Quantile based study of income distributions and income inequality measures

Abstract

Income distributions and income inequality measures are key topics in econom- ics and statistics, focusing on the allocation of wealth and resources across different segments of a population. Understanding these concepts is crucial for evaluating economic policies, social equity, and economic development. There are two primary approaches to modeling data: the distribution function approach and the quantile function approach. This thesis emphasizes a quantile-based analysis of income dis- tributions and income inequality measures. We explore various quantile functions from the literature and assess their potential for modeling income data. We conduct a comprehensive quantile-based income analysis of the Power-Pareto (PP) distribu- tion by deriving key income inequality measures and examining the Lorenz ordering associated with it. Additionally, simulation, estimation, and application aspects are investigated. This study introduces the Singh-Maddala-Dagum (SMD) distribution, defined as the sum of the quantile functions of the Singh-Maddala (SM) and Dagum distributions. Its distributional properties, along with measures of income inequality and poverty, are derived. The poverty gap ratio and Foster-Greer-Thorbecke (FGT) measures are formulated in quantile terms. Estimation of parameters and prac- tical applications are conducted. Furthermore, this thesis includes a quantile-based comparative analysis of income inequality across Indian states. Six parametric mod- els with closed-form quantile functions, including Weibull, PP, SM, Dagum, SMD, and Modified Lambda Family (MLF), are employed to model per capita household income across Indian states using data from the India Human Development Survey- II (IHDS-II). Parameter estimation and validation are performed for each model. For every state, empirical income inequality measures, including the Gini, Pietra, Atkinson, generalized entropy, Bonferroni, and Frigyes measures, are derived and compared with theoretical values from the best-fitting model. This thesis concludes by highlighting the significance of quantile functions in income modeling and out- lining potential directions for future research