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

• DOI: http://doi.org/10.1111/ijet.12153
• Author: Asis Kumar Banerjee
• Date: 01 September 2018
• Published date: 01 September 2018

Normative properties of multidimensional inequality

indices with data-driven dimensional weights: The case of a

Gini index

Asis Kumar Banerjee

*

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.

Key words multidimensional inequality index, data-driven weight, eigenvector

eigenvalue

JEL classification D60, D63

Accepted 16 November 2016

1 Introduction

The need for a multidimensional index of inequality (MII) in the distribution of an attribute arises

whenever the attribute in question has more than one dimension. The standard of living is an

important example of such an attribute. The task of constructing any multidimensional index

(whether an index of inequality or otherwise) can be interpreted as essentially one of devising

suitable weights on the various dimensions. In the existing literature on multidimensional standard

of living the dominant tradition has been to use fixed (i.e. data-independent) weights. Different

weighting schemes (or classes of such schemes) have been derived by imposing different sets of

norms on the index (or on the underlying social values). For a recent review of MIIs, see Aaberge and

Brandolini (2015).

In practice, however, in many circumstances it would seem natural to hypothesize that the

appropriateness or otherwise of a weighting scheme may depend on the prevailing circumstances

regarding the distribution of the various dimensions. There seems to be some empirical evidence that

opinions of individuals regarding what weights are appropriate do depend on circumstances. See, for

instance, Esposito and Chiappero-Martinetti (2013). If society does not completely ignore the

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Institute of Development Studies Kolkata, Salt Lake, Kolkata, India. Email: asisbanerjee.cu@gmail.com

I am indebted to an anonymous referee of this journal for comments on an earlier version of the paper. Comments from

participants in various Annual Conferences of the Indian Econometric Society and in a seminar at the Indian Statistical

Institute, Kolkata are also gratefully acknowledged.

doi: 10.1111/ijet.12153

International Journal of Economic Theory 14 (2018) 279–288 ©IAET 279

International Journal of Economic Theory