Technical and environmental inefficiency measurement in agriculture using a flexible by‐production stochastic frontier model

In light of the urgent need for farms to mitigate greenhouse gas emissions while maintaining economic viability, this paper analyses technical and environmental inefficiencies and their determinants based on a flexible multi‐equation by‐production stochastic frontier model, which accounts for the stochastic dependence between good and bad outputs via a copula function. An empirical application to Dutch dairy farms illustrates the distortions in the inefficiency scores and in the estimates of their determinants that occur when the dependence between good and bad outputs is ignored. The empirical results indicate a strong positive dependence between the good output (milk) and the bad output (methane emissions), which is particularly pronounced in the upper tail of the distribution. Notably, farms exhibit high efficiency in maximising their good output and minimising their bad output. Subsidies are negatively related to good output inefficiency but positively related to bad output inefficiency, while stock density exhibits a negative association with inefficiencies in both outputs. Disregarding output dependence leads to distortions in inefficiency estimates, particularly affecting the estimates for their determinants.