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A New Generalized Variance Approach for Measuring Multidimensional Inequality and Poverty

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  • 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
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    1. Buhong Zheng, 1997. "Aggregate Poverty Measures," Journal of Economic Surveys, Wiley Blackwell, vol. 11(2), pages 123-162, June.
    2. 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.
    3. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    4. 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.
    5. 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.
    6. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    7. 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.
    8. Dagum, Camilo, 1997. "A New Approach to the Decomposition of the Gini Income Inequality Ratio," Empirical Economics, Springer, vol. 22(4), pages 515-531.
    9. Atkinson, A B, 1987. "On the Measurement of Poverty," Econometrica, Econometric Society, vol. 55(4), pages 749-764, July.
    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. 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.
    12. 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.
    13. 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.
    14. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-231, March.
    15. repec:ebl:ecbull:v:4:y:2003:i:7:p:1-6 is not listed on IDEAS
    16. Maria Ana Lugo, 2005. "Comparing Multidimensional Indices of Inequality: methods and application," Working Papers 14, ECINEQ, Society for the Study of Economic Inequality.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. Zheng, Buhong, 1997. "Aggregate Poverty Measures," Journal of Economic Surveys, Wiley Blackwell, vol. 11(2), pages 123-162, June.
    22. 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.
    23. Jean-Yves Duclos & David Sahn & Stephen D. Younger, 2006. "Robust Multidimensional Poverty Comparisons with Discrete Indicators of Well-being," Cahiers de recherche 0628, CIRPEE.
    24. 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.
    25. Sen, Amartya, 1997. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198292975.
    26. 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.
    27. 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.
    28. Maasoumi, Esfandiar, 1986. "The Measurement and Decomposition of Multi-dimensional Inequality," Econometrica, Econometric Society, vol. 54(4), pages 991-997, July.
    29. Shorrocks, Anthony F, 1995. "Revisiting the Sen Poverty Index," Econometrica, Econometric Society, vol. 63(5), pages 1225-1230, September.
    30. Abdelkrim Araar, 2009. "The Hybrid Multidimensional Index of Inequality," Cahiers de recherche 0945, CIRPEE.
    31. 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.
    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.
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