On modeling pollution-generating technologies

TLDR

The intended‑production technology satisfies standard disposability properties, whereas the residual‑generation set violates free (strong) disposability of pollution and pollution‑causing inputs. The authors argue that prevailing models of pollution‑generating technologies, which treat pollution as a freely disposable input or weakly disposable output, lead to unacceptable trade‑off implications, and they propose an alternative index with superior properties. They use data envelopment analysis on an electric‑power‑plant database to show shortcomings of two popular efficiency indexes under by‑production and develop an alternative index with superior properties. The study finds that modeling pollution‑generating technology as the intersection of intended‑production and nature’s residual‑generation set—.

Abstract

We argue analytically that many commonly used models of pollution-generating technologies, which treat pollution as a freely disposable input or as a weakly disposable and null-joint output, may generate unacceptable implications for the trade-offs among inputs, outputs, and pollution. We show that the correct trade-offs in production are best captured if a pollution-generating technology is modeled as an intersection of an intended-production technology of the firm and nature's residual-generation set. The former satisfies standard disposability properties, while the latter violates free (strong) disposability of pollution and pollution-causing inputs. As a result, the intersection—which we call a by-production technology—violates standard free disposability of pollution and pollution-causing inputs. Employing data envelopment analysis on an electric-power-plant database, we illustrate shortcomings, under by-production, of two popular efficiency indexes: the hyperbolic and directional-distance-function indexes. We propose and implement an alternative index with superior properties. Under by-production, most efficiency indexes decompose very naturally into intended-production and environmental efficiency indexes. This decomposition is difficult to find under alternative specifications of pollution-generating technologies.