IDEAS home Printed from https://ideas.repec.org/a/eee/pubeco/v95y2011i3-4p225-238.html
   My bibliography  Save this article

Partial multidimensional inequality orderings

Author

Listed:
  • Duclos, Jean-Yves
  • Sahn, David E.
  • Younger, Stephen D.

Abstract

The paper investigates how comparisons of multivariate inequality can be made robust to varying the intensity of focus on the share of the population that are more relatively deprived. It is in the spirit of Sen (1970)'s partial orderings and follows the dominance approach to making inequality comparisons. By focusing on those below a multidimensional inequality "frontier", we are able to reconcile the literature on multivariate relative poverty and multivariate inequality. Some existing approaches to multivariate inequality actually reduce the distributional analysis to a univariate problem, either by using a utility function first to aggregate an individual's multiple dimensions of well-being, or by applying a univariate inequality analysis to each dimension independently. One of our innovations is that unlike previous approaches, the distribution of relative well-being in one dimension is allowed to affect how other dimensions influence overall inequality. Our methods are also robust to choices of individual "utility" or aggregation functions. We apply our approach to data from India and Mexico to show inter alia how dependence between dimensions of well-being can influence relative poverty and inequality comparisons between two populations.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:pubeco:v:95:y:2011:i:3-4:p:225-238
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-2727(10)00158-1
    Download Restriction: Full text for ScienceDirect subscribers only

