Economic Properties of Statistical Indices: The Case of a Multidimensional Gini Index

This paper seeks to construct a Gini index of the distribution of standard of living. Since standard of living has various dimensions, we need a multidimensional Gini index (MGI). The literature on index numbers contains two distinct approaches: the statistical and the economic. In the context of MGIs the statistical approach (which obtains the indices from conditions based on statistical or data-related considerations) seems to be open to the criticism that it sometimes yields indices that violate economic norms. However, the economic approach (where the indices are derived from norms based on economic theory) also does not seem to have succeeded so far in obtaining an MGI satisfying the various normative requirements that have been proposed in the literature. This paper shows that it is possible to obtain an MGI from the statistical approach ensuring, at the same time, that the economic norms are satisfied. In this sense it is an attempt to bring the two disparate traditions in index construction referred to above closer to each other. The index that is developed here does not appear in the existing literature. Moreover, the literature does not seem to contain any other MGI satisfying all of the proposed economic norms.