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Ordinal Multidimensional Inequality

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  • Christoffer Sonne-Schmidt
  • Finn Tarp
  • Lars Peter Østerdal

Abstract

This paper proposes a concept of inequality comparisons with ordinal multidimensional categorical data. In our model, one population is more unequal than another when they have common arithmetic median outcomes and the first can be obtained from the second by correlation-increasing switches and/or median-preserving spreads. For the 2x2 case (with two binary indicators), we derive an operational procedure for checking ordinal inequality relations in practice. As an illustration, we apply the model to childhood poverty in Mozambique.

Suggested Citation

  • Christoffer Sonne-Schmidt & Finn Tarp & Lars Peter Østerdal, 2013. "Ordinal Multidimensional Inequality," WIDER Working Paper Series wp-2013-097, World Institute for Development Economic Research (UNU-WIDER).
    • Handle: RePEc:unu:wpaper:wp-2013-097
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    File URL: https://www.wider.unu.edu/sites/default/files/WP2013-097.pdf
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    as
    1. Benedicte Apouey, 2007. "Measuring health polarization with self‐assessed health data," Health Economics, John Wiley & Sons, Ltd., vol. 16(9), pages 875-894, September.
    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. Valentino Dardanoni & Antonio Forcina, 1999. "Inference for Lorenz curve orderings," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 49-75.
    4. Alkire, Sabina, 2002. "Dimensions of Human Development," World Development, Elsevier, vol. 30(2), pages 181-205, February.
    5. Nicolas Gravel & Abhiroop Mukhopadhyay, 2010. "Is India better off today than 15 years ago? A robust multidimensional answer," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 8(2), pages 173-195, June.
    6. Ian Crawford, 2005. "A nonparametric test of stochastic dominance in multivariate distributions," School of Economics Discussion Papers 1205, School of Economics, University of Surrey.
    7. Duclos, Jean-Yves & Sahn, David E. & Younger, Stephen D., 2011. "Partial multidimensional inequality orderings," Journal of Public Economics, Elsevier, vol. 95(3-4), pages 225-238, April.
    8. Meyer, Margaret & Strulovici, Bruno, 2012. "Increasing interdependence of multivariate distributions," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1460-1489.
    9. Christoffer Sonne-Schmidt & Finn Tarp & Lars Peter Østerdal, 2008. "Ordinal Comparison of Multidimensional Deprivation: theory and application," Discussion Papers 08-33, University of Copenhagen. Department of Economics.
    10. Gravel, Nicolas & Moyes, Patrick, 2012. "Ethically robust comparisons of bidimensional distributions with an ordinal attribute," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1384-1426.
    11. J. Behrman & T.N. Srinivasan (ed.), 1995. "Handbook of Development Economics," Handbook of Development Economics, Elsevier, edition 1, volume 3, number 3.
    12. Moyes, Patrick, 2012. "Comparisons of heterogeneous distributions and dominance criteria," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1351-1383.
    13. Sen, Amartya, 1997. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198292975.
    14. Arndt, Channing & Distante, Roberta & Hussain, M. Azhar & Østerdal, Lars Peter & Huong, Pham Lan & Ibraimo, Maimuna, 2012. "Ordinal Welfare Comparisons with Multiple Discrete Indicators: A First Order Dominance Approach and Application to Child Poverty," World Development, Elsevier, vol. 40(11), pages 2290-2301.
    15. Nicolas Gravel & Patrick Moyes & Benoît Tarroux, 2009. "Robust International Comparisons of Distributions of Disposable Income and Regional Public Goods," Economica, London School of Economics and Political Science, vol. 76(303), pages 432-461, July.
