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November 2002 On Modeling Pollution-Generating Technologies

By Sushama Murty and R. Robert Russell


This paper takes issues with standard, single-equation modeling of pollutiongenerating technologies and suggests an alternative approach. Our approach takes account of the material-balance condition, in which pollution is an unintended by-product, or incidental output, of the intended production activities of firms. We distinguish between the notions of joint production and by-production and show that single-equation modeling of technologies that include pollution as another commodity capture pollution as a joint product and not as a by-product of intended production. For modeling pollution-generating technologies, we propose, in addition to the technology that depicts transformation of inputs into intended outputs, an explicit delineation of the externality-generating mechanism. We show that such aspecification of the technology yields, in a manner consistent with the material-balance condition, the (intuitively desirable) positive correlation between generation of pollution and the production of intended outputs. The technology specified this way, however, is a manifold in the full commodity space and, in contrast to the technologies employed in much of the literature, satisfies neither strong nor weak disposability in the subspace of pollution and intended outputs. Moreover, shadow prices of pollution variables are undefined. Modeling abatement as an intermediate input (produced and used by the firm) yields a positive trade-off between pollution and conventional outputs, but the trade-offs among conventional inputs and outputs in the “reduced form ” technology do not satisfy conventional sign requirements; hence, standard DEA methods of constructing the reduced-form technology and of calculating the shadow price of pollution are problematic. We believe these results have implications for empirical work that models and estimates pollution-generating technologies and the shadow price of pollution. Acknowledgment: Our understanding of the issues addressed in this paper has been enhanced by many stimulating discussions with M. N. Murty

Year: 2013
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