The Squared Coefficient of Variation as an Inequality Index: A Social Evaluation Characterization

The squared coefficient of variation (C2) is a well-known index of relative inequality. However, the existing economic theory of inequality does not contain a characterization of this index in terms of the properties of the underlying social evaluation function. It is well-known that if the Atkinson-Kolm-Sen (AKS) index of relative inequality derived from a social evaluation relation defined on a space of distributions is C2, it is necessary that the relation satisfies a ¡®transfer neutrality¡¯ condition. This paper obtains a complete characterization of the index by proving the converse. It is shown that, in the presence of other standard assumptions on the social evaluation relation, transfer neutrality implies a particular social evaluation function and that the corresponding AKS relative inequality index coincides with C2. This inequality index and the corresponding social evaluation function is then applied in a relatively unexplored area of empirical research. It is shown that in India inequality (as measured by C2) in the distribution of a variable that indicates the width of accessibility of bank credit increased in the ten or so years following the introduction of economic reforms in the early 1990s. At the same time there was an increase in the average value of this indicator. The question, therefore, arises as to the direction of change of over-all social welfare from this particular attribute. The social evaluation underlying C2 implies that, on balance, there was a decline in the welfare of the country in this respect.