The by-production models for benchmarking

By-production models, as a new class of efficiency estimation models for assessing pollution-generating technologies with undesirable outputs, are becoming increasingly popular in benchmarking studies recently. Yet the performance of these models is not well understood. In this study, we investigate the accuracy of three widely-used by-production models (by-production slacks-based measure or BP-SBM, by-production directional distance function or BP-DDF, by-production Färe-Grosskopf-Lovell or BP-FGL) through Monte-Carlo simulation, accounting for different returns-to-scale, sample sizes, noise levels, and endogeneity in data. We find that the BP-FGL model achieves the highest-ranking accuracy, as measured by Kendall's ranking correlation, under all simulated scenarios, falling in the range between 0.553 and 0.758. BP-DDF model, being the predominantly used model in literature, has the worst performance and should be deprioritized in future studies. All models exhibit better accuracy for larger samples and lower noise levels. The presence of endogeneity in data degrades the model accuracy, with the degradation effect being symmetric for positive and negative endogeneity levels. The applications of by-production models are further illuminated through a case study of coal-fired power plants in the United States to highlight the importance of model selection in applying the by-production approach, a critical issue that has been ignored by existing literature.