Advancing Green TFP Calculation: A Novel Spatiotemporal Econometric Solow Residual Method and Its Application to China’s Urban Industrial Sectors

Abstract

The Solow residual method, traditionally pivotal for calculating total factor productivity (TFP), is typically not applied to green TFP calculations due to its exclusion of undesired outputs. Diverging from traditional approaches and other frontier methodologies such as Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA), this paper integrates undesired outputs and three types of spatial spillover effects into the conventional Solow framework, thereby creating a new spatiotemporal econometric Solow residual method (STE-SRM). Utilizing this novel method, the study computes the industrial green TFPs for 280 Chinese cities from 2003 to 2019, recalculates these TFPs using DEA-SBM and Bayesian SFA for the same cities and periods, and assesses the accuracy of the STE-SRM-derived TFPs through comparative analysis. Additionally, the paper explores the statistical properties of China’s urban industrial green TFPs as derived from the STE-SRM, employing Dagum’s Gini coefficient and spatial convergence analyses. The findings first indicate that by incorporating undesired outputs and spatial spillover into the Solow residual method, green TFPs are computable in alignment with the traditional Solow logic, although the allocation of per capita inputs and undesired outputs hinges on selecting the optimal empirical production function. Second, China’s urban industrial green TFPs, calculated using the STE-SRM with the spatial Durbin model with mixed effects as the optimal model, show that cities like Huangshan, Fangchenggang, and Sanya have notably higher TFPs, whereas Jincheng, Datong, and Taiyuan display lower TFPs. Third, comparisons of China’s urban industrial green TFP calculations reveal that those derived from the STE-SRM demonstrate broader but more concentrated results, while Bayesian SFA results are narrower and less concentrated, and DEA-SBM findings sit between these extremes. Fourth, the study highlights significant spatial heterogeneity in China’s urban industrial green TFPs across different regions—eastern, central, western, and northeast China—with evident sigma convergence across the urban landscape, though absolute beta convergence is significant only in a limited subset of cities and time periods.