Abstract
In the popular class of multidimensional poverty measures introduced by Alkire and Foster (2011), a threshold switching function is used to identify who is multidimensionally poor. This paper shows that the weights and cut-off employed in this procedure are generally not unique and that such functions implicitly assume all groups of deprivation indicators of some fixed size are perfect substitutes. To address these limitations, I show how the identification procedure can be extended to incorporate any type of positive switching function, represented by the set of minimal deprivation bundles that define a unit as poor. Furthermore, the Banzhaf power index, uniquely defined from the same set of minimal bundles, constitutes a natural and robust metric of the relative importance of each indicator, from which the adjusted headcount can be estimated. I demonstrate the merit of this approach using data from Mozambique, including a decomposition of the adjusted headcount using a ‘one from each dimension’ non-threshold function.
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31 July 2021
A Correction to this paper has been published: https://doi.org/10.1007/s10888-021-09503-9
References
Abdu, M., Delamonica, E.: Multidimensional child poverty: from complex weighting to simple representation. Soc. Indic. Res. 136(3), 881–905 (2018)
Alkire, S., Foster, J.: Counting and multidimensional poverty measurement. J. Public Econ. 95, 476–487 (2011a)
Alkire, S.: Understandings and misunderstandings of multidimensional poverty measurement. J. Econ. Inequal. 9(2), 289–314 (2011b)
Alkire, S., Foster, J., Santos, M.: Where did identification go? J. Econ. Inequal. 9(3), 501–505 (2011)
Alkire, S., Santos, M.E.: Measuring acute poverty in the developing world: Robustness and scope of the multidimensional poverty index. World Dev. 59, 251–274 (2014)
Alkire, S., Seth, S.: Multidimensional poverty reduction in India between 1999 and 2006: Where and how? World Dev. 72, 93–108 (2015)
Anand, P., Durand, M., Heckman, J.: The measurement of progress – some achievements and challenges. Journal of the Royal Statistical Society: Series A (Statistics in Society) 174(4), 851–855 (2011)
Anderson, G.: Multilateral Wellbeing Comparison in a Many Dimensioned World: Ordering and Ranking Collections of Groups. Palgrave Macmillan, Cham (2019)
Angulo, R., Díaz, Y., Pardo, R.: The Colombian multidimensional poverty index: Measuring poverty in a public policy context. Soc. Indic. Res. 127 (1), 1–38 (2016)
Arndt, C., Hussain, M.A., Jones, E.S., Nhate, V., Tarp, F., Thurlow, J.: Explaining the evolution of poverty: the case of Mozambique. American Journal of Agricultural Economics. https://doi.org/10.1093/ajae/aas022 (2012)
Atkinson, A.: Multidimensional deprivation: contrasting social welfare and counting approaches. J. Econ. Inequal. 1(1), 51–65 (2003)
Bennett, C., Mitra, S.: Multidimensional poverty: measurement, estimation and inference. Econ. Rev. 32(1), 57–83 (2013)
Bourguignon, F., Chakravarty, S.: The measurement of multidimensional poverty. J. Econ. Inequal. 1(1), 25–49 (2003)
Crama, Y., Hammer, P.L.: Boolean Functions: Theory, Algorithms, and Applications. Cambridge University Press, Cambridge (2011)
Decancq, K., Lugo, M.A.: Weights in multidimensional indices of wellbeing: an overview. Econ. Rev. 32(1), 7–34 (2013)
DEEF: Pobreza e bem-estar em Moçambique: Quarta avaliação nacional (IOF 2104/15). Technical report, Direcção de Estudos Económicos e Financeiros, Ministério de Economia e Finanças, República de Moçambique. https://www.wider.unu.edu/sites/default/files/Final_QUARTAAVALIA (2016)
DNEAP: Pobreza e bem-estar em Moçambique: Terceira avaliação nacional. Technical report, Ministry of Planning and Development, Government of Mozambique. www.dneapmpd.gov.mz/index.php?option=com_docman&task=doc_download&gid=133&Itemid=54 (2010)