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. Formby, John P. & Smith, W. James & Zheng, Buhong, 1999. "The coefficient of variation, stochastic dominance and inequality: A new interpretation," Economics Letters, Elsevier, vol. 62(3), pages 319-323, March.
    2. David E. Sahn & David Stifel, 2003. "Exploring Alternative Measures of Welfare in the Absence of Expenditure Data," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 49(4), pages 463-489, December.
    3. Russell Davidson & Jean-Yves Duclos, 2013. "Testing for Restricted Stochastic Dominance," Econometric Reviews, Taylor & Francis Journals, vol. 32(1), pages 84-125, January.
    4. 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.
    5. Sen, Amartya, 1970. "Interpersonal Aggregation and Partial Comparability," Econometrica, Econometric Society, vol. 38(3), pages 393-409, May.
    6. Sen, Amartya, 1983. "Poor, Relatively Speaking," Oxford Economic Papers, Oxford University Press, vol. 35(2), pages 153-169, July.
    7. A. B. Atkinson & F. Bourguignon, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," Review of Economic Studies, Oxford University Press, vol. 49(2), pages 183-201.
    8. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
    9. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    10. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-766, May.
    11. Foster, James E. & Shorrocks, Anthony F., 1988. "Inequality and poverty orderings," European Economic Review, Elsevier, vol. 32(2-3), pages 654-661, March.
    12. Maasoumi, Esfandiar & Jeong, Jin Ho, 1985. "The trend and the measurement of world inequality over extended periods of accounting," Economics Letters, Elsevier, vol. 19(3), pages 295-301.
    13. Maasoumi, Esfandiar & Nickelsburg, Gerald, 1988. "Multivariate Measures of Well-Being and an Analysis of Inequality in the Michigan Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(3), pages 326-334, July.
    14. Sahn, David E. & Stifel, David C., 2000. "Poverty Comparisons Over Time and Across Countries in Africa," World Development, Elsevier, vol. 28(12), pages 2123-2155, December.
    15. Tsui Kai-Yuen, 1995. "Multidimensional Generalizations of the Relative and Absolute Inequality Indices: The Atkinson-Kolm-Sen Approach," Journal of Economic Theory, Elsevier, vol. 67(1), pages 251-265, October.
    16. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-231, March.
    17. Ernesto Savaglio, 2006. "Multidimensional inequality with variable population size," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(1), pages 85-94, May.
    18. Jean-Yves Duclos & David Sahn & Stephen D. Younger, 2006. "Robust Multidimensional Spatial Poverty Comparisons in Ghana, Madagascar, and Uganda," World Bank Economic Review, World Bank Group, vol. 20(1), pages 91-113.
    19. Horton, S. & Ross, J., 2003. "The economics of iron deficiency," Food Policy, Elsevier, vol. 28(1), pages 51-75, February.
    20. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    21. David Sahn & Stephen Younger, 2005. "Improvements in children’s health: Does inequality matter?," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 3(2), pages 125-143, August.
    22. 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(05), pages 849-866, December.
    23. Datt, Gaurav & Ravallion, Martin, 1992. "Growth and redistribution components of changes in poverty measures : A decomposition with applications to Brazil and India in the 1980s," Journal of Development Economics, Elsevier, vol. 38(2), pages 275-295, April.
    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. Rolf Aaberge & Andrea Brandolini, 2014. "Multidimensional poverty and inequality," Discussion Papers 792, Statistics Norway, Research Department.
    2. Channing Arndt & Kristi Mahrt & M. Azhar Hussain & Finn Tarp, 2017. "A human rights-consistent approach to multidimensional welfare measurement applied to sub-Saharan Africa," WIDER Working Paper Series 076, World Institute for Development Economic Research (UNU-WIDER).
    3. Christoffer Sonne-Schmidt & Finn Tarp & Lars Peter Østerdal, 2016. "Ordinal Bivariate Inequality: Concepts and Application to Child Deprivation in Mozambique," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 62(3), pages 559-573, September.
    4. Martyna Kobus, 2014. "Multidimensional polarization for ordinal data," Working Papers 326, ECINEQ, Society for the Study of Economic Inequality.
    5. Maasoumi, Esfandiar & Racine, Jeffrey S., 2016. "A solution to aggregation and an application to multidimensional ‘well-being’ frontiers," Journal of Econometrics, Elsevier, vol. 191(2), pages 374-383.
    6. Stergios Athanassoglou, 2015. "Multidimensional welfare rankings under weight imprecision: a social choice perspective," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(4), pages 719-744, April.
    7. M. Azhar Hussain & Mette Møller Jørgensen & Lars Peter Østerdal, 2016. "Refining Population Health Comparisons: A Multidimensional First Order Dominance Approach," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 129(2), pages 739-759, November.
    8. Sonne-Schmidt, Christoffer & Tarp, Finn & Peter, Lars, 2011. "Ordinal multidimensional inequality: theory and application to the 2x2 case," MPRA Paper 72838, University Library of Munich, Germany.
    9. Echevin, Damien, 2011. "Vulnerability to asset-poverty in Sub-Saharan Africa," MPRA Paper 35660, University Library of Munich, Germany.
    10. Sonne-Schmidt, Christoffer & Tarp, Finn & Østerdal, Lars Peter, 2013. "Ordinal Multidimensional Inequality," WIDER Working Paper Series 097, World Institute for Development Economic Research (UNU-WIDER).
    11. Bosmans, Kristof & Decancq, Koen & Ooghe, Erwin, 2015. "What do normative indices of multidimensional inequality really measure?," Journal of Public Economics, Elsevier, vol. 130(C), pages 94-104.
    12. Athanassoglou, Stergios, 2013. "Multidimensional welfare rankings," MPRA Paper 51642, University Library of Munich, Germany.
    13. Esfandiar Maasoumi & Jeffrey S. Racine, 2013. "Multidimensional Poverty Frontiers: Parametric Aggregators Based on Nonparametric Distributions," Department of Economics Working Papers 2013-07, McMaster University.
    14. Nicholas Rohde & Ross Guest, 2013. "Multidimensional Racial Inequality in the United States," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 114(2), pages 591-605, November.

    More about this item

    Keywords

    Inequality Multidimensional comparisons Stochastic dominance;

    JEL classification:

    • D3 - Microeconomics - - Distribution
    • I3 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty

    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:eee:pubeco:v:95:y:2011:i:3-4:p:225-238. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/inca/505578 .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.