  The classic censored regression model (tobit model) has been widely used in
the economic literature. This model assumes normality for the error
distribution and is not recommended for cases where positive skewness is
present. Moreover, in regression analysis, it is well-known that a quantile
regression approach allows us to study the influences of the explanatory
variables on the dependent variable considering different quantiles. Therefore,
we propose in this paper a quantile tobit regression model based on
quantile-based log-symmetric distributions. The proposed methodology allows us
to model data with positive skewness (which is not suitable for the classic
tobit model), and to study the influence of the quantiles of interest, in
addition to accommodating heteroscedasticity. The model parameters are
estimated using the maximum likelihood method and an elaborate Monte Carlo
study is performed to evaluate the performance of the estimates. Finally, the
proposed methodology is illustrated using two female labor supply data sets.
The results show that the proposed log-symmetric quantile tobit model has a
better fit than the classic tobit model.
