A Rank-Dependent Multidimensional Deprivation Index (MDI) for Binary Data
Keywords:
multidimensional poverty analysis, inequality, Gini index, dominanceAbstract
This article demonstrates the extension of the Sen-Shorrocks poverty index to the analysis of multidimensional deprivation, particularly when only dichotomous variables are available to assess deprivation across various domains, which is the most common case in the literature. More precisely, it introduces a rank-dependent multidimensional poverty index using a counting approach. The resulting multidimensional deprivation index, or MDI, offers a visually appealing representation (PUB curve), which turns out to be an extension of the so-called “Three I’s of Poverty” (TIP) curve of Jenkins and Lambert to the case of multiple deprivations. This representation is similar to the SD curve introduced by Lasso de la Vega (2010) while also emphasising the third “I” of multidimensional deprivation: inequality. The MDI is sensitive to inequality and satisfies desirable properties, but it cannot be broken down by population subgroups when using a standard decomposition method. Furthermore, it lacks the property of dimensional breakdown as typically defined in the literature. The article proves, however, the existence of an alternative decomposition method by population subgroups that can be applied to the MDI. It also derives a decomposition by deprivation domain, analogous to the breakdown of the Gini index by factor components. An empirical illustration, based on deprivation data from four Central American countries (Guatemala, El Salvador, Honduras, and Nicaragua), highlights the usefulness of the MDI.
References
Aaberge, R., and E. Peluso 2012 “A counting approach for measuring multidimensional deprivation”, Discussion paper No. 700, Research Department, Statistics Norway.
—–, and A. Brandolini 2015 “Multidimensional Poverty and Inequality,” in A.B. Atkinson and F. Bourguignon eds, Handbook of Income Distribution, Volume 2A, North Holland: Amsterdam. doi.org/10.1016/B978-0-444-59428-0.00004-7
—–, E. Peluso and H. Sigstad 2019 “The dual approach for measuring multidimensional deprivation: Theory and empirical evidence”, Journal of Public Economics 177: 104036. doi.org/10.1016/j.jpubeco.2019.06.004
Alkire, S., and J. Foster 2007 “Counting and multidimensional poverty measurement”, Oxford Poverty and Human Development Initiative (OPHI) Working Paper No. 7. Oxford, UK: Queen Elizabeth House (QEH).
—– 2011 “Counting and multidimensional poverty measurement,” Journal of Public Economics 95(7–8): 476–487. doi.org/10.1016/j.jpubeco.2010.11.006
—– 2016 “Dimensional and Distributional Contributions to Multidimensional Poverty”, OPHI Working Paper No. 100. Oxford, UK: Queen Elizabeth House (QEH).
—– 2019 “The Role of Inequality in Poverty Measurement”, OPHIWorking Paper No. 126. Oxford, UK: Queen Elizabeth House (QEH).
—–, S. Seth, M.E. Santos, J.M. Roche, and P. Ballon 2015 Multidimensional Poverty Measurement and Analysis Oxford and New York: Oxford University Press.
Anand, S., and A. Sen 1997 “Concepts of human development and poverty: A multidimensional perspective”, Human Development Papers 1997. United Nation Development Program (UNDP), New York. pp. 138-151.
Atkinson, A.B. 1970 “On the Measurement of Inequality”, Journal of Economic Theory 2: 244–263.
—– 2003 “Multidimensional Deprivation: Contrasting Social Welfare and Counting Approaches”, The Journal of Economic Inequality 1: 51–65. doi.org/10.1023/A:1023903525276
—–, and F. Bourguignon 1982 “The comparison of multi-dimensioned distributions of economic status’’, Review of Economic Studies 49(2): 183–201. doi.org/10.2307/2297269
Azpitarte, F., J. Gallegos, G. Yalonetzky 2020 “On the robustness of multidimensional counting poverty orderings”, Journal of Economic Inequality 18: 339–364. doi.org/10.1007/s10888-019-09435-5
Berrebi, Z.M., and J. Silber 1987 “Dispersion, Asymmetry and the Gini Index of Inequality”, International Economic Review 28(2): 331–338.
