Research on “Finance-Trade-Consumption” Based on the “Entropy-Coupling” Model: A Case Study of Hebei Province

China’s progress in high-quality economic development continues to deepen, with clear requirements for “enhancing the ability of financial services to serve the real economy” and “promoting the expansion and improvement of consumption.” Against this backdrop, the finance-trade-consumption link, as a key link connecting financial supply and real economic demand, holds strategic significance for promoting regional economic structural optimization and consumption upgrades. However, existing research has largely focused on the national level or single dimensions, such as the linear impact of digital finance on consumption or regional heterogeneity analysis. Comprehensive exploration of the synergistic mechanisms across multiple subsystems, including the economic foundation, trade environment, and consumer behavior, is lacking. In-depth synergistic analysis is particularly weak in typical regions such as Hebei Province. Therefore, this study uses the “entropy-coupling” model to examine the finance-trade-consumption system in Hebei Province, selecting data from 2019 to 2023 to explore its overall development and internal coupling. The conclusions are as follows: In terms of comprehensive scores, Hebei’s finance-trade-consumption score increased from 0.07 to 0.34 between 2019 and 2023. In the subsystem analysis, finance achieved an average annual growth rate of 31%, consumption experienced a V-shaped rebound of 3.5 times, and trade increased nearly 10,000 times. The coupling synergy analysis found that the coupling degree (D) of “finance-trade-consumption” in Hebei Province jumped from 0.17 to nearly 1.00 between 2019 and 2023, and a transition from imbalance to high-quality coordination was achieved between 2021 and 2023. Therefore, the study suggests that the Hebei Provincial Government needs to focus its policies on new productivity driven by the integration of data elements and AI. With the deep integration of AI, new productivity, and regional policies, the high-quality development of financial consumption and trade in Hebei Province will gain sustainable endogenous momentum.