By-production modeling of technical and environmental inefficiency in Brazilian dairy farms

This study develops a by-production stochastic frontier model to assess farm technical and environmental inefficiency, applied to a panel of Brazilian dairy farms observed from 2014 to 2021. The model specifies a good output (mainly milk production) and a bad output (CO₂-equivalent emissions) equation, capturing the dependence between the inefficiency terms and between the noise terms across the two equations using two distinct copulas. A Bayesian estimation framework is introduced for parameter estimation. Results indicate that milk production is primarily driven by feed inputs, while emissions are mostly influenced by herd size. Technical inefficiency averages 0.066, while environmental inefficiency averages 0.061, reflecting relatively high efficiency levels in both dimensions. Strong upper tail dependence between the inefficiency terms and between the noise terms across the two equations highlights the interconnected nature of these processes, suggesting shared inefficiency drivers and external shocks.