Bhattacharya, N., and B. Mahalanobis 1967 “Regional Disparities in Household Consumption in India”, Journal of the American Statistical Association 62(317): 143–161. doi.org/10.1080/01621459.1967.10482896
Blackorby, C., and D. Donaldson 1980 “Ethical indices for the measurement of poverty”, Econometrica 48(4): 1053–1060.
Bossert, W., S.R. Chakravarty, V. Peragine 2007 “Deprivation and social exclusion”, Economica 74: 777–803. doi.org/10.1111/j.1468-0335.2006.00572.x
—–, S. Chakravarty, and C. D’Ambrosio 2013 “Multidimensional poverty and material deprivation with discrete data”, Review of Income and Wealth 59(1): 29–43. doi.org/10.1111/j.1475-4991.2012.00519.x
Bourguignon, F. 1999 “Comment on “Multidimensional Approaches to Welfare Analysis,” in J. Silber (Ed.) Handbook on Income Inequality Measurement Dordrecht, The Netherlands: Kluwer Academic Publishers. pp. 477–484.
—–, and S.R. Chakravarty 2003 “The Measurement of Multidimensional Poverty,” Journal of Economic Inequality 1: 25–49. doi.org/10.1023/A:1023913831342
Brandolini, A., and G. D’Alessio 2009 “Measuring well-being in the functioning space” in E. Chiappero Martinetti (Ed.) Debating Global Society: Reach and Limits of the Capability Approach Milano: Fondazione Giangiacomo Feltrinelli. pp. 91–156.
Chakravarty, S.R. 1983 “Measures of poverty based on representative income gaps”, Sankhya: The Indian Journal of Statistics Series B 45(1): 69–74.
—– 1997 “On Shorrocks’ Reinvestigation of the Sen Poverty Index”, Econometrica 65(5): 1241–1242.
—– 2006 “An axiomatic approach to multidimensional poverty measurement via fuzzy sets”, in A. Lemmi and G. Betti (Eds.) Fuzzy set approach to multidimensional poverty measurement New York: Springer. Pp. 49–72. doi.org/10.1007/978-981-13-3432-0_9
—– 2009 Inequality, Polarization and Poverty. Advances in Distributional Analysis Springer: New York.
—–, and C. D’Ambrosio 2006 “The Measurement of Social Exclusion”, Review of Income and Wealth 52(3): 377–398. doi.org/10.1111/j.1475-4991.2006.00195.x
—–, D. Mukherjee, and R.R. Renade 1998 “On the Family of Subgroup and Factor Decomposable Measures of Multidimensional Poverty”, Research on Economic Inequality 8: 175–194.
Clark, S., R. Hemming, D. Ulph 1981 “On indices of the measurement of poverty”, Economic Journal 91(362): 515–526. doi.org/10.2307/2232600
Datt, G. 2019 “Distribution-sensitive multidimensional poverty measures”, World Bank Economic Review 33(3): 551–572. doi.org/10.1093/wber/lhx017
Deaton, A. 2016 “Measuring and understanding behavior, welfare, and poverty”, American Economic Review 106(6): 1221–1243. doi.org/10.1257/aer.106.6.1221.
