Semiparametric estimation of sample selection model with Box-Cox transformation

The sample selection model is widely used in microeconometrics, especially for the case with nonrandom missing dependent variables. The linear assumption between the potential dependent variable and covariates is often mentioned in the literature. However, nonlinear structures between variables are prevalent in reality, in which case the assumption of linearity can lead to serious model misspecification. To mitigate model misspecification caused by linear assumption, the Box-Cox transformation is applied to the potential dependent variable in the sample selection model, and then the estimation of the corresponding parameters is given under the linear relationship between the transformed variable and covariates. Finite sample properties are investigated by Monte Carlo simulation. Eventually, the new model is applied to analyze the potential wage equation in the labor market in China.The result indicates that ordinary logarithmic transformation of the latent dependent variable is likely to be invalid for this dataset. Furthermore, the findings suggest the presence of a notable gender wage disparity in this particular labor market.