Modeling Production Efficiency and Greenhouse Gas Objectives as a Function of Forage Production of Dairy Farms Using Copula Models

Dairy farms are systems with multiple dependent variables whose practices influence their economic and environmental performances. Decisions made and actions taken to improve environmental performances of dairy farms carry the risk of decreasing farm profitability. Correlations among multiple variables must therefore be considered to reliably assess risks of improving environmental performances of farms. We applied copula models to a dataset of conventional dairy farms surveyed in France to decscribe relationships among their characteristics, such as forage dry matter (DM) production, milk production, and greenhouse gas (GHG) emissions. By modeling relationships among farm characteristics, copula models can identify the characteristics’ joint distributions, unlike other statistical methods. For dairy farms, copula models are useful for estimating probabilities of reaching a milk production goal or not exceeding a regulatory emission limit as a function of forage production. For instance, when a farm produced at least 4,500 kg DM/livestock unit/year of maize silage, the probability of producing at least 7,000 l milk/cow/year was 75%, while the probability of emitting less than 7,000 kg CO₂ eq./farm/year (a value close to the mean of 6669 kg CO₂ eq./farm/year for all of the farms) was 48%. When the same amount of grass from pasture was produced, these probabilities changed to 48% and 78%, respectively (i.e., decreased probability of reaching a production goal, but increased probability of not exceeding an emission threshold). Farmers must make trade-offs, since increased milk production goals are likely to increase GHG emissions per farm and/or reduce GHG emission intensities per l of milk, but are less likely to be reached for a given amount of forage DM. By providing information about relationships among farm characteristics that other statistical approaches cannot, copula models are useful for investigating these trade-offs.