Measuring income inequality: A robust semi-parametric approach

In practice, income distributions are often contaminated with outliers that can affect the estimation of the income inequality. In this study, we propose a robust method for measuring income inequality based on a semi-parametric approach that applicable to positive income data. The semi-parametric approach introduced here combines the inverse-Pareto, empirical, and Pareto distributions. In addition, a robust estimation method based on probability integral transform statistic is applied to estimate the shape parameters of the inverse-Pareto and Pareto models to allow for the presence of outliers in the lower and upper tails of an income distribution. Then, a semi-parametric form of the Lorenz curve and three inequality measures are derived, including the Gini coefficient, generalized entropy index, and Atkinson index. We conduct a simulation study to compare the performance of the proposed semi-parametric approach with that of the conventional non-parametric method for estimating income inequality in the presence of outliers. The results show that the income inequality measure based on the proposed semi-parametric approach outperforms the conventional non-parametric method. Lastly, we apply the proposed semi-parametric approach in the measurement of income inequality among households in Malaysia based on survey data of household incomes for the years 2007, 2009, 2012, and 2014. (C) 2020 Elsevier B.V. All rights reserved.