Measuring Well-being Inequality with a Multidimensional Gini Index

Individual well-being is inherently a multidimensional concept. Any attempt to measure inequality of well-being should take this multidimensionality explicitly into account. In this paper we propose to measure well-being inequality by a multidimensional generalization of the Gini coe¢ cient. We follow a normative procedure and derive two Gini indices of well-being inequality from their underlying multidimensional social evaluation functions. The social evaluation functions themselves are conceived as a double aggregation functions. One aggregation is across the dimensions of well-being. The other aggregation is across individuals and depends on the level and the position of the individual in the total distribution. The two social evaluation functions considered only di¤er with respect to the sequencing of both aggregations. We investigate the role of the sequencing on the compliance of the proposed indices to a multidimensional version of the Pigou-Dalton transfer principle and their sensitivity to changes in the correlation between the dimensions. The resulting multidimensional Gini inequality indices are illustrated using Russian household data on three dimensions of well-being: material standard of living, health and education.