Measuring Multidimensional Inequality: A Gini Index

Abstract

A very common criticism of globalisation is that it has led to an increase in inequality. To check the validity of the criticism, one would need an inequality index. Presumably, inequality here means inequality in the distribution of well-being. However, well-being is a multidimensional concept. Hence, we need a multidimensional inequality index. Moreover, since in the unidimensional context, the most widely used inequality index is the Gini index, and it is natural to want to use a multidimensional Gini index (MGI) for the purpose. However, while the unidimensional Gini is uniquely defined, an MGI is not. The existing literature contains various suggestions as to how an MGI can be defined. Unfortunately, none of the suggested MGIs seems to have all the properties that one would, on intuitive grounds, expect such an index to possess. Moreover, some of the suggested MGIs are mathematically quite complex. In this paper, we first mathematically characterise a specific MGI and then show that it possesses all the intuitively expected properties. It is also seen to be very simple and transparent in nature. It is hoped that while this paper is theoretical, the derived index can be used by empirical researchers to investigate the effect of globalisation on inequality somewhat more satisfactorily than has hitherto been the case.