Bad Outputs

This draft chapter, prepared for inclusion in the (prospective) Handbook of Production Economics, Vol. 1 (Theory), edited by Subash Ray, Robert Chambers, and Subal Kumbhakar, analyses recent developments in the modeling of pollution-generating technologies. We first lay out the inadequacies of the traditional, single-equation representations of models of such technologies prominently associated with the classic 1975 (and 1988) book by William J. Baumol and Wallace E.Oates on The Theory of Environmental Policy. In particular, these models lack the “degrees of freedom” needed to capture the complex array of trade-offs that are integral to the production of unintended as well as intended outputs using emission-generating inputs. We reprise the insight, articulated in the classic 1965 book by Ragner Frisch on the Theory of Production, that the representation of specific technologies may require the use of multiple functional restrictions. The relevance of this insight for modeling pollution-generating technologies was first highlighted in 1972 and 1998 papers by Finn Førsund. We show that the use of a particular set of functional restrictions, a phenomenon referred to as by-production in our 2012 paper with Steven Levkoff, facilitates the modeling of pollution-generating technologies. In particular, a by-production technology is obtained as the intersection of an intended-output sub-technology and an unintendedoutput sub-technology. We illustrate these principles by sketching a model of coal-fired electrical-power generation and demonstrate the use of the model for the measurement of both output-based and graph-based technical efficiency. ∗Email: [email protected] †Email: [email protected]