IDEAS home Printed from https://ideas.repec.org/a/spr/soinre/v158y2021i3d10.1007_s11205-021-02720-9.html
   My bibliography  Save this article

A New Generalized Variance Approach for Measuring Multidimensional Inequality and Poverty

Author

Listed:
  • Ottó Hajdu

    (Eötvös Loránd University)

Abstract

The paper suggests a new generalized variance concept for measuring multidimensional inequality of a stratified society, based on multivariate statistical methods, where the members of society form a cloud in the oblique space of dimensions of inequality, such as income, expenditure and property. The cloud presents the multidimensional inequality capsulized in the cloud. The goal is to condense all the inequality information embodied by the cloud into a composite compact metric characterizing both the shape and the inner structure of the cloud. Contrary to the conventional literature that considers multidimensionality as a unidimensional weighted combination of the dimensions, our new composite index measures the inequality of the configuration of the points in the cloud. Our aim is twofold. First, we introduce the Inequality Covariance Matrix (ICM) assigned to the cloud, with elements measuring the correlations among dimensions. Having ICM, we propose the Generalized Variance (GV) of ICM to measure the composite Generalized Variance Inequality (GVI) level. Second, to evaluate the stratum-specific structure of the overall inequality, we suggest a new two-stage procedure. In the first stage, we divide the total GVI into between-groups and within-groups effects. Then, in the second stage the contributions of the strata to the within-groups inequality and, the contributions of the dimensions to the between-groups inequality are calculated. This GVI approach is sensitive to the correlation system, decomposable into stratum effects and, the number of dimensions is not limited. Moreover, including the log-dimensions in the analysis, GVI yields an Entropy Covariance Matrix giving a new Generalized Variance Entropy index. Finally, the GVI of censored poverty indicators means multidimensional poverty measurement. This special complex task is not yet solved in the traditional literature so far.

Suggested Citation

  • Ottó Hajdu, 2021. "A New Generalized Variance Approach for Measuring Multidimensional Inequality and Poverty," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 158(3), pages 839-861, December.
  • Handle: RePEc:spr:soinre:v:158:y:2021:i:3:d:10.1007_s11205-021-02720-9
    DOI: 10.1007/s11205-021-02720-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11205-021-02720-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s11205-021-02720-9?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. Cowell, Frank A. & Kuga, Kiyoshi, 1981. "Additivity and the entropy concept: An axiomatic approach to inequality measurement," Journal of Economic Theory, Elsevier, vol. 25(1), pages 131-143, August.
    2. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    3. Maria Ana Lugo & Esfandiar Maasoumi, 2008. "Multidimensional Poverty Measures from an Information Theory Perspective," Working Papers 85, ECINEQ, Society for the Study of Economic Inequality.
    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. Atkinson, A B, 1987. "On the Measurement of Poverty," Econometrica, Econometric Society, vol. 55(4), pages 749-764, July.
    6. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-766, May.
    7. Satya R. Chakravarty, 2019. "Ethically Flexible Measures of Poverty," Themes in Economics, in: Satya R. Chakravarty (ed.), Poverty, Social Exclusion and Stochastic Dominance, pages 13-26, Springer.
    8. 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.
    9. Hagenaars, Aldi J M, 1987. "A Class of Poverty Indices," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(3), pages 583-607, October.
    10. Maria Ana Lugo, 2005. "Comparing Multidimensional Indices of Inequality: methods and application," Working Papers 14, ECINEQ, Society for the Study of Economic Inequality.
    11. Anthony F. Shorrocks & James E. Foster, 1987. "Transfer Sensitive Inequality Measures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(3), pages 485-497.
    12. Zheng, Buhong, 1997. "Aggregate Poverty Measures," Journal of Economic Surveys, Wiley Blackwell, vol. 11(2), pages 123-162, June.
    13. Jean-Yves Duclos & David Sahn & Stephen D. Younger, 2006. "Robust Multidimensional Poverty Comparisons with Discrete Indicators of Well-being," Cahiers de recherche 0628, CIRPEE.
    14. Sen, Amartya, 1997. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198292975.
    15. Dominique Thon, 1979. "On Measuring Poverty," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 25(4), pages 429-439, December.
    16. Abdelkrim Araar, 2009. "The Hybrid Multidimensional Index of Inequality," Cahiers de recherche 0945, CIRPEE.
    17. Stéphane Mussard & Michel Terraza & Françoise Seyte, 2003. "Decomposition of Gini and the generalized entropy inequality measures," Economics Bulletin, AccessEcon, vol. 4(7), pages 1-6.
    18. Buhong Zheng, 1997. "Aggregate Poverty Measures," Journal of Economic Surveys, Wiley Blackwell, vol. 11(2), pages 123-162, June.
    19. Oihana Aristondo & Casilda Lasso De La Vega & Ana Urrutia, 2010. "A New Multiplicative Decomposition For The Foster–Greer–Thorbecke Poverty Indices," Bulletin of Economic Research, Wiley Blackwell, vol. 62(3), pages 259-267, July.
    20. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    21. Dagum, Camilo, 1997. "A New Approach to the Decomposition of the Gini Income Inequality Ratio," Empirical Economics, Springer, vol. 22(4), pages 515-531.
    22. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-231, March.
    23. repec:ebl:ecbull:v:4:y:2003:i:7:p:1-6 is not listed on IDEAS
    24. Kai-yuen Tsui, 2002. "Multidimensional poverty indices," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(1), pages 69-93.
    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 Group, vol. 20(1), pages 91-113.
    26. Clark, Stephen & Hemming, Richard & Ulph, David, 1981. "On Indices for the Measurement of Poverty," Economic Journal, Royal Economic Society, vol. 91(362), pages 515-526, June.
    27. Thon, Dominique, 1979. "On Measuring Poverty," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 25(4), pages 429-439, December.
    28. Sudhir Anand, 1977. "Aspects Of Poverty In Malaysia," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 23(1), pages 1-16, March.
    29. Takayama, Noriyuki, 1979. "Poverty, Income Inequality, and Their Measures: Professor Sen's Axiomatic Approach Reconsidered," Econometrica, Econometric Society, vol. 47(3), pages 747-759, May.
    30. Maasoumi, Esfandiar, 1986. "The Measurement and Decomposition of Multi-dimensional Inequality," Econometrica, Econometric Society, vol. 54(4), pages 991-997, July.
    31. Shorrocks, Anthony F, 1995. "Revisiting the Sen Poverty Index," Econometrica, Econometric Society, vol. 63(5), pages 1225-1230, September.
    32. James E. Foster & Artyom A. Shneyerov, 1999. "A general class of additively decomposable inequality measures," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(1), pages 89-111.
    Full references (including those not matched with items on IDEAS)

