Maximum likelihood estimation of stochastic frontier models with endogeneity

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 present some of its asymptotic properties, and we showcase its finite sample behavior in Monte-Carlo simulations and an empirical application to farmers in Nepal. (c) 2021 Elsevier B.V. All rights reserved.

Automated summary

We propose and study a maximum likelihood estimator for stochastic frontier models with endogeneity in cross-section data. 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 and provide a computationally fast and easy-to-implement estimator. We also analyze its asymptotic properties and demonstrate its performance in finite samples through simulations and an empirical application.