    16. Gordon Anderson, 2008. "The empirical assessment of multidimensional welfare, inequality and poverty: Sample weighted multivariate generalizations of the Kolmogorov–Smirnov two sample tests for stochastic dominance," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 6(1), pages 73-87, March.
    17. David Madden, 2010. "Ordinal and cardinal measures of health inequality: an empirical comparison," Health Economics, John Wiley & Sons, Ltd., vol. 19(2), pages 243-250, February.
    18. Arndt, Channing & Distante, Roberta & Hussain, M. Azhar & Østerdal, Lars Peter & Huong, Pham Lan & Ibraimo, Maimuna, 2012. "Ordinal Welfare Comparisons with Multiple Discrete Indicators: A First Order Dominance Approach and Application to Child Poverty," World Development, Elsevier, vol. 40(11), pages 2290-2301.
    19. A. B. Atkinson & F. Bourguignon, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(2), pages 183-201.
    20. N. GRAVEL & Patrick MOYES, 2008. "Bidimensional Inequalities with an Ordinal Variable," Cahiers du GREThA (2007-2019) 2008-14, Groupe de Recherche en Economie Théorique et Appliquée (GREThA).
    21. Nicolas Gravel & Patrick Moyes, 2011. "Bidimensional Inequalities with an Ordinal Variable," Studies in Choice and Welfare, in: Marc Fleurbaey & Maurice Salles & John A. Weymark (ed.), Social Ethics and Normative Economics, pages 101-127, Springer.
    22. Muller, Christophe & Trannoy, Alain, 2011. "A dominance approach to the appraisal of the distribution of well-being across countries," Journal of Public Economics, Elsevier, vol. 95(3), pages 239-246.
    23. Decancq, Koen, 2012. "Elementary multivariate rearrangements and stochastic dominance on a Fréchet class," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1450-1459.
    24. Martyna Kobus, 2014. "Multidimensional polarization for ordinal data," Working Papers 326, ECINEQ, Society for the Study of Economic Inequality.
    25. Jean-Yves Duclos & David Sahn & Stephen D. Younger, 2006. "Robust Multidimensional Spatial Poverty Comparisons in Ghana, Madagascar, and Uganda," The World Bank Economic Review, World Bank, vol. 20(1), pages 91-113.
    26. François Bourguignon & Satya R. Chakravarty, 2019. "The Measurement of Multidimensional Poverty," Themes in Economics, in: Satya R. Chakravarty (ed.), Poverty, Social Exclusion and Stochastic Dominance, pages 83-107, Springer.
    27. Abul Naga, Ramses H. & Yalcin, Tarik, 2008. "Inequality measurement for ordered response health data," Journal of Health Economics, Elsevier, vol. 27(6), pages 1614-1625, December.
    28. Orazem, Peter F. & King, Elizabeth M., 2008. "Schooling in Developing Countries: The Roles of Supply, Demand and Government Policy," Handbook of Development Economics, in: T. Paul Schultz & John A. Strauss (ed.), Handbook of Development Economics, edition 1, volume 4, chapter 55, pages 3475-3559, Elsevier.
    29. Magnus Lindelow, 2006. "Sometimes more equal than others: how health inequalities depend on the choice of welfare indicator," Health Economics, John Wiley & Sons, Ltd., vol. 15(3), pages 263-279, March.
    30. Kaur, Amarjot & Prakasa Rao, B.L.S. & Singh, Harshinder, 1994. "Testing for Second-Order Stochastic Dominance of Two Distributions," Econometric Theory, Cambridge University Press, vol. 10(5), pages 849-866, December.
    31. Alkire, Sabina & Foster, James, 2011. "Counting and multidimensional poverty measurement," Journal of Public Economics, Elsevier, vol. 95(7), pages 476-487.
    32. Wagstaff, Adam & Paci, Pierella & van Doorslaer, Eddy, 1991. "On the measurement of inequalities in health," Social Science & Medicine, Elsevier, vol. 33(5), pages 545-557, January.
    33. J. Behrman & T.N. Srinivasan (ed.), 1995. "Handbook of Development Economics," Handbook of Development Economics, Elsevier, edition 1, volume 3, number 4.
    34. Sabina Alkire, Maria Emma Santos, 2010. "Acute Multidimensional Poverty: A New Index for Developing Countries," OPHI Working Papers 38, Queen Elizabeth House, University of Oxford.
