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What do normative indices of multidimensional inequality really measure?

Author Info

Listed author(s):
  • BOSMANS, Kristof

    ()

    (Department of Economics, Maastricht University, NL-6211 LM Maastricht, The Netherlands)

  • DECANCQ, Koen

    ()

    (Herman Deleeck Centre for Social Policy, University of Antwerp, B-2000 Antwerp, Belgium; Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

  • OOGHE, Erwin

    ()

    (Center for Economic Studies, KU Leuven, B-3000 Leuve, Belgium)

Abstract

We argue that normative indices of multidimensional inequality do not only measure a distribution’s extent of inequity (i.e., the gaps between the better-off and the worse-off), but also its extent of inefficiency (i.e., the non-realized mutually beneficial exchanges of goods). We provide a decomposition that allows quantifying these two parts of inequality. Exact formulas of the inequity and inefficiency components are provided for a generic class of social welfare functions. The inequity component turns out to be a two-stage measure, which applies a unidimensional inequality measure to the vector of well-being levels. We critically discuss two prominent transfer principles, viz., uniform majorization and correlation increasing majorization, in the light of the decomposition. A decomposition of inequality in human development illustrates the analysis.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2013035.

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Date of creation: 09 Jul 2013
Handle: RePEc:cor:louvco:2013035
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Keywords: multidimensional inequality measurement; efficiency; uniform majorization; correlation increasing majorization;

Other versions of this item:

Find related papers by JEL classification:
  • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
  • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
  • I31 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - General Welfare, Well-Being

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Cited by:

  1. Koen Decancq, 2017. "Measuring Multidimensional Inequality in the OECD Member Countries with a Distribution-Sensitive Better Life Index," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 131(3), pages 1057-1086, April.
  2. Rolf Aaberge & Andrea Brandolini, 2014. "Multidimensional poverty and inequality," Discussion Papers 792, Statistics Norway, Research Department.
  3. Öztürk Z.E. & Bosmans K.G.M., 2013. "An axiomatic approach to the measurement of envy," Research Memorandum 063, Maastricht University, Graduate School of Business and Economics (GSBE).
  4. Shatakshee Dhongde & Yi Li & Prasanta K. Pattanaik & Yongsheng Xu, 2016. "Binary data, hierarchy of attributes, and multidimensional deprivation," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 14(4), pages 363-378, December.
  5. Paolo Giovanni Piacquadio, 2016. "A Fairness Justification of Utilitarianism," CESifo Working Paper Series 5785, CESifo Group Munich.
  6. Lidia Ceriani & Chiara Gigliarano, 2016. "Multidimensional well-being: A Bayesian Networks approach," Working Papers 399, ECINEQ, Society for the Study of Economic Inequality.
  7. Kristof Bosmans & Koen Decancq & Erwin Ooghe, 2016. "Who's afraid of aggregating money metrics?," Working Papers Department of Economics 551153, KU Leuven, Faculty of Economics and Business, Department of Economics.

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