A Distance Function Model with Good and Bad Outputs

We present an approach that pursues an adequate representation of product transformation possibilities for a technology generating, in addition to marketed (good) products, some environmentally detrimental non-marketed byproducts (bad outputs). As the shadow price of a non-marketed output depends on its marginal transformation rates with marketed outputs, representation of technological relationships between different groups of outputs deserves a particular attention. We model the technology by using two functions: an input distance function describing technically feasible input-output combinations, and a hedonic output function capturing relationships among good and bad outputs. This procedure offers more appropriate consideration and modeling of the interactions between different groups of outputs. An empirical application of the approach to the case of Dutch dairy farms1 demonstrates the complexity of interactions between outputs and the value of more elaborate representations of production possibilities. The analysis indicates that nitrogen surplus abatement costs vary widely among Dutch dairy farms and that these costs have increased substantially over time.