    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. James E. Foster & Joel Greer & Erik Thorbecke, 2010. "The Foster-Greer-Thorbecke (FGT) Poverty Measures: Twenty-Five Years Later," Working Papers 2010-14, The George Washington University, Institute for International Economic Policy.
    2. James Foster & Joel Greer & Erik Thorbecke, 2010. "The Foster–Greer–Thorbecke (FGT) poverty measures: 25 years later," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 8(4), pages 491-524, December.
    3. Sreenivasan Subramanian, 2004. "Indicators of Inequality and Poverty," WIDER Working Paper Series RP2004-25, World Institute for Development Economic Research (UNU-WIDER).
    4. Buhong Zheng, 2021. "Stochastic dominance and decomposable measures of inequality and poverty," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(2), pages 228-247, April.
    5. Jean–Yves Duclos & Phillipe Grégoire, 2002. "Absolute and Relative Deprivation and the Measurement of Poverty," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 48(4), pages 471-492, December.
    6. Suman Seth, Sabina Alkire, 2014. "Measuring and Decomposing Inequality among the Multidimensionally Poor Using Ordinal Data: A Counting Approach," OPHI Working Papers 68, Queen Elizabeth House, University of Oxford.
    7. Zheng, Buhong, 2000. "Minimum Distribution-Sensitivity, Poverty Aversion, and Poverty Orderings," Journal of Economic Theory, Elsevier, vol. 95(1), pages 116-137, November.
    8. 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.
    9. Maria Ana Lugo & Esfandiar Maasoumi, 2008. "Multidimensional Poverty Measures from an Information Theory Perspective," Working Papers 85, ECINEQ, Society for the Study of Economic Inequality.
    10. 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.
    11. Buhong Zheng, 2007. "Unit-Consistent Poverty Indices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(1), pages 113-142, April.
    12. Chakravarty, Satya R. & Deutsch, Joseph & Silber, Jacques, 2008. "On the Watts Multidimensional Poverty Index and its Decomposition," World Development, Elsevier, vol. 36(6), pages 1067-1077, June.
    13. Srinivas Goli & Nagendra Kumar Maurya & Moradhvaj & Prem Bhandari, 2019. "Regional Differentials in Multidimensional Poverty in Nepal: Rethinking Dimensions and Method of Computation," SAGE Open, , vol. 9(1), pages 21582440198, March.
    14. 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.
    15. LABAR, Kelly & BRESSON, Florent, 2011. "A multidimensional analysis of poverty in China from 1991 to 2006," China Economic Review, Elsevier, vol. 22(4), pages 646-668.
    16. Dipesh Gangopadhyay & Robert B. Nielsen & Velma Zahirovic-Herbert, 2021. "Methodology and Axiomatic Characterization of a Multidimensional and Fuzzy Measure of Deprivation," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 153(1), pages 1-37, January.
    17. Bibi, Sami & Duclos, Jean-Yves, 2007. "Equity and policy effectiveness with imperfect targeting," Journal of Development Economics, Elsevier, vol. 83(1), pages 109-140, May.
    18. Wen-Hao Chen & Jean-Yves Duclos, 2011. "Testing for poverty dominance: an application to Canada," Canadian Journal of Economics, Canadian Economics Association, vol. 44(3), pages 781-803, August.
    19. Koen Decancq & Marc Fleurbaey & François Maniquet, 2019. "Multidimensional poverty measurement with individual preferences," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 17(1), pages 29-49, March.
    20. Zheng, Buhong, 2001. "Statistical inference for poverty measures with relative poverty lines," Journal of Econometrics, Elsevier, vol. 101(2), pages 337-356, April.

    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:spr:soinre:v:158:y:2021:i:3:d:10.1007_s11205-021-02720-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.