Weak Disposability in Nonparametric Production Analysis with Undesirable Outputs

TLDR

Weak disposability of outputs means firms can abate harmful emissions by reducing activity, but modeling it has caused confusion because conventional formulations assume uniform abatement factors across firms. The article proposes a simple formulation of weak disposability that permits non‑uniform abatement factors while preserving linearity. This formulation maintains the model’s linear structure by allowing varying abatement factors. The study finds that cost‑effective abatement is achieved by targeting firms with the lowest marginal abatement costs.

Abstract

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 unintentionally 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.