A copula-based semiparametric by-production stochastic frontier model

This paper introduces a flexible semiparametric approach to by-production stochastic frontier analysis. We model a firm’s production process using two interrelated technologies: one for generating good output and another for generating bad output, both driven by a common set of inputs. Technical inefficiency is defined as the failure to maximize good output, while environmental inefficiency reflects the failure to minimize bad output. Unlike previous studies, our method employs splines to capture nonlinear relationships between inputs and outputs, as well as between firm characteristics and inefficiencies, while also incorporating random firm effects. We model output dependence using copulas and compare alternative specifications. Applying the framework to Dutch dairy farming, where milk is the good output and methane emissions the bad, we find evidence of nonlinearities, low inefficiency levels, and moderate positive dependence between outputs. Neglecting nonlinearities and random effects inflates inefficiency estimates, highlighting the importance of flexible modeling in future applications.