The shadow prices of CO2 and SO2 for Chinese Coal-fired Power Plants: A partial frontier approach

Shadow prices are widely employed in guiding environmental policies. This paper contributes to the literature by developing a novel partial frontier approach for estimating shadow prices. The proposed method is advanced in handling outliers, and provides a precise estimation of the marginal rate of substitution along the production frontier. To cope with the different disposability characteristics of undesirable emissions, SO2 is treated as an environmental input that is strongly disposable. Because most different undesirable outputs are jointly reduced, this study is the first to use directional derivatives instead of partial derivatives and proposes a new separation method that separates individual directional shadow price from the cost of joint reduction of multiple undesirable outputs. We apply the proposed method to a sample of 93 coal-fired power plants covering six years. The estimated average shadow prices of CO2 and SO2 are 69 $/tonne and 2525 $/tonne under the newly developed partial frontiers. When assuming some undesirable output to be strongly disposable, both shadow prices fall (20.32 $/tonne and 1018.23 $/tonne). The present paper suggests the estimated shadow prices will be much different across different levels of disposability. The cost of joint reduction is calculated as 91.05 $/unit given the current production level, which leads to a directional shadow price for the two undesirable outputs of 91.32 $/tonne and 1250.06 $/tonne. The estimated shadow prices for both undesirable outputs dispersed widely under the partial frontiers. Spatial distribution of estimated shadow prices shows that coastal provinces and municipalities have higher CO2 shadow prices but lower SO2 shadow prices, whereas the northeast provinces are the opposite. The CO2 shadow price is comparatively stable over the study period while the SO2 shadow price fluctuates. Policy implications are discussed.