IDEAS home Printed from https://ideas.repec.org/a/taf/emetrv/v32y2013i1p126-163.html
   My bibliography  Save this article

Stochastic Dominance with Ordinal Variables: Conditions and a Test

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/07474938.2012.690653
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/07474938.2012.690653?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sen, Amartya, 2001. "Development as Freedom," OUP Catalogue, Oxford University Press, number 9780192893307, Decembrie.
    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. Ian Crawford, 2005. "A nonparametric test of stochastic dominance in multivariate distributions," School of Economics Discussion Papers 1205, School of Economics, University of Surrey.
    4. James Foster & Mark McGillivray & Suman Seth, 2009. "Rank Robustness of Composite Indices," OPHI Working Papers 26, Queen Elizabeth House, University of Oxford.
    5. Martin Ravallion, 2012. "Mashup Indices of Development," The World Bank Research Observer, World Bank, vol. 27(1), pages 1-32, February.
    6. Suman Seth, 2009. "A Class of Association Sensitive Multidimensional Welfare Indices," OPHI Working Papers 27, Queen Elizabeth House, University of Oxford.
    7. Christophe Muller & Alain Trannoy, 2003. "A Dominance Approach to Well-Being Inequality across Countries," IDEP Working Papers 0313, Institut d'economie publique (IDEP), Marseille, France.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Jeni Klugman & Francisco Rodríguez & Hyung-Jin Choi, 2011. "The HDI 2010: new controversies, old critiques," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(2), pages 249-288, June.
    4. 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.
    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. Tendai Zawaira & Matthew W. Clance & Carolyn Chisadza, 2020. "Social Institutions and Gender-Biased Outcomes in sub-Saharan Africa," Working Papers 2020101, University of Pretoria, Department of Economics.
    7. Chen Yu, 2020. "Targeted industrial poverty alleviation in China’s Rural Areas: Evidence From Yulin Township," Journal of Advances in Humanities and Social Sciences, Dr. Yi-Hsing Hsieh, vol. 6(2), pages 78-88.
    8. Ángeles Sánchez-Domínguez & Maria J. Ruiz Martos, 2013. "Europe 2020 strategy: a strategy for which type of growth?," ThE Papers 13/11, Department of Economic Theory and Economic History of the University of Granada..
    9. Brandon D. Lundy & Kezia Darkwah, 2018. "Measuring Community Integration of Lusophone West African Immigrant Populations Through Needs Assessment, Human Security, and Realistic Conflict Theory," Journal of International Migration and Integration, Springer, vol. 19(2), pages 513-526, May.
    10. Kaspar Walter Meili & Anna Månsdotter & Linda Richter Sundberg & Jan Hjelte & Lars Lindholm, 2022. "An initiative to develop capability-adjusted life years in Sweden (CALY-SWE): Selecting capabilities with a Delphi panel and developing the questionnaire," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-21, February.
    11. Jing Yang & Pundarik Mukhopadhaya, 2019. "Is the ADB’s Conjecture on Upward Trend in Poverty for China Right? An Analysis of Income and Multidimensional Poverty in China," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 143(2), pages 451-477, June.
    12. Christophe Muller & Asha Kannan & Roland Alcindor, 2016. "Multidimensional Poverty in Seychelles," Working Papers halshs-01264444, HAL.
    13. Shikha Silwal, 2017. "On peace and development economics," Economics of Peace and Security Journal, EPS Publishing, vol. 12(2), pages 5-9, October.
    14. Vizard, Polly, 2005. "The contributions of Professor Amartya Sen in the field of human rights," LSE Research Online Documents on Economics 6273, London School of Economics and Political Science, LSE Library.
    15. Roy, Shalini & Hidrobo, Melissa & Hoddinott, John F. & Ahmed, Akhter, 2021. "Transfers, behavior change communication, and intimate partner violence: Post-program evidence from rural Bangladesh," IFPRI book chapters, in: Securing food for all in Bangladesh, chapter 15, pages 549-590, International Food Policy Research Institute (IFPRI).
    16. Schmid, Günther, 2004. "Gewährleistungsstaat und Arbeitsmarkt: Neue Formen von Governance in der Arbeitsmarktpolitik," Discussion Papers, Research Unit: Labor Market Policy and Employment SP I 2004-107, WZB Berlin Social Science Center.
    17. Chei Bukari & Millicent Abigail Aning-Agyei & Christian Kyeremeh & Gloria Essilfie & Kofi Fosu Amuquandoh & Anthony Akwesi Owusu & Isaac Christopher Otoo & Kpanja Ibrahim Bukari, 2022. "Effect of COVID-19 on Household Food Insecurity and Poverty: Evidence from Ghana," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 159(3), pages 991-1015, February.
    18. Isaac G. K. Ansah & Munkaila Lambongang & Samuel A. Donkoh, 2020. "Ghana’s Planting for Food and Jobs Programme: A Look at the Role of Capability in Farmers’ Participation," Journal of Human Development and Capabilities, Taylor & Francis Journals, vol. 21(2), pages 161-182, April.
    19. Raymond Lang & Marguerite Schneider & Maria Kett & Ellie Cole & Nora Groce, 2019. "Policy development: An analysis of disability inclusion in a selection of African Union policies," Development Policy Review, Overseas Development Institute, vol. 37(2), pages 155-175, March.
    20. Emily Lewis & Sophie Mitra & Jaclyn Yap, 2022. "Do Disability Inequalities Grow with Development? Evidence from 40 Countries," Sustainability, MDPI, vol. 14(9), pages 1-13, April.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:emetrv:v:32:y:2013:i:1:p:126-163. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: http://www.tandfonline.com/LECR20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.