Does urban density always boost smart productivity? Evidence of an inverted U-shaped relationship in Chinese cities

Does urban density always boost smart productivity? Based on panel data from 28 major Chinese cities (2011-2021), this study reveals an inverted U-shaped relationship between urban density and smart productivity. Using entropy weight method, we construct comprehensive indices to measure both urban density and smart productivity levels. Our findings demonstrate that urban density positively influences smart productivity up to a threshold of 0.497, beyond which the relationship becomes negative. The results from fixed effects modeling show that a 1% increase in urban density is associated with a 0.114% increase in smart productivity before reaching the threshold. Through mediation analysis, we find that urbanization level serves as a significant mediator, accounting for 49.1% of the total effect. Furthermore, heterogeneity analysis reveals distinct regional patterns: urban density exhibits stronger positive effects in western regions (coefficient = 0.181) compared to central regions (coefficient = 0.156), while showing negative impacts in eastern regions. These findings suggest that optimal urban density levels vary across regions, and cities should adopt differentiated development strategies accordingly. Our study contributes to the literature by quantifying the non-linear relationship between urban density and smart productivity, while providing empirical evidence for urban planning policies.