Normative properties of multidimensional inequality indices with data-driven dimensional weights: The case of a Gini index

Abstract

A central problem in constructing multidimensional inequality indices is that of devising weights on the dimensions. There are two different approaches to the problem: the normative and the data‐driven. Indices derived from data‐driven weights have the limitation that they may violate normatively desired properties. This paper asks whether it is possible to obtain normatively acceptable inequality indices from a data‐driven approach. A multidimensional Gini index is derived from an endogenous weighting scheme and is shown to possess a number of desired properties. The existing literature does not seem to contain a Gini index that satisfies all of these properties.