Abstract:The rationality and accuracy of shadow price estimation for undesirable outputs are the scientific basis for formulating firms’ plans about production and emission reduction, and implementing government policies on environmental regulatory. The traditional models on shadow price estimation have some limits such as ignoring data uncertainty, individual and environmental heterogeneity, and the diversity of emission reduction measures. Thus, this paper proposes a semi-nonparametric theoretical model for measuring the shadow price of undesirable outputs based on the production frontier theory. This model introduces the undesirable outputs into the convex nonparametric least squares (CNLS) model that considers both inefficiency and random noise, and directly integrates exogenous variables representing individual characteristics and operating environment of firms in the objective function. At the same time, this model combines the marginal rates of transformation between desirable outputs and undesirable outputs, and the marginal rates of substitution between inputs and undesirable outputs, to define and calculate the optimal shadow price of undesirable outputs. This semi-nonparametric theoretical model provides a more scientific and rigorous framework for effectively estimating the shadow price of undesirable outputs.