Nash marginal abatement cost estimation of air pollutant emissions using the stochastic semi-nonparametric frontier

Emissions trading (or cap and trade) is a market-based approach providing economic incentives for achieving reductions in the emissions of pollutants. Marginal abatement costs (MAC), also termed shadow prices of air pollution emissions, provide valuable guidelines to support environmental regulatory policies for CO₂, SO₂ and NO_x, the key contributors to climate change, smog, and acid rain. This study estimates the marginal abatement cost of undesirable outputs with respect to the Nash equilibrium on the stochastic semi-nonparametric envelopment of data (StoNED) in an imperfectly competitive market. Considering an endogenous price function of electricity, the mixed complementarity problem (MiCP) is formulated to identify the Nash equilibrium in a production possibility set. The proposed model addresses the four issues of MAC estimation in the existing literature. Applying the proposed method to an empirical study of 33 coal-fired power plants operating in China in 2013 shows that StoNED provides a robust frontier that is not sensitive to the outlier and the proposed interval of MAC estimation validates the shadow prices corresponding to the Nash equilibrium in an imperfectly competitive market.