A Note On Inequality Measures And The Pigou-Dalton Principle Of Transfers

Abstract

The question whether a given function is a suitable measure of income inequality is mostly answered in the following way: it is obvious that the proposed function satisfies some properties that are desiderable in the context. In our opinion, the only way is to derive inequality measures axiomatically. Our aim is therefore to characterize inequality measures with a minimal number of “essential” and “natural” properties. There are many properties that either seem to be “natural” or are satisfied by functions being introduced as inequality measures: the principle of transfers, homogeneity of degree zero, symmetry, decomposability, extensibility, etc.. For a discussion of these properties see C.E. Bonferroni (1930, 1940), G.S. Fei and Y.C.H. Fields (1978), S.C. Kolm (1976 a,b) W. Eichhorn and W. Gehrig (1982), W. Gehrig (1983, 1984). In this paper we will focus on the Pigou-Dalton principle of transfers without any further requirement. The Pigou-Dalton criterion has central role in the theory of inequality measurement and is at the heart of several well-known results. The intuitive appeal of the principle of transfers is further supported by the results of A.B. Atkinson (1970), P. Dasgupta, A. Sen and D. Starret (1973) M. Rothschild and J.E. Stigliz (1970), which relate it to the well-known Lorenz criterion and to the social welfare approach to inequality. As a basis for inequality comparisons, however, its scope is severely limited (e. g. when the distributions are defined over populations of different sizes, or having different means). Transfer sensitivity has been seen as a means of strengthening the Pigou- Dalton principle by ensuring that a higher weigth in the inequality assessment is attached to transfers taking place in the lower tail of the distribution. A transfer sensitivity requirement of this type has been discussed by many authors: A.B.KeywordsIncome InequalityLorenz CurveInequality MeasurePoverty MeasureElementary TransferThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.