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A counting approach for measuring multidimensional deprivation

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  • Rolf Aaberge
  • Eugenio Peluso

    ()
    (Statistics Norway)

Abstract

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”, representing the number of dimensions for which the individual suffers from deprivation. Next, by drawing on the rank-dependent social evaluation framework that originates from Sen (1974) and Yaari (1988) the individual deprivation counts are aggregated into summary measures of deprivation, which prove to admit decomposition into the mean and the dispersion of the distribution of multiple deprivations. Moreover, second-degree upward and downward count distribution dominance are shown to be useful criteria for dividing the measures of deprivation into two separate subfamilies. To provide a normative justification of the dominance criteria we introduce alternative principles of association (correlation) rearrangements, where either the marginal deprivation distributions or the mean deprivation are assumed to be kept fixed.

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Bibliographic Info

Paper provided by Research Department of Statistics Norway in its series Discussion Papers with number 700.

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Date of creation: Aug 2012
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Handle: RePEc:ssb:dispap:700

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Keywords: Multidimensional deprivation; counting approach; partial orderings; rank-dependent measures of deprivation; principles of association rearrangements;

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References

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  1. 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.
  2. 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.
  3. 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).
  4. Le Breton, Michel & Peluso, Eugenio, 2010. "Smooth inequality measurement: Approximation theorems," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 405-415, July.
  5. Atkinson, Tony & Cantillon, Bea & Marlier, Eric & Nolan, Brian, 2002. "Social Indicators: The EU and Social Inclusion," OUP Catalogue, Oxford University Press, number 9780199253494.
  6. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  7. Rolf Aaberge, 2000. "Characterizations of Lorenz curves and income distributions," Social Choice and Welfare, Springer, vol. 17(4), pages 639-653.
  8. Rolf Aaberge, 2000. "Ranking intersectiong Lorenz Curves," ICER Working Papers 08-2000, ICER - International Centre for Economic Research.
  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.
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Citations

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Cited by:
  1. Ive Marx & Brian Nolan & Javier Olivera, 2014. "The Welfare State and Anti-Poverty Policy in Rich Countries," Working Papers 1403, Herman Deleeck Centre for Social Policy, University of Antwerp.
  2. HILDEBRAND Vincent & PI ALPERIN Maria Noel & VAN KERM Philippe, 2012. "Measuring and accounting for the deprivation gap of Portuguese immigrants in Luxembourg," CEPS/INSTEAD Working Paper Series 2012-33, CEPS/INSTEAD.
  3. Bérenger, Valérie & Deutsch, Joseph & Silber, Jacques, 2013. "Durable goods, access to services and the derivation of an asset index: Comparing two methodologies and three countries," Economic Modelling, Elsevier, vol. 35(C), pages 881-891.

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