Coupling dynamics between urban freight and economic development in China: A scaling law and Grey–Markov model

Amid rapid urbanization and industrial restructuring, understanding the relationship between freight transportation and economic growth is essential for sustainable urban development. Using multispatial convergent cross mapping and scaling law, this study analyzes data from 288 prefecture-level cities in China (2000–2023) to examine causality, nonlinear coupling, and spatiotemporal evolution. By linking scaling exponents with elasticity coefficients, a Modified Grey–Markov model is developed for forecasting the elastic relationship between urban freight transportation and economic development. Results reveal significant bidirectional causality and a predominantly sublinear scaling relationship with declining coupling strength, alongside a spatial diffusion pattern from eastern to central and western regions. And elasticity coefficients generally exceed 1 and, overall, exhibit an increasing trend, although a few indicators display declining tendencies, suggesting that freight demand may show relatively high responsiveness to changes in economic development in the short term. These findings provide quantitative evidence for optimizing transport systems and supporting sustainable regional development.