The Advantages of Using Group Means in Estimating the Lorenz Curve and Gini Index from Grouped Data

A recent article proposed a histogram-based method for estimating the Lorenz curve and Gini index from grouped data that did not utilize the group means reported by government agencies. When comparing their method to one based on group means, the authors assume a uniform density in each grouping interval, which leads to an overestimate of the overall average income. After reviewing the additional information in the group means, it will be shown that as the number of groups increases, the bounds on the Gini index obtained from the group means become narrower. This is not necessarily true for the histogram method. Two simple interpolation methods using the group means are described and the accuracy of the estimated Gini index they yield and the histogram-based one are compared to the published Gini index for the 1967-2013 period. The average absolute errors of the estimated Gini index obtained from the two methods using group means are noticeably less than that of the histogram based method.