A modification of Silber’s algorithm to derive bounds on Gini’s concentration ratio from grouped observations

Abstract

Silber (1990) devised an algorithm to derive the bounds of Gini’s concentration ratio from grouped data, which does not require information on the limits of the income brackets, the group mean incomes, or the overall mean income. In the case of the upper bound, Silber’s algorithm entails determining the coordinates of the points of intersection of the tangents to the Lorenz Curve (LC) at the observed points, which are then used in conjunction with the G-matrix operator. In this note we derive modified coordinates of the points of intersection of the tangents to the LC at the observed points assuming that there is information on the limits of the income brackets and full or sparse information on mean incomes. We also show that if the modified coordinates are incorporated into Silber’s algorithm, the resulting estimate of the upper bound is identical to estimates of the upper bound proposed by Gastwirth, Fuller, and Ogwang.