistent Testing for Poverty Dominance," WIDER Working Paper Series RP2005-64, World Institute for Development Economic Research (UNU-WIDER).
    3. Suman Seth, 2009. "A Class of Association Sensitive Multidimensional Welfare Indices," OPHI Working Papers 27, Queen Elizabeth House, University of Oxford.
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    5. Ian Crawford, 2005. "A nonparametric test of stochastic dominance in multivariate distributions," School of Economics Discussion Papers 1205, School of Economics, University of Surrey.
    6. James Foster & Mark McGillivray & Suman Seth, 2009. "Rank Robustness of Composite Indices," OPHI Working Papers 26, Queen Elizabeth House, University of Oxford.
    7. Martin Ravallion, 2012. "Mashup Indices of Development," The World Bank Research Observer, World Bank, vol. 27(1), pages 1-32, February.
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    Cited by:

    1. David M Kaplan & Wei Zhao, 2023. "Comparing latent inequality with ordinal data," The Econometrics Journal, Royal Economic Society, vol. 26(2), pages 189-214.
    2. Gunawan, David & Griffiths, William E. & Chotikapanich, Duangkamon, 2018. "Bayesian inference for health inequality and welfare using qualitative data," Economics Letters, Elsevier, vol. 162(C), pages 76-80.
    3. Martyna Kobus & Radosław Kurek, 2019. "Multidimensional polarization for ordinal data," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 17(3), pages 301-317, September.
    4. Andrew Jones & John Roemer & Pedro Rosa Dias, 2014. "Equalising opportunities in health through educational policy," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(3), pages 521-545, October.
    5. Gaston Yalonetzky, 2012. "Poverty measurement with ordinal variables: A generalization of a recent contribution," Working Papers 246, ECINEQ, Society for the Study of Economic Inequality.
    6. M. Azhar Hussain & Nikolaj Siersbæk & Lars Peter Østerdal, 2020. "Multidimensional welfare comparisons of EU member states before, during, and after the financial crisis: a dominance approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(4), pages 645-686, December.
    7. Mehmet Pinar & Thanasis Stengos & Nikolas Topaloglou, 2022. "Stochastic dominance spanning and augmenting the human development index with institutional quality," Annals of Operations Research, Springer, vol. 315(1), pages 341-369, August.
    8. Raymond Elikplim Kofinti & Samuel Kobina Annim, 2015. "Child deprivation and income poverty in Ghana," WIDER Working Paper Series 150, World Institute for Development Economic Research (UNU-WIDER).
    9. Sabina Alkire & James Foster, 2011. "Understandings and misunderstandings of multidimensional poverty measurement," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(2), pages 289-314, June.
    10. Gaston Yalonetzky, 2011. "Conditions for the Most Robust Poverty Comparisons Using the Alkire-Foster Family of Measures," OPHI Working Papers ophiwp044b, Queen Elizabeth House, University of Oxford.
    11. Deniz Sevinc, 2020. "How Poor is Poor? A novel look at multidimensional poverty in the UK," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 149(3), pages 833-859, June.
    12. Raymond Elikplim Kofinti & Samuel Kobina Annim, 2015. "Child deprivation and income poverty in Ghana," WIDER Working Paper Series wp-2015-150, World Institute for Development Economic Research (UNU-WIDER).
    13. Johanna Fajardo-Gonzalez, 2016. "Inequality of opportunity in adult health in Colombia," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 14(4), pages 395-416, December.
    14. Ramses Abul Naga & Christopher Stapenhurst & Gaston Yalonetzky, 2020. "Asymptotic Versus Bootstrap Inference for Inequality Indices of the Cumulative Distribution Function," Econometrics, MDPI, vol. 8(1), pages 1-15, February.
    15. Gaston Yalonetzky, 2014. "Conditions for the most robust multidimensional poverty comparisons using counting measures and ordinal variables," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 773-807, December.
    16. Anand, Paul & Roope, Laurence & Peichl, Andreas, 2016. "Wellbeing Evidence for the Assessment of Progress," IZA Discussion Papers 9840, Institute of Labor Economics (IZA).
    17. David Gunawan & William Griffths & Duangkamon Chotikapanich, 2017. "Bayesian Inference for Health Inequality and Welfare Using Qualitative Data "Abstract: We show how to use Bayesian inference to compare two ordinal categorical distributions commonly occurring wi," Department of Economics - Working Papers Series 2031, The University of Melbourne.
    18. Nicholas Rohde & Ross Guest, 2018. "Multidimensional Inequality Across Three Developed Countries," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 64(3), pages 576-591, September.
    19. Suman Seth and Gaston Yalonetzky, 2018. "Assessing Deprivation with Ordinal Variables: Depth Sensitivity and Poverty Aversion," OPHI Working Papers ophiwp123.pdf, Queen Elizabeth House, University of Oxford.
    20. Nicolas Gravel & Brice Magdalou & Patrick Moyes, 2019. "Inequality measurement with an ordinal and continuous variable," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(3), pages 453-475, March.
    21. Andrew M. Jones; Nigel Rice, Silvana Robone; & Nigel Rice; & Silvana Robone:, 2012. "A comparison of parametric and non-parametric adjustments using vignettes for self-reported data," Health, Econometrics and Data Group (HEDG) Working Papers 12/10, HEDG, c/o Department of Economics, University of York.
    22. Suman Seth & Gaston Yalonetzky, 2021. "Assessing Deprivation with an Ordinal Variable: Theory and Application to Sanitation Deprivation in Bangladesh," The World Bank Economic Review, World Bank, vol. 35(3), pages 793-811.
    23. Martyna Kobus & Olga Półchłopek & Gaston Yalonetzky, 2019. "Inequality and Welfare in Quality of Life Among OECD Countries: Non-parametric Treatment of Ordinal Data," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 143(1), pages 201-232, May.
    24. Chrysanthi Hatzimasoura & Christopher J. Bennett, 2011. "Poverty Measurement with Ordinal Data," Working Papers 2011-14, The George Washington University, Institute for International Economic Policy.
    25. Pinar, Mehmet & Stengos, Thanasis & Topaloglou, Nikolas, 2020. "On the construction of a feasible range of multidimensional poverty under benchmark weight uncertainty," European Journal of Operational Research, Elsevier, vol. 281(2), pages 415-427.

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