Dubey, P., Shapley, L.S.: Mathematical properties of the Banzhaf power index. Math. Oper. Res. 4(2), 99–131 (1979)
Foster, J., Greer, J., Thorbecke, E.: A class of decomposable poverty measures. Econometrica 52(3), 761–766 (1984)
Foster, J.E., McGillivray, M., Seth, S.: Composite indices: rank robustness, statistical association, and redundancy. Econom. Rev. 32(1), 35–56 (2013)
Freixas, J., Gambarelli, G.: Common internal properties among power indices. Control. Cybern. 26, 591–604 (1997)
Houy, N., Zwicker, W.S.: The geometry of voting power: weighted voting and hyper-ellipsoids. Games and Economic Behavior 84, 7–16 (2014)
Jones, S.: Measuring what’s missing: practical estimates of coverage for stochastic simulations. J. Stat. Comput. Simul. 86(9), 1660–1672 (2016)
de Keijzer, B., Klos, T.B., Zhang, Y.: Solving weighted voting game design problems optimally: Representations, synthesis, and enumeration. ERIM Report Series Reference No. ERS-2012-006-LIS, Erasmus Research Institute of Management. arXiv:1204.5213 (2012)
Lucas, W.F.: Measuring power in weighted voting systems. In: Brams, S.J., Lucas, W.F., Straffin, P.D. (eds.) Political and Related Models, pp 183–238. Springer, New York (1983)
Maasoumi, E.: The measurement and decomposition of multi-dimensional inequality. Econometrica 54, 991–997 (1986)
Mitra, S.: Re-assessing “trickle-down” using a multidimensional criteria: the case of India. Soc. Indic. Res. 136(2), 497–515 (2018)
Pasha, A.: Regional perspectives on the multidimensional poverty index. World Dev. 94, 268–285 (2017)
Permanyer, I.: Measuring poverty in multidimensional contexts. Soc. Choice Welf. 53(4), 677–708 (2019)
Ravallion, M.: Mashup indices of development. The World Bank Research Observer 27(1), 1–32 (2012)
Rippin, N.: Efficiency and distributive justice in multidimensional poverty issues. In: White, R. (ed.) Measuring Multidimensional Poverty and Deprivation: Incidence and Determinants in Developed Countries, chapter 3, pp. 31–67. Springer International Publishing (2017)
Santos, M.E., Villatoro, P.: A multidimensional poverty index for Latin America. Rev. Income Wealth 64(1), 52–82 (2018)
Sen, A., Anand, S.: Concepts of Human Development and poverty: A Multidimensional perspective, pp. 1–20. New York: United Nations Development Programme. Reprinted in S. Fukuda-Parr and A. K. Shiva Kumar, eds. Readings in Human Development (New Delhi: Oxford University Press, 2003) (1997)
Seth, S.: Inequality, interactions, and human development. J. Hum. Dev. Capab. 10(3), 375–396 (2009)
Seth, S., Alkire, S.: Did poverty reduction reach the poorest of the poor? Complementary measures of poverty and inequality in the counting approach. Research on Economic Inequality 25, 63–102 (2017)
Taylor, A., Zwicker, W.: A characterization of weighted voting. Proc. Am. Math. Soc. 115(4), 1089–1094 (1992)
de la Vega, M.C.L., Urrutia, A.: Characterizing how to aggregate the individuals’ deprivations in a multidimensional framework. J. Econ. Inequal. 9(2), 183–194 (2011)
Acknowledgements
Thanks to the editor, referees, Paul Anand, Paola Ballon, James Foster, Simon Quinn, Vincenzo Salvucci, Ricardo Santos, Suman Seth, Finn Tarp, Erik Thorbecke and Gaston Yalonetzky for comments and encouragement on my investigation of this topic. This is a revised and updated version of a study originally commissioned by UNU-WIDER (Helsinki), under the project ‘Inclusive Growth in Mozambique: scaling-up research and capacity’. All errors and omissions are my own.
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Jones, S. Extending multidimensional poverty identification: from additive weights to minimal bundles. J Econ Inequal 20, 421–438 (2022). https://doi.org/10.1007/s10888-021-09477-8
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DOI: https://doi.org/10.1007/s10888-021-09477-8