How producer services agglomeration affects urban green innovation efficiency in China: a spatial correlation and nonlinear perspective

The pursuit of urban green innovation efficiency (UGIE) has emerged as a pivotal driver for attaining green economic growth. It is crucial to improve UGIE through the producer services agglomeration (PSA) for China. Based on the perspective of spatial correlation, we investigate the spatial spillover effect, mechanism, and nonlinear characteristics of PSA on UGIE. The results indicate that: (1) China's UGIE exhibits an upward trend with fluctuations, with growth poles in the Guangdong-Hong Kong-Macao Greater Bay Area, Yangtze River Delta, and Bohai Rim. China's PSA initially declines, gradually increases, and then decreases. There is still room for progress in both UGIE and PSA. (2) The direct and spatial spillover effects of PSA on UGIE exhibit a U-shaped pattern, initially inhibiting and then promoting. However, the spatial spillover effects are only observed within a geographical range of 350 km. Cities in the eastern region or with advanced high-end producer services have lower inflection points. (3) PSA can enhance UGIE in local cities by facilitating knowledge spillover and optimizing labor allocation, while also impacting UGIE in neighboring cities through improved capital allocation. (4) Under varying levels of industrial agglomeration and marketization, the nonlinear impact of PSA on UGIE exhibits a single threshold effect and a double threshold effect, respectively. When the threshold value of PSA reaches 0.548 and the threshold values of marketization reach 8.269 and 11.373, the impact of PSA on UGIE gradually transitions from inhibition to promotion. This study provides insights for rationalizing the layout of urban producer services to enhance green innovation.