Modelling environmental technical efficiency and phosphorus pollution abatement cost in dairy farms

The dairy sector is an important sector in Northern Ireland being the single largest contributor to its agricultural economy. However, the sector contributes more to soil phosphorus (P) surplus compared to other agricultural sectors. Consequently, the goal of this research is to analyse the environmental technical efficiency of dairy farms making use of a novel parametric hyperbolic distance function approach. The model is able to internalise P surplus as undesirable output in the dairy production process by treating desirable and undesirable outputs asymmetrically. The stochastic production frontier model is analysed simultaneously with an inefficiency model to explain variability in efficiency scores assuming the existence of heteroskedasticity in the idiosyncratic error term. Additionally, we estimated the shadow price and pollution cost ratio of P surplus in dairy farms. This paper contributes to the existing literature as it provides the first attempt to empirically estimate the pollution abatement cost of P surplus in dairy farms. Besides, the hyperbolic environmental technology distance function methodology employed to achieve the study objectives is less restrictive compared to the radial output/input distance function approach employed in previous studies. This allows for the estimation of a more robust environmental efficiency measure and shadow price of P surplus that is consistent with public policy goals that seek to simultaneously reduce pollution and increase production of desirable outputs. Our results showed that the average environmental technical efficiency estimates for dairy farms in Northern Ireland is 0.93 and the shadow price (marginal abatement cost) of P surplus evaluated at the mean is £12.29/kg. Intensification resulting in increased use of concentrates feed was found to be negatively related to environmental technical efficiency. We also found that age of the farmer and share of milk output have a positive relationship with environmental technical efficiency.