Spatial differences and formation mechanisms of innovation ecosystem dynamic operational efficiency along the yellow river.

To scientifically evaluate the dynamic operational efficiency, spatial differences, as well as the formation mechanisms of the urban Innovation Ecosystem within the Yellow River Basin is highly important for the high-quality development of China. In the present research, both the economic circulation theory with the Innovation Ecosystem and the Data Envelopment Analysis - Malmquist Productivity Index (DEA-Malmquist) model were adopted to analysis the database from 59 cities along the Yellow River Basin. In parallel, the kernel density estimation, the Gini coefficient, and Panel Vector Autoregression (PVAR) model were applied for further comparison. The results revealed that the dynamic operational efficiency of the Innovation Ecosystem within the Yellow River Basin exhibited an obvious fluctuating downwards trend. The efficiency of spatial distribution in the upstream and midstream basins shows a left-skewed and polarized pattern, whereas the downstream basins exhibited a right-skewed distribution with less pronounced polarization. The results also revealed that the overall Gini coefficients for dynamic operational efficiency (TFP) and technical efficiency (EFF) in the Yellow River Basin tended to convergence, whereas those for technological change (TECH) are of an increasing trend. Moreover, the hypervariable density emerged as the primary factor driving disparities in TFP, TECH, and EFF within the basin. Furthermore, the relationships among TFP, TECH, and EFF were featured with the regional heterogeneity. In the midstream areas, there existed a self-improvement mechanism for the TFP, TECH, as well as the EFF. However, there was a stronger self-improvement mechanism for TECH but a self-weakening mechanism for TFP and EFF in the downstream regions.