Abstract
Ensuring equitable and efficient allocation of educational resources is critical for advancing high-quality compulsory education, particularly in large, internally diverse provinces like Shandong, China. This study addresses critical gaps in understanding spatiotemporal efficiency dynamics by developing an integrated analytical framework. We evaluate the static and dynamic efficiency (2018–2023), coupling coordination with regional economic resilience, and future trends (2024-2030) of compulsory education resource allocation across Shandong’s 16 prefecture-level cities. The framework uniquely combines the super-efficiency slacks-based measure (SBM) model, Malmquist index (MI), Coupling Coordination Degree Model (CCDM), and Fractional-order Grey Model (FGM). Key findings reveal: (1) Persistent and widening regional disparities in static efficiency, with an overall declining provincial average indicating systemic deterioration risk; (2) Marginal yet unstable TFP growth, primarily driven by technological progress, but undermined by emerging scale inefficiency, exacerbated post-pandemic; (3) A distinct “high in East Shandong, low in Southwest Shandong” spatial pattern in education-economy coupling coordination, with core-periphery divergence intensifying over time. These results underscore an “efficiency trap” where sustained investment fails to translate into systemic efficiency gains due to economic resilience thresholds. The study emphasizes the necessity for spatially differentiated policies targeting region-specific bottlenecks. It provides a comprehensive methodological framework and empirical evidence to inform targeted resource optimization strategies, promoting educational equity and sustainable development in Shandong and comparable regions facing significant internal disparities.
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Data availability
The datasets generated and analyzed during the current study are available as supplementary material to this article. To ensure full transparency and facilitate replication, we have shared the following materials: All raw and processed data supporting the findings of this study have been deposited in the supplementary material. These include: the original data and Super-SBM analysis results for educational resource allocation efficiency across 16 prefecture-level cities in Shandong Province from 2018 to 2023; the Malmquist index analysis results for dynamic efficiency evaluation; the raw data for economic resilience indicators; the entropy method weighting results; the relative closeness values derived from entropy-weighted TOPSIS analysis; and the coupling coordination degree calculation results. Additionally, we have provided the analytical code used in this study, including the fractional-order grey model data and code, the revenue analysis code, and the code used to generate Figures 3, 4, and 8b. All materials are available in the online supplementary material accompanying this article.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (62007020), the Shandong Provincial Natural Science Foundation (ZR2024QF058, ZR2025QC648), and the Shandong Provincial Social Science Planning Research Project (25CLJJ47). The authors gratefully acknowledge these funding agencies for their financial support.
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Wanli Xie: Writing – original draft, Data curation, Conceptualization, Visualization. Huaiyan Zhao: Writing – review & editing, Data curation, Conceptualization, Visualization. Xu Liang: Project administration, Data Curation, Conceptualization. Zhenguo Xu: Project administration, Writing – review, Supervision, Conceptualization. Tongtong Dang: Writing – editing, Supervision, Conceptualization. All authors have read and agreed to the published version of the manuscript.
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Xie, W., Zhao, H., Liang, X. et al. Spatiotemporal evolution and predictive analysis of educational resource allocation efficiency in Shandong Province. Humanit Soc Sci Commun (2026). https://doi.org/10.1057/s41599-026-06994-7
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DOI: https://doi.org/10.1057/s41599-026-06994-7