Decancq, K., and M.A. Lugo 2013 “Weights in Multidimensional Indices of Well-Being: An Overview”, Econometrics Review 32(1): 7–34. doi.org/10.1080/07474938.2012.690641
Deutsch, J., and J. Silber 1999 “Inequality Decomposition by Population Subgroups and the Analysis of Inter-distributional Inequality”, in J. Silber (Ed.) Handbook on Income Inequality Measurement Dordrecht: Kluwer Academic Publishers. Pp. 363–397. doi.org/10.1007/
-94-011-4413-1_14
—– 2005 “Comparing Segregation by Gender in the Labor Force Across Ten European Countries in the 1990s. An analysis based on the use of normative segregation indices”, International Journal of Manpower 26(3): 237–264. doi.org/10.1108/01437720510604947
Dhongde, S., Y. Li., P.K. Pattanaik, Y. Xu 2016 “Binary data, hierarchy of attributes, and multidimensional deprivation”, Journal of Economic Inequality 14: 363–378. doi.org/10.1007/s10888-016-9336-4
Donaldson, D., and J. Weymark 1980 “A Single-Parameter Generalization of the Gini Indices of Inequality”, Journal of Economic Theory 22(1): 67–87. doi.org/10.1016/0022-0531(80)90065-4
Duclos, J.Y., D.E. Sahn, S.D. Younger 2008 “Using an ordinal approach to multidimensional poverty analysis”, in N. Kakwani and J. Silber (Eds.) Quantitative approaches to multidimensional poverty measurement New York: Palgrave MacMillan. doi.org/10.1057/9780230582354_14
—–, and L. Tiberti 2016 “Multidimensional poverty indices: A critical assessment”, in M. Adler and M. Fleurbaey (eds) The Oxford Handbook of Well-Being and Public Policy Oxford: Oxford University Press. doi.org/10.1093/oxfordhb/9780199325818.013.19
Dutta, I., R. Nogales, and G. Yalonetzky 2021 “Endogenous weights and multidimensional poverty: a cautionary tale”, Journal of Development Economics 151: 102649. doi.org/10.1016/j.jdeveco.2021.102649
Espinoza-Delgado, J., and J. Silber 2018 “Multidimensional poverty among adults in Central America and gender differences in the three I’s of poverty: Applying inequality sensitive poverty measures with ordinal variables”, Discussion Paper No. 237, Ibero-America Institute
for Economic Research, University of Goettingen.
—– 2021 “Using Rippin’s approach to estimate multi-dimensional poverty in Central America”, in G. Betti and A. Lemmi (Eds.) Analysis of socio-economic conditions: Insights from a fuzzy multidimensional approach United Kingdom: Routledge.
Fei, J.C.H., G. Ranis, and W.Y. Kuo 1979 Growth with Equity. The Taiwan Case London: Oxford University Press.
Foster, J., J. Greer, E. Thorbecke 1984 “A class of decomposable poverty measures”, Econometrica 52(3), 761–766.
Fusco, A., and P. Dickes 2008 “The Rasch model and multidimensional poverty measurement”, in N. Kakwani and J. Silber (eds) Quantitative Approaches to Multidimensional Poverty Measurement London: Palgrave-Macmillan. doi.org/10.1057/9780230582354_3
Hamada, K., and N. Takayama 1977 “Censored income distributions and the measurement of poverty” Bulletin of the International Statistical Institute XLVII(1): 617–632.
Jayaraj, D., and S. Subramanian 2010 “A Chakravarty-D’Ambrosio View of Multidimensional Deprivation: Some Estimates for India”, Economic and Political Weekly, 45(6): 53–65; rpt. 2018 in S. Klasen (ed.), Measuring Poverty The International Library of Critical Writings in Economics series. Cheltenham, UK: Edward Elgar Publishing, Ch. 31.
Jenkins, S.P., and P.J. Lambert 1993 “Poverty Orderings, Poverty Gaps, and Poverty Lines” Discussion Paper No. 93-07, Economics Department, University College of Swansea.
—– 1997 “Three ‘I’s of Poverty curves, with an analysis of UK poverty trends”, Oxford Economic Papers 49(3): 317–327. doi.org/10.1093/oxfordjournals.oep.a028611
—– 1998a “Ranking Poverty Gap Distributions: Further TIPS for Poverty Analysis”, Research on Economic Inequality 8: 31–38.
—– 1998b “Three ‘I’s of Poverty Curves and Poverty Dominance: TIPS for Poverty Analysis”, Research on Economic Inequality 8: 39–56.
Kakwani, N., and J. Silber 2008 Quantitative Approaches to Multidimensional Poverty Measurement London: Palgrave-Macmillan.
Kendall, M.G., and A. Stuart 1969 The Advanced Theory of Statistics London: Charles Griffin and Company Limited.
Klasen, S., and M. Fleurbaey 2019 “Leaving no one behind: some conceptual and empirical issues”, Journal of Globalization and Development 9(2): 1–9. doi.org/10.1515/jgd-2018-0045
Kolm, S.-C. 1969 “The optimal production of social justice,” in J. Margolis and H. Guitton (eds.) Public Economics London: Macmillan.
