We provide a closed-form maximum likelihood estimation of stochastic frontier models with endogeneity . We consider cross-section data when both components of the composite error term may be correlated with inputs and environmental variables. Under appropriate restrictions, we show that the conditional distribution of the stochastic inefficiency term  is a folded normal distribution . The latter reduces to the half-normal distribution when both inputs and environmental variables are independent of the stochastic inefficiency term. Our framework is thus a natural generalization of the normal half-normal stochastic frontier model with endogeneity. Among other things, this allows us to provide a generalization of the Battese-Coelli estimator of technical efficiency . Our maximum likelihood estimator is computationally fast and easy to implement. We showcase its finite sample properties in monte-carlo simulations and an empirical application to farmers in Nepal.
We study a closed-form maximum likelihood estimator of stochastic frontier models with endogeneity in cross-section data when both error components may be correlated with inputs and environmental variables. 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. 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. Our estimator is computationally fast and easy to implement. We showcase its finite sample properties in Monte-Carlo simulations and an empirical application to farmers in Nepal.
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