On a log-symmetric quantile tobit model applied to female labor supply data

TL;DR

This paper introduces a novel quantile tobit regression model based on log-symmetric distributions, effectively modeling positively skewed data and analyzing different quantiles, with improved fit over traditional models in female labor supply data.

Contribution

It develops a new quantile tobit model using log-symmetric distributions to handle skewness and heteroscedasticity, enhancing analysis of censored economic data.

Findings

Model outperforms classic tobit in fit

Effectively captures skewed data

Provides detailed quantile analysis

Abstract

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.