The (α, β)-multi-level α-Gini decomposition with an illustration to income inequality in France in 2005

We propose a generalization of the decomposition by population subgroups of the alpha-Gini index, the so-called multi-level subgroup decomposition. We demonstrate that all components obtained from the decomposition, can integrate in their functional forma parameter of inequality sensitivity being either related to overall inequalities (alpha) or to between-group non-overlappings (beta). We prove that a decision maker who behaves in accordance with the alpha-Gini indices is sensitive to the inequalities between the groups when this sensitivity may differ for each partition of groups. For that purpose, we check the axiomatic foundations of this new family of measures providing also a characterization for the alpha-Gini indices where alpha > 2. An illustration of the multi-level alpha-Gini decomposition is performed for the analysis of the income disparities in France in 2005. (C) 2013 Published by Elsevier B.V.