The Bonferroni, Gini, and De Vergottini indices. Inequality, welfare, and deprivation in the European union in 2000

Purpose: This paper studies the Bonferroni (B) and De Vergottini (V) inequality measures, evaluating their differences and similarities, both normatively and statistically. Design: We highlight the similarities of these two indices with the well-known Gini index (G) and use the AKS [Atkinson (1970), Kolm (1976), Sen (1973)] approach to relate social welfare functions and inequalities indices. In addition, we propose two formulations for relative deprivation, alternative to Yitzhaki (1979) and Hey and Lambert (1980) approach. Findings: The three indices belong to the same family and introduce different and, in some sense, complementary value judgments in the measurement of inequality and welfare; each of them evaluates in a different way the local inequality in the income distribution. The three indices present inequality aversion (satisfy the Pigou-Dalton Principle of Transfers). But only B satisfies the Principle of Positional Transfer Sensitivity. The three absolute indices are interpreted as measures of the mean social deprivation starting from different definitions of individual deprivation. Originality: The originality of this paper lies in the joint use of the three indices in the measurement of inequality, welfare, and deprivation. We apply these indices to obtain rankings of the European Union countries, using the European Community Household Panel data (2000). A sensitivity analysis of the rankings to different equivalence scales is also included.