Approximating pollution abatement costs via alternative specifications of a multi-output production technology: a case of the US electric utility industry

Using a panel of observations from the US electric utility industry, we analyze the output set frontiers that are produced by modeling the technology with different functional forms. Our specifications rely on a series of mapping regimes, based on the paths in which the outputs are scaled toward the frontier, and their outcomes are assessed against the general axiomatic framework of the production model. We demonstrate that different parameterization methodologies produce different empirical analogues of the output set and, as a consequence, can generate rather different estimates of the shadow prices of socially undesirable outputs, or 'bads,' as well. We benchmark our results by assessing the shadow price estimates, often interpreted as the opportunity cost of pollution reduction, against the market prices of pollution permits. The outcomes of our analysis suggest that the estimate of the output set boundary varies with the choice of a parameterization technique, which provides a possible explanation for the sizeable differences between the shadow prices of bads reported in the literature. We also demonstrate that among a variety of existing parametric methodologies no single technique is superior to all others.