Semi-parametric Estimation of Convex and Nonconvex By-Production Technologies

The emergence of the by-production technology as an alternative foundation for a pollution-generating technology represents a turning point in the environmental literature given its compatibility with the law of thermodynamics and the material balance principle. This approach considers two independent technologies: a primary production technology, and a residual-generating technology. The classical by-production technology can be estimated using parametric and nonparametric techniques. Alternatively, this study aims to identify the impact of the convexity assumption in a semi-parametric framework. We examine four specifications: (i) two relate to the error term, which may be either composite or deterministic, and (ii) other specifications incorporate either convexity or nonconvexity assumptions. Furthermore, we evaluate the out of-sample predictive performance of these alternative approaches. To validate our estimation approach, we conduct an empirical case study encompassing 47 Chinese cities from 2011 to 2019. Our findings reveal that both StoNED by-production models exhibit a higher consistency than deterministic ones. Moreover, we witness a parallel behavior in that relaxing convexity/concavity assumption generates a lower bound for both sub-technologies. Exploring the predictive power of nonconvex estimators on unseen data yields more precise out-of-sample predictions in both stochastic and deterministic settings.