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.