Maximum likelihood estimation of the stochastic frontier model with endogenous switching or sample selection

Heckman’s (Ann Econ Soc Meas 15:475–492, 1976; Econometrica 47(1):153–161, 1979) sample selection model has been employed in many applications of linear or nonlinear regression studies. It is well known that ignoring the sample selectivity may result in estimation bias of the estimator. Although the stochastic frontier (SF) model with sample selection has been investigated in Greene (J Product Anal 34:15–24, 2010), we intend to extend the model in several directions in this paper. First, we extend the distribution of the inefficiency from the half normal to truncated normal distribution. Second, we discuss the likelihood estimation method for the SF model with sample selection and also its most common incarnation, endogenous switching. Third, we suggest a simple framework to derive the closed form of the likelihood function using the closed skew-normal distribution. Fourth, we propose the estimator for the technical efficiency index due to Battese and Coelli (Empir Econ 20(2):325–332, 1995) based on the sample selection information. Finally, we also demonstrate the approach using the Taiwan hotel industry data.