Before revision:  We achieve identification using a control function assumption. 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 .
After revision:  Our framework is a generalization of the normal half-normal stochastic frontier model with endogeneity. We derive the likelihood function in closed form using three fundamental assumptions: the existence of control functions that fully capture the dependence between regressors and unobservables; the conditional independence of the two error components 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 .