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A Counting Approach for Measuring Multidimensional Deprivation

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  • Aaberge, Rolf

    ()
    (Statistics Norway)

  • Peluso, Eugenio

    ()
    (University of Verona)

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 Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 6589.

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Length: 24 pages
Date of creation: May 2012
Date of revision:
Handle: RePEc:iza:izadps:dp6589

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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. Rolf Aaberge, 2000. "Ranking Intersecting Lorenz Curves," Discussion Papers 271, Research Department of Statistics Norway.
  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, 2012. "Elementary multivariate rearrangements and stochastic dominance on a Fréchet class," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1450-1459.
  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. 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.
  6. Atkinson, Tony & Cantillon, Bea & Marlier, Eric & Nolan, Brian, 2002. "Social Indicators: The EU and Social Inclusion," OUP Catalogue, Oxford University Press, number 9780199253494, Octomber.
  7. 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.
  8. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  9. 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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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. 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.
  3. 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.

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