Hausman test results.

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.城市密度总能提升智慧生产力吗？本研究基于中国28个主要城市2011至2021年的面板数据，揭示了城市密度与智慧生产力之间的倒U型关联。本研究采用熵权法（Entropy Weight Method）构建了衡量城市密度与智慧生产力水平的综合指标体系。研究结果显示，在阈值0.497之前，城市密度对智慧生产力具有正向影响；越过该阈值后，二者关系转为负向。固定效应模型（Fixed Effects Modeling）的结果表明，在达到阈值前，城市密度每提升1%，智慧生产力可提升0.114%。通过中介效应分析（Mediation Analysis），本研究发现城市化水平发挥了显著的中介作用，其解释力占总效应的49.1%。此外，异质性分析（Heterogeneity Analysis）揭示了鲜明的区域异质性特征：相较于中部地区（系数为0.156），城市密度对西部地区智慧生产力的正向影响更为显著（系数为0.181），而在东部地区则呈现负向影响。上述研究结果表明，最优城市密度水平因区域而异，各城市应据此采取差异化发展策略。本研究通过量化城市密度与智慧生产力间的非线性关联，丰富了相关学术研究，并为城市规划政策制定提供了实证依据。