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

Abstract

The study of female labor supply has been a topic of relevance in the economic literature. Generally, the data are left-censored and the classic tobit model has been extensively used in the modeling strategy. This model, however, assumes normality for the error distribution and is not recommended for data with positive skewness, heavy-tails and heteroscedasticity, as is the case of female labor supply data. Moreover, it is well-known that the quantile regression approach accounts for the influences of different quantiles in the estimated coefficients. We take all these features into account and propose a parametric quantile tobit regression model based on quantile log-symmetric distributions. The proposed method allows one to model data with positive skewness (which is not suitable for the classic tobit model), to study the influence of the quantiles of interest, and to account for heteroscedasticity. The model parameters are estimated by maximum likelihood and a Monte Carlo experiment is performed to evaluate alternative estimators. The new method is applied to two distinct female labor supply data sets. The results indicate that the log-symmetric quantile tobit model fits better the data than the classic tobit model.

Keywords:

• Log-symmetric distributions
• quantile regression
• Monte Carlo simulation
• PNAD
• PSID

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Available at https://www.ibge.gov.br/

2 https://www.ibge.gov.br/.

3 We do not use the most recent Continuous PNAD data set because of a lack clarity in some variables of interest in its dictionary. This is case of the labor experience/skill variable, which are the years of work in the main activity, and marital status, which is also not clearly defined in the Continuous PNAD. It is worth mention that is not necessary the variables of the two samples, PNAD and PSID, are similar. We only need to have a censored variable for female hours worked. The 2015 PNAD data set also be used only to illustrate the proposed methodology.

Additional information

Funding

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brazil (CAPES) Finance Code 001. Danúbia Rodrigues thanks CAPES-PROEX for the doctorate scholarship. Jose Angelo Divino and Helton Saulo acknowledge Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) for financial support.