A GENERAL MEASURE OF MULTIDIMENSIONAL INEQUALITY
| Author | David R. Ross,Ralph M. Bradburd |
| Date | 01 November 1988 |
| DOI | http://doi.org/10.1111/j.1468-0084.1988.mp50004006.x |
| Published date | 01 November 1988 |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 50,4(1988)
0305-9049 $3.00
A GENERAL MEASURE OF
MULTIDIMENSIONAL INEQUALITY
Ralph M. Bradburd and David R. Ross f
I. INTRODUCTION
Measures of inequality or dissimilarity are required in empirical studies of a
wide variety of economic phenomena. There exists an extensive literature
(Atkinson, 1983; Cowell, 1977; Theil, 1967) on measuring inequality over a
scalar measure, such as income, and, in this context, a large number of
summary measures of inequality from which to choose. However, if the
research need is to capture in a summary measure the extent to which one
multidimensional characterization differs from another, the choice is con-
siderably more constrained. The only existing measure comparing multi-
dimensional categorizations is the vector cosine index, discussed in Allen
(1966, p. 381), the use of which has been confined to comparisons of two
unidimensional categorizations.1
The problem we encountered in a recent research project was a bit more
complex. We needed a readily interpretable summary measure of the extent
to which the members of a group of multidimensional entities are similar or
dissimilar to each other, that is, form a homogeneous or heterogeneous
group. Specifically, we needed to know if the firms classified as operating
within each US Standard Industrial Classification System 'industry' distribute
their output in similar proportions among the various 'product categories'
subsumed within each industry and thus, whether or not, in this particular
sense, the firms in each industry can be said to form a homogeneous group.
Our response was to develop a general summary measure of multidimen-
sional inequality, which we think may be applied usefully in a number of areas
of research. In Section II, we describe the attributes and calculation of our
measure in the most general terms. We clarify the nature of the measure in
IThis paper was written while Ross was Visiting Lecturer in Economics at the University of
Pennsylvania and while Ross and Bradburd were consultants to the Line of Business Program
of the Federal Trade Commission. The representations and conclusions herein have not been
adopted by the Federal Trade Commission or its Bureau of Economics. Reference is made only
to Line of Business aggregates previously made public in our earlier paper.
1Examples of its use in empirical studies of international trade can be found in Linnemann
(1966) and Hufbauer (1970). In these studies, the vector cosine index was employed to
measure the similarity of one country's export (import) patterns to that of another.
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