On the Use of Incomplete Moments for Measuring Income Inequalities

• Activity Number: 74 - Statistical Methods and Applications: Domestic and International
• Type: Contributed
• Date/Time: Sunday, July 28, 2019 : 4:00 PM to 5:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Sayed A Mostafa* and Ibrahim A Ahmad
• Companies: North Carolina A&T State University and Oklahoma State University
• Keywords: Income inequality; incomplete moments; conditional incomplete moments; kernel smoothing

Abstract

Among the most widely used measures of income inequality are the measures based on incomplete “truncated” moments such as those of Butler and McDonald (1987, J. Bus & Econ Stat, pp. 13-18). In this investigation, we complement the work of Gastwirth et al. (1989, J. Econometrics, pp. 5-19) by establishing the asymptotic distribution of an unsmoothed estimator of the measure of income inequality due to Butler and McDonald. We also define and study a smoothed estimator for their measure. Further, we introduce a new class of income inequality measures based on conditional incomplete moments. Unlike the measures based on unconditional incomplete moments, the new measures are not sensitive to right tail probabilities. We define and study both unsmoothed and smoothed estimators for the new measures. Finally, we compare the different measures under various income distributions, and demonstrate their applicability using a real data set.