Before revision:  We show that the conditional distribution of the stochastic inefficiency term given the control functions is a folded normal distribution, which reduces to the half-normal distribution when both inputs and environmental variables are independent of the stochastic inefficiency term . Hence, our framework is a natural generalization of the normal half-normal stochastic frontier model with endogeneity. We further provide a Battese-Coelli estimator of technical efficiency in this context .
After revision:  We show that the conditional distribution of the stochastic inefficiency term given the control functions is a folded normal distribution, which reduces to the half-normal distribution when both inputs and environmental variables are independent of the stochastic inefficiency term given the control functions being a folded normal distribution. We also provide a Battese-Coelli estimator of technical efficiency in this context .