A Class of Association Sensitive Multidimensional Welfare Indices

The last few decades have seen increased theoretical and empirical interest in multidimensional measures of welfare. This paper develops a two-parameter class of welfare indices that is sensitive to two distinct forms of inter-personal inequality in the multidimensional framework. The first form of inequality pertains to the spread of each dimensional achievement across the population, as would be reflected in the multidimensional version of the usual Lorenz criterion. The second one regards association or correlation across dimensions, reflecting the key observation that inter-dimensional association may alter evaluation of individual as well as overall inequality. Most existing multi-dimensional welfare indices are, however, either completely insensitive to inter-personal inequality or are only sensitive to the first. The class of indices developed in this paper is sensitive to both forms of multidimensional inequality. An axiomatic characterization of the class is provided, and it is shown that other multidimensional indices, such as the ones developed by Bourguignon (1999) and Foster, Lopez-Calva, and Székely (2005), are sub-classes of this new broader class. Finally, essential statistical tests are constructed to verify the reliability of the evaluations generated by the indices.