On the Accuracy of Inequality Measures Calculated from Aggregated Data

Abstract

Our aim in this study is to compare the typically used methods of calculating inequality measures for aggregated data with the modified approaches by the relative error. We start with the individual observations (obtained from the tax office) and calculate the exact values of a few inequality measures. Then, we construct the interval distribution in the form that is usually available in the statistical yearbooks. The standard approach is to treat all observations from a given class as if concentrated in the exact middle of this class. We have investigated a few other approaches, including the one that assumes the knowledge of the accurate mean values of subsequent classes (although these exact means are usually not available).The accuracy of each method is rated by comparing the results obtained by different methods with the exact ones. The inequality measures which are the matter of interest here are the Gini index which is the most commonly used, and also the Theil and Atkinson indexes.(original abstract)