Weak disposability in nonparametric production analysis: reply to Fare and Grosskopf

Weak disposability of outputs means that firms can abate harmful emissions by decreasing the activity level. Modeling weak disposability in nonparametric production analysis has caused some confusion. This article identifies a dilemma in these approaches: conventional formulations implicitly and unin-tentionally assume all firms apply uniform abatement factors. However, it is usually cost-effective to abate emissions in those firms where the marginal abatement costs are lowest. This article presents a simple formulation of weak disposability that allows for non-uniform abatement factors and preserves the linear structure of the model. Key words: activity analysis, data envelopment analysis, environmental performance analysis, non-parametric productivity analysis, pollution abatement, production theory, undesirable outputs. Modeling undesirable outputs (such as emis-sions of harmful substances in air, water, and ground) and other detrimental side-effects of production activities (such as noise) has attracted considerable attention among production economists. A common approach is to treat detrimental variables as inputs, based on the economic argument that both inputs and detrimental side-effects incur costs for a firm and thus firms are usually interested in decreasing both types of variables as much as possible (Cropper and Oates). From technical perspective, however, emissions to the envi-ronment usually represent outputs for a firm. According to Färe and Grosskopf (2003, 2004), the treatment of undesirable outputs as inputs is inconsistent with the physical laws and the standard axioms of production theory. These authors advocate an alternative approach that models undesirable emissions as outputs, im-posing an assumption that these undesirable outputs are weakly disposable. Weak dispos-ability generally means that it is possible to abate emissions by decreasing the level of pro-duction activity