Measuring the Coordinated Development of Urban Agglomerations from the Perspective of New Quality Productive Forces: Evidence from the Beijing–Tianjin–Hebei Region

New quality productive forces are increasingly recognized as important drivers of coordinated regional development, with urban agglomerations acting as key vehicles for their spatial implementation. Based on the theory of new quality productive forces, this study takes the 13 cities in the Beijing–Tianjin–Hebei (BTH) urban agglomeration as its research subjects, spanning the period from 2005 to 2023, and constructs a four-dimensional evaluation index system for new quality productive forces covering economic, social, ecological, and technological dimensions. It employs the entropy method to determine indicator weights and calculate development indices for each dimension and utilizes a coupling coordination model to measure the overall and subsystem-level coordination by analyzing their spatiotemporal evolution characteristics. The results indicate a steady upward trend in the overall coordination level, progressing from a low level to an intermediate level, with the state of coordination continuously improving; spatial differentiation is significant, forming a gradient development pattern centered on Beijing, with marked disparities in coordination levels among cities. Subsystem analysis reveals an imbalanced synergy structure: while economic and ecological synergy levels are relatively high, the coupling and synergy between science and technology and the economy and society remain prominent weaknesses. Most cities in Hebei Province lack sufficient scientific and technological innovation capabilities, resulting in a weak supportive role for economic and social development. Based on these findings, this study proposes policy recommendations such as establishing a regional innovation community, promoting the integration of factor markets, and strengthening collaborative governance of the ecological environment, with the aim of leveraging new quality productive forces to drive a qualitative leap in the coordinated development of the BTH urban agglomeration.