The measurement of welfare change

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.