A Study on the Coupled Coordination Between Tourism Efficiency and Economic Development Level in the Beijing–Tianjin–Hebei City Cluster in the Past 10 Years

This longitudinal study applies decade-spanning socioeconomic indicators (2013–2022) from the Beijing–Tianjin–Hebei urban agglomeration. An integrated analytical framework was developed, merging the super-efficiency slack-based measurement (SBM) methodology with entropic weighting techniques to quantify tourism efficiency and economic development. Subsequent phases employed a multi-method analytical cascade: coupling coordination assessment modeling for system interaction analysis, standard deviation ellipses for spatial dispersion characterization, and Markovian transition matrices for temporal pattern identification. The investigation concludes with evolutionary trajectory projections using gray system forecasting GM(1,1) modeling. The analytical findings reveal the following patterns: (1) Within the Beijing–Tianjin–Hebei metropolitan cluster, tourism efficiency demonstrates a consistent upward trajectory, manifesting spatial differentiation characteristics characterized by a dual-core structure centered on Tianjin and Baoding, with higher values observed in northwestern areas compared to southeastern regions. Concurrently, regional disparities exhibit progressive convergence over temporal progression. (2) The level of economic development in the Beijing–Tianjin–Hebei city cluster has been rising steadily, demonstrating a geospatial distribution of ‘central concentration with peripheral attenuation, with the north-east being better than the southwest’, and the gap between the regional differences has become broader over time. (3) The coupling between tourism efficiency and the level of economic development in the Beijing–Tianjin–Hebei city cluster has generally improved, with Beijing and Tianjin predominantly in a coordinated regime, and some cities in Hebei Province about to shift from dysfunctional to coordinated, and, spatially, the coupling and coordination in northern sectors demonstrate superior performance compared to southern counterparts nationally. (4) The coupling coordination degree of the Beijing–Tianjin–Hebei city cluster in the next eight years is predicted by the gray GM(1,1) prediction model and the overall continuation of the growth trend of the Beijing–Tianjin–Hebei city cluster over the past ten years, thus verifying the importance of the regional integrated policy frameworks in the system integration of the Beijing–Tianjin–Hebei metropolitan system.