Abstract
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.
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References
Atkinson AB (1970) On the measurement of inequality. J Econ Theory 2:244–263
Bossert W (1990) An axiomatization of the single-series Ginis. J Econ Theory 50:82–92
Bourguignon F (2011) Non-anonymous growth incidence curves, income mobility and social welfare dominance. J Econ Inequal 9:605–627
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 53:1–28
Dalton H (1920) The measurement of the inequality of incomes. Econ J 30:348–361
Dasgupta P, Sen A, Starrett D (1973) Notes on the measurement of inequality. J Econ Theory 6:180–187
Donaldson D, Weymark JA (1980) A single-parameter generalization of the Gini indices of inequality. J Econ Theory 22:67–86
Jenkins SP, Van Kerm P (2006) Trends in income inequality, pro-poor income growth, and income mobility. Oxf Econ Pap 58:531–548
Kakwani NC (1977) Measurement of tax progressivity: an international comparison. Econ J 87:71–80
Kakwani NC (1984) Welfare ranking of income distributions. In: Basman RL, Rhodes GF (eds) Advances in econometrics, vol 3. JAI Press, Greenwich, pp 191–213
Kolm S-Ch (1969) The optimal production of social justice. In: Margolis J, Guitton S (eds) Public economics. Macmillan, London, pp 145–200
Marshall AW, Olkin I (1979) Inequalities: theory of majorization and its applications. Academic Press, New York
Mehran F (1976) Linear measures of income inequality. Econometrica 44:805–809
Pigou AC (1912) Wealth and welfare. Macmillan, London
Ravallion M, Chen S (2003) Measuring pro-poor growth. Econ Lett 78:93–99
Shorrocks AF (1983) Ranking income distributions. Economica 50:3–17
Sen A (1973) On economic inequality. Clarendon Press, Oxford
Son HH (2004) A note on pro-poor growth. Econ Lett 82:307–314
Weymark JA (1981) Generalized Gini inequality indices. Math Soc Sci 1:409–430
Acknowledgements
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.
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Bossert, W., Dutta, B. The measurement of welfare change. Soc Choice Welf 53, 603–619 (2019). https://doi.org/10.1007/s00355-019-01201-w
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DOI: https://doi.org/10.1007/s00355-019-01201-w