—– 1977 “Multidimensional Egalitarianisms”, Quarterly Journal of Economics 91(1): 1–13. doi.org/10.2307/1883135
Lambert, P.J., and J.R. Aronson 1993 “Inequality Decomposition Analysis and the Gini Coefficient Revisited”, Economic Journal 103(420): 1221–1227. doi.org/10.2307/2234247
Lasso de la Vega, M.C. 2010 “Chapter 7 Counting Poverty Orderings and Deprivation Curves”, Research on Economic Inequality, In Studies in Applied Welfare Analysis: Papers from the Third ECINEQ Meeting Bingley, UK: Emerald Group Publishing Limited. pp. 153–172
Lemmi, A., and G. Betti 2006 Fuzzy set approach to multidimensional poverty measurement New York: Springer.
—– 2013 Poverty and social exclusion: New methods of analysis Oxford: Routledge.
Lerman, R.I., and S. Yitzhaki 1985 “Income Inequality Effects by Income Source: A New Approach and Applications to the United States”, The Review of Economic and Statistics 67(1): 151–156.
Levy, H., J. Paroush, B. Peleg 1975 “Efficiency Analysis for Multivariate Distributions”, Review of Economic Studies 42: 87–91.
Maasoumi, E. 1986 “The measurement and decomposition of multidimensional inequality”, Econometrica 54: 771–779.
—– 1999 “Multidimensional Approaches to Welfare Analysis”, in J. Silber (Ed.) Handbook on Income Inequality Measurement Dordrecht, The Netherlands: Kluwer Academic Publishers. pp. 437–477.
Pattanaik, P.K., S.G. Reddy, Y. Xu 2012 “On measuring deprivation and living standards of societies in a multi-attribute framework”, Oxford Economic Papers 64(1): 43–56. doi.org/10.1093/oep/gpr034
—–, and Y. Xu 2018 “On Measuring Multidimensional Deprivation”, Journal of Economic Literature 56(2): 657–672. doi.org/10.1257/jel.20161454
Podder, N. 1993 “A New Decomposition of the Gini Coefficient Among Groups and Its Interpretation with Applications to Australian Data”, Sankhya: The Indian Journal of Statistics (Series B) 55(2): 262–271.
Pogge, T., and S. Wisor 2016 “Measuring poverty: A proposal”, in M.D. Adler and M. Fleurbaey (eds) The Oxford Handbook of Well-Being and Public Policy Oxford: Oxford University Press. doi.org/10.1093/oxfordhb/9780199325818.013.20
Rasch G. 1960 Probabilistic models for some intelligence and attainment tests Copenhagen: Nielsen and Lydiche.
Rippin, N. 2010 “Poverty severity in a multidimensional framework: the issue of inequality between dimensions”, Discussion paper no. 47, Courant Research Center, University of Göttingen.
—– 2013 Considerations of efficiency and distributive justice in multidimensional poverty measurement Doctoral Dissertation. George-August-Universität Göttingen, Germany.
—– 2017 “Efficiency and distributive justice in multidimensional poverty issues”, in R. White (ed.) Measuring multidimensional poverty and deprivation. Incidence and determinants in developed countries. London: Palgrave Macmillan. doi.org/10.1007/978-3-319-58368-6_3
Sastry, D.V.S., and U.R. Kelkar 1994 “Note on the Decomposition of Gini Inequality”, The Review of Economics and Statistics 76(3): 84–586.
Sen, A.K. 1976 “Poverty: An Ordinal Approach to Measurement”, Econometrica 44(2): 219–231.
—– 1985 Commodities and Capabilities Amsterdam: North-Holland.
—– 1992 Inequality reexamined Cambridge, MA: Harvard University Press.
—– 1993 “Capability and Well-Being”, in M.C. Nussbaum and A. Sen (Eds.) The Quality of Life London: Clarendon Press. pp. 30-53.
—– 1997 On Economic Inequality. Expanded edition with a substantial annexe by James E. Foster and Amartya Sen Oxford: Clarendon Press.
