Shadow pricing of electricity generation using stochastic and deterministic materials balance models

Marginal abatement cost is an essential input to optimal environmental policies. Shadow pricing has become a popular method for estimating abatement costs subject to parsimonious data requirement. This paper provides a novel contribution to the literature on shadow pricing by considering the implication of the materials balance principle for shadow prices. To that end, the paper establishes a Convex Nonparametric Least Squares estimator for the weak G-disposable production model, which for the first time enables modeling a composite error term and joint estimation of the production frontier and contextual variables within this production model framework. Applying the Directional Distance Function, environmental efficiencies and shadow prices for carbon dioxide emissions are estimated for a sample of power producers using both stochastic and deterministic frontier models. Average shadow price estimates for carbon dioxide range between 14,000 and 40,000 $/ton CO2 for the weak G-disposable model and between 70 and 77 $/ton CO2 for the conventional production model that ignores the materials balance. These findings cast doubt on previous shadow price estimates since a majority of comparable studies ignore the strict technical relationship among pollution-generating inputs and bad outputs under the materials balance condition.