    35. Jean-Yves Duclos & David E. Sahn & Stephen D. Younger, 2006. "Robust Multidimensional Poverty Comparisons," Economic Journal, Royal Economic Society, vol. 116(514), pages 943-968, October.
    36. James P. Quirk & Rubin Saposnik, 1962. "Admissibility and Measurable Utility Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 29(2), pages 140-146.
    37. Østerdal, Lars Peter, 2010. "The mass transfer approach to multivariate discrete first order stochastic dominance: Direct proof and implications," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1222-1228, November.
    38. Wagstaff, Adam & van Doorslaer, Eddy & Paci, Pierella, 1989. "Equity in the Finance and Delivery of Health Care: Some Tentative Cross-country Comparisons," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 5(1), pages 89-112, Spring.
    39. Nicolas Gravel & Patrick Moyes, 2006. "Ethically Robust Comparisons of Distributions of Two Individual Attributes," IDEP Working Papers 0605, Institut d'economie publique (IDEP), Marseille, France, revised Aug 2006.
    40. Brian McCaig & Adonis Yatchew, 2007. "International welfare comparisons and nonparametric testing of multivariate stochastic dominance," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(5), pages 951-969.
    41. Bourguignon, Francois, 1989. "Family size and social utility : Income distribution dominance criteria," Journal of Econometrics, Elsevier, vol. 42(1), pages 67-80, September.
    42. Jean-Yves Duclos & David Sahn & Stephen D. Younger, 2006. "Robust Multidimensional Poverty Comparisons with Discrete Indicators of Well-being," Cahiers de recherche 0628, CIRPEE.
    43. Naga, Ramses H. Abul & Yalcin, Tarik, 2010. "Median Independent Inequality Orderings," SIRE Discussion Papers 2010-118, Scottish Institute for Research in Economics (SIRE).
    44. Handa, Sudhanshu, 1996. "Expenditure behavior and children's welfare: An analysis of female headed households in Jamaica," Journal of Development Economics, Elsevier, vol. 50(1), pages 165-187, June.
    45. Marc Fleurbaey & Maurice Salles & John A. Weymark (ed.), 2011. "Social Ethics and Normative Economics," Studies in Choice and Welfare, Springer, number 978-3-642-17807-8, December.
    46. Boland, Philip J. & Proschan, Frank, 1988. "Multivariate arrangement increasing functions with applications in probability and statistics," Journal of Multivariate Analysis, Elsevier, vol. 25(2), pages 286-298, May.
    47. Buvinic, Mayra & Gupta, Geeta Rao, 1997. "Female-Headed Households and Female-Maintained Families: Are They Worth Targeting to Reduce Poverty in Developing Countries?," Economic Development and Cultural Change, University of Chicago Press, vol. 45(2), pages 259-280, January.
    48. Strauss, John & Thomas, Duncan, 1995. "Human resources: Empirical modeling of household and family decisions," Handbook of Development Economics, in: Hollis Chenery & T.N. Srinivasan (ed.), Handbook of Development Economics, edition 1, volume 3, chapter 34, pages 1883-2023, Elsevier.
    49. repec:unu:wpaper:wp2012-36 is not listed on IDEAS
    50. Erreygers, Guido, 2009. "Correcting the Concentration Index," Journal of Health Economics, Elsevier, vol. 28(2), pages 504-515, March.
    51. Allison, R. Andrew & Foster, James E., 2004. "Measuring health inequality using qualitative data," Journal of Health Economics, Elsevier, vol. 23(3), pages 505-524, May.
    52. A. Atkinson, 2003. "Multidimensional Deprivation: Contrasting Social Welfare and Counting Approaches," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 1(1), pages 51-65, April.
    53. Kakwani, Nanak & Wagstaff, Adam & van Doorslaer, Eddy, 1997. "Socioeconomic inequalities in health: Measurement, computation, and statistical inference," Journal of Econometrics, Elsevier, vol. 77(1), pages 87-103, March.
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