Urban green total factor productivity in China: A generalized Luenberger productivity indicator and its parametric decomposition

In this study, by taking the distance elasticity shares as the input weights in the production function, the generalized Luenberger productivity indicator (GLPI) was proposed to analyze the urban GTFP in China, and the stochastic frontier analysis (SFA) was used for parametric decomposition to obtain the technological change (TC), technical efficiency change (TEC), and scale efficiency change (SEC). The results show that the entire model and specific parameters passed the test, and the production function equation has good economic and statistical significance, which shows that it is feasible to use the parameter approach to measure and decompose the GLPI. Second, the value of the GLPI showed a rapid growth trend between 2000 and 2019, with a cumulative increase of 140.59%, indicating that various inputs were saved by 3.43% in a specific proportion, and that remarkable achievements have been made in the sustainable development of Chinese cities. Third, TC, TEC, and SEC all showed significant spatiotemporal heterogeneity, in which SEC was the main numerical component and TC was the driving force of the GLPI. Through mathematical proof in theory and data matching in reality, it is confirmed that the GLPI proposed in this study is scientific and applicable.