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A Counting Approach for Measuring Multidimensional Deprivation

  • Rolf Aaberge

    ()

    (Statistics Norway)

  • Eugenio Peluso

    ()

    (Department of Economics (University of Verona))

This paper is concerned with the problem of ranking and quantifying the extent of deprivation exhibited by multidimensional distributions, where the multiple attributes in which an individual can be deprived are represented by dichotomized variables. To this end we first aggregate deprivation for each individual into a “deprivation count” indicating the number of dimensions for which the individual suffers from deprivation. Then we compare distributions of deprivation counts through summary measures of deprivation, by drawing on the rank-dependent social evaluation framework (Sen 1974, Yaari 1987). This approach proves to allow decomposition of the summary measures into extent of and dispersion in the distribution of multiple deprivations. To provide a normative justification of the proposed deprivation measures, an intervention principle affecting the association between the different deprivation indicators is adopted. Moreover, we introduce a family of measures of concentration in the distribution of deprivation experienced by the population. Concentration is defined to occur if dispersion in the observed distribution of deprivation is higher than the dispersion attained when the single deprivation indicators are treated as independent random variables, under the constraint of unchanged marginal distributions.

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Paper provided by University of Verona, Department of Economics in its series Working Papers with number 07/2011.

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Date of creation: Jun 2011
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Handle: RePEc:ver:wpaper:07/2011
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  1. Aaberge, Rolf, 2008. "Ranking Intersecting Lorenz Curves," IZA Discussion Papers 3852, Institute for the Study of Labor (IZA).
  2. BOSSERT, Walter & CHAKRAVARTY, Satya R. & D’AMBROSIO, Conchita, 2008. "Poverty and Time," Cahiers de recherche 2008-05, Universite de Montreal, Departement de sciences economiques.
    • Walter Bossert & Satya R. Chakravarty & Conchita D’Ambrosio, 2008. "Poverty and Time," Working Papers 87, ECINEQ, Society for the Study of Economic Inequality.
    • Bossert, Walter & Chakravarty, Satya R. & d’Ambrosio, Conchita, 2010. "Poverty and Time," Working Paper Series wp2010-74, World Institute for Development Economic Research (UNU-WIDER).
    • BOSSERT, Walter & CHAKRAVARTY, Satya R. & D’AMBROSIO, Conchita, 2008. "Poverty and Time," Cahiers de recherche 05-2008, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  3. Atkinson, Tony & Cantillon, Bea & Marlier, Eric & Nolan, Brian, 2002. "Social Indicators: The EU and Social Inclusion," OUP Catalogue, Oxford University Press, number 9780199253494, March.
  4. Bourguignon, F. & Chakravarty, S.R., 1998. "The Measurement of Multidimensional Poverty," DELTA Working Papers 98-12, DELTA (Ecole normale supérieure).
  5. DECANCQ, Koen, . "Elementary multivariate rearrangements and stochastic dominance on a Fréchet class," CORE Discussion Papers RP -2425, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Aaberge, Rolf, 2001. "Axiomatic Characterization of the Gini Coefficient and Lorenz Curve Orderings," Journal of Economic Theory, Elsevier, vol. 101(1), pages 115-132, November.
  7. Le Breton, Michel & Peluso, Eugenio, 2010. "Smooth inequality measurement: Approximation theorems," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 405-415, July.
  8. Guio, Anne-Catherine & Fusco, Alessio & Marlier, Eric, 2009. "A European Union Approach to Material Deprivation using EU-SILC and Eurobarometer data," IRISS Working Paper Series 2009-19, IRISS at CEPS/INSTEAD.
  9. M. Lasso de la Vega & Ana Urrutia, 2011. "Characterizing how to aggregate the individuals’ deprivations in a multidimensional framework," Journal of Economic Inequality, Springer, vol. 9(2), pages 183-194, June.
  10. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  11. Rolf Aaberge, 2000. "Characterizations of Lorenz curves and income distributions," Social Choice and Welfare, Springer, vol. 17(4), pages 639-653.
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