Roy L. Crum, Darwin D. Klingman, Lee A. Tavis, Implementation of Large-Scale Financial Planning Models: Solution Efficient Transformations, The Journal of Financial and Quantitative Analysis, Vol. 14, No. 1 (Mar., 1979), pp. 137-152

There appears to be an inconsistency Morton Paglin's recent article this Review. The effect of that inconsistency is to exaggerate the difference between the traditional Gini coefficient and a Gini coefficient which is adjusted for the average age-earnings relationship. Paglin observes that the Gini coefficient is often used normative evaluations of the income distribution. What begins as a measure of inequality is finally treated, with or without intervening statements of qualification, as if it were a measure of inequity. This being so we must ask whether all deviations from the mean income of the population-the inequalities that give magnitude to the Gini coefficent, G-are unjustifiable. For Paglin the answer is no, and on this point one suspects that he belongs, to a comfortable majority. The question is what to do. Paglin proposes that use be made of the average age-income relationship. Perfect equality or equity exists when all families at the same stage their life cycle have the same annual income. The deviation of any one family's income from the mean income for its age cohort is taken to be an unjustifiable deviation that gives magnitude to some adjusted Gini coefficient. Since the actual age-income profile has a definite hump, it is expected that the adjusted Gini coefficient will be less than G. My points will be that Paglin, giving mathematical expression to his normative position, has made a structural change the Gini formula which does not fully conform with the logic of the Gini measure, and that consequence the magnitude of inequality which he has measured is determinately too small. Suppose that the income scale and the age scale are partitioned into a finite number of segments. Each family belongs to one of the income ranges and to one of the age (of head) ranges so defined. Let nii represent the number of families that have an annual income income range i and whose family heads are age range j. They will be said to be in cell (i, j). The income level of every family cell (i, j) is denoted by yij.' The mean income level for all families age range j is denoted mj, and the grand mean is m. There are N families the population. The Gini coefficient,