The Gini Index and the Measurement of Multidimensional Inequality
| Published date | 01 May 1994 |
| DOI | http://doi.org/10.1111/j.1468-0084.1994.mp56002007.x |
| Date | 01 May 1994 |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 56,2(1994)
0305-9049
The Gini Index and the Measurement of
Multidimensional Inequality
Yves Fluckiger and Jacques Silber
I. INTRODUCTION
In a recent note, Bradburd and Ross (1988) proposed a new summary index
of multidimensional inequality, whose purpose is to measure the extent to
which one multidimensional characterization differs from another. Using an
example taken from the field of industrial organization and calling rn the
market share of firm i in the industry, m1 the proportion of all industry
shipments made in product category j and my the proportion of all industry
shipments made by firm j in product code j, they stated that an industry could
be considered as heterogeneous if the share rn,1 was different from the
product rn X m1.
To measure such a heterogeneity, they defined an index HET derived from
the z2 statistic used with contingency tables and concluded that the closer
their index HET is to 1, the greater 'the degree of inequality among or hetero-
geneity across the categorizations, while a value near O indicates complete
concordance'.
It will be shown that the Gini Index may also be used to measure such a
heterogeneity. The advantage of such an approach is that it may be given a
graphical representation, since the Gini Index is related to the Lorenz Curve,
and it will be shown that a curve similar to the Lorenz Curve may be drawn
when measuring this heterogeneity.
II. MULTIDIMENSIONAL CATEGORIZATION AND THE GINT INDEX
Silber (1989) has recently proved that the Gini Index 'G of income inequality
could be written as
IG=eGs (1)
where e' is a row vector of the shares in the total population and s a column
vector of the shares in the total income of the different income classes which
have been distinguished. Both vectors are ranked by decreasing value of the
average income of each income class. Finally, the matrix G is a n by n matrix
(n being the number of income classes) whose typical element g,7 is equal to O
if i =j, to - 1 if j j.
C Basil Blackwell Ltd. 1994. Published by Blackwell Publishers, 108 Cowley Road, Oxford 0X4 IJF,
UK & 238 Main Street. Cambridge, MA 02142, USA.
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