Digital Economy, Spatial Imbalance, and Coordinated Growth: Evidence from Urban Agglomerations in the Middle and Lower Reaches of the Yellow River Basin

Amid the rapid evolution of the digital economy reshaping global competitiveness, China has advanced regional coordination through the Digital China initiative and the “Data Elements ×” Three-Year Action Plan (2024–2026). To further integrate digital transformation with high-quality growth in the urban agglomerations of the middle and lower Yellow River, this study aims to strengthen regional competitiveness, expand digital industries, foster new productivity, refine the development pathway, and safeguard balanced economic, social, and ecological progress. Taking the Yellow River urban clusters as the research object, a comprehensive assessment framework encompassing seven subsystems is established. By employing a mixed-weighting approach, entropy-based TOPSIS, hotspot analysis, coupling coordination models, spatial gravity shift techniques, and grey relational methods, this study investigates the spatiotemporal dynamics between the digital economy and high-quality development. The findings reveal that: (1) temporally, the coupling–coordination process evolves through three distinct phases—initial fluctuation and divergence (1990–2005), synergy consolidation (2005–2015), and high-level stabilization (2015–2022)—with the average coordination index rising from 0.21 to 0.41; (2) spatially, a persistent “core–periphery” structure emerges, while subsystem coupling consistently surpasses coordination levels, reflecting a pattern of “high coupling but insufficient coordination”; (3) hot–cold spot analysis identifies sharp east–west contrasts, with the gravity center shift and ellipse trajectory showing weaker directional stability but greater dispersion; and (4) grey correlation results indicate that key drivers have transitioned from economic scale and infrastructure inputs to green innovation performance and data resource allocation. Overall, this study interprets the empirical results in both temporal and spatial dimensions, offering insights for policymakers seeking to narrow the digital divide and advance sustainable, high-quality development in the Yellow River region.