Parametric quantile regression for income data

Univariate normal regression models are statistical tools widely applied in many areas of economics. Nevertheless, income data have asymmetric behavior and are best modeled by non-normal distributions. The modeling of income plays an important role in determining workers' earnings, as well as being an important research topic in labor economics. Thus, the objective of this work is to propose parametric quantile regression models based on two important asymmetric income distributions, namely, Dagum and Singh-Maddala distributions. The proposed quantile models are based on reparameterizations of the original distributions by inserting a quantile parameter. We present the reparameterizations, some properties of the distributions, and the quantile regression models with their inferential aspects. We proceed with Monte Carlo simulation studies, considering the maximum likelihood estimation performance evaluation and an analysis of the empirical distribution of two residuals. The Monte Carlo results show that both models meet the expected outcomes. We apply the proposed quantile regression models to a household income data set provided by the National Institute of Statistics of Chile. We showed that both proposed models had a good performance both in terms of model fitting. Thus, we conclude that results were favorable to the use of Singh-Maddala and Dagum quantile regression models for positive asymmetric data, such as income data.