International audience ; The agricultural sector is currently confronted with the challenge to reduce greenhouse gas (GHG) emissions, whilst maintaining or increasing production. Energy-saving technologies are often proposed as a partial solution, but the evidence on their ability to reduce GHG emissions remains mixed. Production economics provides methodological tools to analyse the nexus of agricultural production, energy use and GHG emissions. Convexity is predominantly maintained in agricultural production economics, despite various theoretical and empirical reasons to question it. Employing non-convex and convex frontier frameworks, this contribution evaluates energy productivity change (the ratio of aggregate output change to energy use change) and GHG emission intensity change (the ratio of GHG emission change to polluting input change) using Hicks-Moorsteen productivity formulations. We consider GHG emissions as by-products of the production process by using a multi-equation model. Given our empirical specification, non-convex and convex Hicks-Moorsteen indices can coincide under certain circumstances, which leads to a series of theoretical equivalence results. The empirical application focuses on 1,510 observations of Dutch dairy farms for the period of 2010–2019. The results show a positive association between energy productivity change and GHG emission intensity change, which calls into question the potential of on-farm, energy-efficiency-increasing measures to reduce GHG emission intensity