Scaling Laws, Poverty Traps, and the UrbanizationCrossover in Chinese County Economies

Urban scaling theory establishes that socioeconomic outputs scale superlinearly with city population (β > 1), attributed to social-interaction density, but its applicability to resource-constrained sectors remains untested. We analyse a panel of ∼ 2 , 800 Chinese counties (2000–2023) with GDP decomposed into primary, secondary, and tertiary sectors. Using the urbanization ratio as a continuous moderator in interaction-term regressions, we estimate sector-specific crossover thresholds from sub- to super-linear scaling; a Scale-Adjusted Agricultural Index (SAAI) quantifies each county’s deviation from size-expected output. A robust sectoral spectrum emerges—βpri = 0.87 < βter = 0.96 < βsec = 1.08—whose rank order is preserved across all 24 sample years. The tertiary sector crosses β = 1 at urbanization ratio u∗ = 0.80 (95% CI [0.72, 0.92]), with interaction coefficient β1 = 1.48 (p < 0.001). Province fixed effects confirm the urbanization interaction for secondary and tertiary sectors (p < 0.001) but not primary (p = 0.248), consistent with the crossover being specific to interaction-intensive activities. China’s 832 designated poverty counties exhibit systematically negative SAAI values (Cohen’s d = 0.55–0.87), revealing a persistent scaling deficit that conventional output comparisons obscure. These results show that the scaling exponent is a continuous function of economic structure, identify a quantifiable urbanization threshold for the onset of increasing returns, and supply a boundary condition for Bettencourt’s theory of urban scaling.