A novel stochastic semi-parametric frontier-based three-stage DEA window model to evaluate China's industrial green economic efficiency

Traditional three-stage data envelopment analysis (DEA) models do not consider the problem of functional form and multicollinearity. This study develops a new stochastic semi-parametric frontier-based three-stage DEA model. The frontier incorporates the effects of both external environmental factors and statistical noise on efficiency. We adopt the StoNED (stochastic non-smooth envelopment of data) approach and use the quasi-likelihood estimation method to estimate the parameters of inefficiency term and stochastic noise. We conduct Monte Carlo experiments to examine the performance of the new frontier under different circumstances. Our results show that the new frontier provides a more realistic and accuracy estimator for efficiency measures. An empirical analysis is used to evaluate green economic efficiency (GEE) in China. We empirically compare different models and the results show that external environmental factors cause significant differences. We provide each provincial average GEE evaluated by the improved QLE-StoNED model, which are outperforms compared with other recently developed estimators. And a gradient difference emerges in the GEE among the eastern, central and western areas of China. The results also offer practical implications for the harmonious development of industrial production and a green economy in China.