Borrowed size, city functional division, and total factor productivity of firms: a study based on city clusters in China

Research indicates that a city’s total factor productivity (TFP) correlates with its size, with larger cities exhibiting higher TFP. However, some smaller cities can achieve high TFP by borrowing their size from surrounding cities, achieving the size necessary to support the benefits of agglomeration. This study uses data from industrial firms in 13 mature city clusters in China to explore how borrowed size influences TFP. The findings reveal that borrowed size significantly enhances firms’ TFP, acting as a substitute for city size. Heterogeneity analysis shows that technology-intensive and downstream industries in the industrial chain are more dependent on borrowed size, whereas state-owned firms face challenges due to intergovernmental competition, making it difficult for them to benefit from borrowed size. The positive effects of borrowed size rely on inter-city connections: lower administrative barriers, a more flattened spatial structure of city clusters, and a denser transportation network amplify its benefits. Mechanism analysis indicates that large cities can borrow size from surrounding smaller cities to develop productive services beyond their capacity, while smaller cities can share the productive service functions of large cities and specialize in manufacturing. This clear functional division helps improve firms’ TFP.