—– 2000 Development as freedom New York: Anchor Books.
Shorrocks, A.F. 1995 “Revisiting the Sen poverty index”, Econometrica 63(5): 1225–1230.
—– 1998 “Deprivation profiles and deprivation indices”, in S.P. Jenkins, A. Kapteyn, B.M.S. van Praag (eds) The distribution of welfare and household production: international perspective Cambridge: Cambridge University Press.
Silber, J. 1989 “Factors Components, Population Subgroups and the Computation of the Gini Index of Inequality”, The Review of Economics and Statistics 71(1): 107–115.
—– 2007 “Measuring Poverty: Taking a Multidimensional Perspective”, Hacienda Pública Española/Review of Public Economics 182(3): 29–73.
—–, and Z.M. Berrebi 1987 “Dispersion, Asymmetry and the Gini Index of Inequality”, International Economic Review 28(2): 331–338.
—–, and G. Yalonetzky 2013 “Measuring Multidimensional Deprivation with Dichotomized and Ordinal Variables”, in G. Betti and A. Lemmi (eds) Poverty and Social Exclusion: New Methods of Analysis New York: Routledge. pp. 9–37.
Spencer, B.D., and S. Fisher 1992 “On Comparing Distributions of Poverty Gaps”, Sankhya: The Indian Journal of Statistics (Series B) 54(1): 114–126.
Stiglitz, J., A. Sen, J.-P. Fitoussi 2009a Report by the commission on the measurement of economic performance and social progress. Retrieved from https://www.insee.fr/en/statistiques/fichier/2662494/stiglitz-rapport-anglais.pdf.
—– 2009b “The Measurement of Economic Performance and Social Progress Revisited - Reflections and Overview”, OFCE Working Paper No. 2009-33, Centre de Recherche en Économie de Sciences Po. Retrieved from http://spire.sciencespo.fr/hdl:/2441/5l6uh8ogmqildh09h4687h53k/resources/wp2009-33.pdf.
Takayama, N. 1979 “Poverty, income inequality and their measures: Professor Sen’s axiomatic approach reconsidered”, Econometrica 47(3): 747–759.
Thon, D. 1979 “On measuring poverty”, Review of Income and Wealth 25(4): 429–439. doi.org/10.1111/j.1475-4991.1979.tb00117.x
Thorbecke, E. 2007 “Multidimensional Poverty: Conceptual and Measurement Issues”, in N. Kakwani and J. Silber (Eds.) The Many Dimensions of Poverty, pp.3–19. London: Palgrave Macmillan. doi.org/10.1057/9780230592407_1
Tsui, K.Y. 1995 “Multidimensional generalizations of the relative and absolute indices: the Atkinson–Kolm–Sen approach”, Journal of Economic Theory 67(1): 251–265. doi.org/10.1006/jeth.1995.1073
—– 2002 “Multidimensional Poverty Indices”, Social Choice and Welfare 19: 69–93. doi.org/10.1007/s355-002-8326-3
United Nations 2015 Resolution adopted by the General Assembly on 25 September 2015. United Nations General Assembly A/RES/70/1, Seventieth Session, Agenda items 15 and 116.
UNDP (United Nations Development Programme) 1997 Human Development Report 1997: Human Development to Eradicate Poverty New York: UNDP.
Yaari, M.E. 1987 “The Dual Theory of Choice under Risk” Econometrica 55(1): 95–115.
—– 1988 “A controversial proposal concerning inequality measurement”, Journal of Economic Theory 44(2): 381–397. doi.org/10.1016/0022-0531(88)90010-5
Yalonetzky, G. 2014 “Conditions for the most robust multidimensional poverty comparisons using counting measures and ordinal variables”, Social Choice and Welfare 43: 773–807. doi.org/10.1007/s00355-014-0810-2
Yitzhaki, S., and R.I. Lerman 1991 “Income Stratification and Income Inequality”, Review of Income and Wealth 37(3): 313–329. doi.org/10.1111/j.1475-4991.1991.tb00374.x
—–, and E. Schechtman 2013 The Gini Methodology. A Primer on Statistical Methodology Springer: New York.
