Multiple-Output Production With Undesirable Outputs: An Application to Nitrogen Surplus in Agriculture

Many production processes yield both good outputs and undesirable ones (e.g. pollutants). In this paper, we develop a generalization of a stochastic frontier model which is appropriate for such technologies. We discuss efficiency analysis and, in particular, define technical and environmental efficiency in the context of our model. Methods for carrying out Bayesian inference are developed and applied to a panel data set of Dutch dairy farms, where excess nitrogen production constitutes an important environmental problem.