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.
We propose and study a maximum likelihood estimator of stochastic frontier models with endogeneity in cross-section data when the composite error term may be correlated with inputs and environmental variables. 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 ; and the conditional distribution of the stochastic inefficiency term given the control functions being a folded normal distribution. We also provide a Battese-Coelli estimator of technical efficiency . Our estimator is computationally fast and easy to implement. We study some of its asymptotic properties, and we showcase its finite sample behavior in Monte-Carlo simulations and an empirical application to farmers in Nepal.
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study a closed-form
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We achieve identification using a control function assumption. We show that the conditional distribution of the stochastic inefficiency term
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
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is a folded normal distribution, which reduces to the half-normal distribution when both inputs and environmental variables are independent
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. Hence, our framework is a natural generalization of the normal half-normal stochastic frontier model with endogeneity. We further
given the control functions being a folded normal distribution. We also
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