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.

中文翻译：

---

使用灵活的副生产随机前沿模型测量农业中的技术和环境低效率


鉴于农场迫切需要在保持经济生存能力的同时减少温室气体排放，本文基于灵活的多方程副生产随机前沿模型分析了技术和环境效率低下及其决定因素，该模型通过 copula 函数解释了好产出和坏产出之间的随机依赖性。对荷兰奶牛场的实证应用说明了当忽略好产出和坏产出之间的依赖关系时，效率低下分数及其决定因素估计的扭曲。实证结果表明，好产出（牛奶）和坏产出（甲烷排放）之间存在很强的正依赖性，这在分布的上尾尤为明显。值得注意的是，农场在最大限度地提高其良好产量和最大限度地减少其不良产量方面表现出高效率。补贴与良好的产出低效率呈负相关，但与不良的产出低效率呈正相关，而库存密度与两种产出的低效率呈负相关。忽视产出依赖性会导致低效率估计的扭曲，特别是影响其决定因素的估计。