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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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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Anand, Paul & Roope, Laurence & Peichl, Andreas, 2016. "Wellbeing Evidence for the Assessment of Progress," IZA Discussion Papers 9840, Institute for the Study of Labor (IZA).
    4. repec:eee:ecolet:v:162:y:2018:i:c:p:76-80 is not listed on IDEAS
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Chrysanthi Hatzimasoura & Christopher J. Bennett, 2011. "Poverty Measurement with Ordinal Data," Working Papers 2011-14, The George Washington University, Institute for International Economic Policy.

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