A Reply to Lampard

Abstract

Two important issues concerning the measurement of segregation are raised by Richard Lampard. He shows the relationship between the Gini coefficient (G) and the marginal matching measure (MM), and he suggests that G may have a particular advantage as a measure of segregation in that it retains more information than MM. It is worth developing these points further, and seeing whether G really does have an advantage. We shall demonstrate that MM retains just as much relevant inform ation as the Gini coefficient and, furthermore, that it has the additional advantage that it allows for better comparisons over time or between situations, making it the most suitable measure of segregation available at present. As a first step we prove that G is just another statistic of association, being a special case of Somers' D. This makes its limitations clearer. We also show that both MM and the Index of Dissimilarity are specific instances of G. The Gini coefficient and MM First of all, it is necessary to point out that the measure described by Lampard is indeed the Gini coefficient. He presents the measure in a novel form, relating the number of women to the number of workers across occupations. However, a little algebraic manipulation will convert it into the form presented below for the Gini coefficient. Lampard is correct in pointing out that MM is a particular case of the Gini coefficient. Indeed we would go further, for it can be shown that in a 2 x 2 table G becomes the difference of proportions, which permits a more systematic understanding of the relation of G to other measures of segregation.