Social Choice and Welfare

, Volume 53, Issue 4, pp 603–619 | Cite as

The measurement of welfare change

  • Walter BossertEmail author
  • Bhaskar Dutta
Original Paper


We propose a class of measures of welfare change that are based on the generalized Gini social welfare functions. We analyze these measures in the context of a second-order dominance property that is akin to generalized Lorenz dominance as introduced by Shorrocks (Economica 50:3–17, 1983) and Kakwani (Advances in econometrics, vol 3. JAI Press, Greenwich, pp 191–213, 1984). Because we consider welfare differences rather than welfare levels, the requisite equivalence result involves affine welfare functions only, as opposed to the entire class of strictly increasing and strictly S-concave welfare indicators. Thus, our measures are associated with those members of the generalized-Gini class that are strictly increasing and strictly S-concave. Moving from second-order dominance to first-order dominance does not change this result significantly: for most intents and purposes, the generalized Ginis remain the only strictly increasing and strictly S-concave measures that are equivalent to this first-order dominance condition phrased in terms of welfare change. Our final result provides a characterization of our measures of welfare change in the spirit of Weymark’s (Math Soc Sci 1:409–430, 1981) original axiomatization of the generalized Gini welfare functions. Journal of Economic Literature Classification No.: D31.



We thank Dirk Van de gaer, Horst Zank, Stéphane Zuber and two referees for comments. Financial support from the Fonds de Recherche sur la Société et la Culture of Québec is gratefully acknowledged.


  1. Atkinson AB (1970) On the measurement of inequality. J Econ Theory 2:244–263CrossRefGoogle Scholar
  2. Bossert W (1990) An axiomatization of the single-series Ginis. J Econ Theory 50:82–92CrossRefGoogle Scholar
  3. Bourguignon F (2011) Non-anonymous growth incidence curves, income mobility and social welfare dominance. J Econ Inequal 9:605–627CrossRefGoogle Scholar
  4. Capéau B, Ooghe E (2007) On comparing heterogeneous populations: is there really a conflict between welfarism and a concern for greater equality in living standards? Math Soc Sci 53:1–28CrossRefGoogle Scholar
  5. Dalton H (1920) The measurement of the inequality of incomes. Econ J 30:348–361CrossRefGoogle Scholar
  6. Dasgupta P, Sen A, Starrett D (1973) Notes on the measurement of inequality. J Econ Theory 6:180–187CrossRefGoogle Scholar
  7. Donaldson D, Weymark JA (1980) A single-parameter generalization of the Gini indices of inequality. J Econ Theory 22:67–86CrossRefGoogle Scholar
  8. Jenkins SP, Van Kerm P (2006) Trends in income inequality, pro-poor income growth, and income mobility. Oxf Econ Pap 58:531–548CrossRefGoogle Scholar
  9. Kakwani NC (1977) Measurement of tax progressivity: an international comparison. Econ J 87:71–80CrossRefGoogle Scholar
  10. Kakwani NC (1984) Welfare ranking of income distributions. In: Basman RL, Rhodes GF (eds) Advances in econometrics, vol 3. JAI Press, Greenwich, pp 191–213Google Scholar
  11. Kolm S-Ch (1969) The optimal production of social justice. In: Margolis J, Guitton S (eds) Public economics. Macmillan, London, pp 145–200CrossRefGoogle Scholar
  12. Marshall AW, Olkin I (1979) Inequalities: theory of majorization and its applications. Academic Press, New YorkGoogle Scholar
  13. Mehran F (1976) Linear measures of income inequality. Econometrica 44:805–809CrossRefGoogle Scholar
  14. Pigou AC (1912) Wealth and welfare. Macmillan, LondonGoogle Scholar
  15. Ravallion M, Chen S (2003) Measuring pro-poor growth. Econ Lett 78:93–99CrossRefGoogle Scholar
  16. Shorrocks AF (1983) Ranking income distributions. Economica 50:3–17CrossRefGoogle Scholar
  17. Sen A (1973) On economic inequality. Clarendon Press, OxfordCrossRefGoogle Scholar
  18. Son HH (2004) A note on pro-poor growth. Econ Lett 82:307–314CrossRefGoogle Scholar
  19. Weymark JA (1981) Generalized Gini inequality indices. Math Soc Sci 1:409–430CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Economics and CIREQUniversity of MontrealMontrealCanada
  2. 2.University of WarwickWarwickUK
  3. 3.Ashoka UniversitySonipatIndia

Personalised recommendations