  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.
