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A Three-Level Meta-Frontier Framework with Machine Learning Projections for Carbon Emission Efficiency Analysis: Heterogeneity Decomposition and Policy Implications

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  • Xiaoxia Zhu

    (Institute of Advanced Studies in Humanities and Social Sciences, Beijing Normal University, Zhuhai 519087, China)

  • Tongyue Feng

    (Institute of Advanced Studies in Humanities and Social Sciences, Beijing Normal University, Zhuhai 519087, China)

  • Yuhe Shen

    (The State Radio Monitoring Center, Beijing 100043, China)

  • Ning Zhang

    (Faculty of Arts and Science, Beijing Normal University, Zhuhai 519087, China)

  • Xu Guo

    (School of Economics & Management, Fuzhou University, Fuzhou 350108, China)

Abstract

This study proposes a three-level meta-frontier framework enhanced with machine learning-driven projection methods to address the dual heterogeneity in carbon emission efficiency analysis arising from regional disparities and industrial diversification. Methodologically, we introduce two novel projection combinations—“exogenous-exogenous-accumulation (E-E-A) and exogenous-exogenous-consistent (E-E-C)”—to resolve the inconsistency of technology gap ratios (TGRs > 1) in traditional nonradial directional distance function (DDF) models. Reinforcement learning (RL) optimizes dynamic direction vectors, whereas graph neural networks (GNNs) encode spatial interdependencies to constrain the TGR within [0, 1]. Empirical analysis of 60 countries reveals that (1) E-E-C eliminates the TGR overestimation by 12–18% in energy-intensive sectors (e.g., reducing Asia’s secondary industry T G R 1 from 1.160 to 1.000); (2) industrial heterogeneity dominates inefficiency in Asia (IHI = 0.207), whereas management gaps drive global secondary sector inefficiency (MI = 0.678); and (3) policy simulations advocate for decentralized renewables in Africa, fiscal incentives for Asian coal retrofits, and expanded EU carbon border taxes. Computational enhancements via Apache Spark achieve a 58% runtime reduction. The framework advances environmental efficiency analysis by integrating machine learning with meta-frontier theory, offering both methodological rigor (via regularization and GNN constraints) and actionable decarbonization pathways. Limitations include static heterogeneity assumptions and data granularity gaps, prompting the future integration of IoT-enabled dynamic models.

Suggested Citation

  • Xiaoxia Zhu & Tongyue Feng & Yuhe Shen & Ning Zhang & Xu Guo, 2025. "A Three-Level Meta-Frontier Framework with Machine Learning Projections for Carbon Emission Efficiency Analysis: Heterogeneity Decomposition and Policy Implications," Mathematics, MDPI, vol. 13(9), pages 1-29, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1542-:d:1651127
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    References listed on IDEAS

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    1. Zhou, P. & Ang, B.W., 2008. "Linear programming models for measuring economy-wide energy efficiency performance," Energy Policy, Elsevier, vol. 36(8), pages 2901-2906, August.
    2. Sueyoshi, Toshiyuki & Goto, Mika, 2011. "DEA approach for unified efficiency measurement: Assessment of Japanese fossil fuel power generation," Energy Economics, Elsevier, vol. 33(2), pages 292-303, March.
    3. Christopher O’Donnell & D. Rao & George Battese, 2008. "Metafrontier frameworks for the study of firm-level efficiencies and technology ratios," Empirical Economics, Springer, vol. 34(2), pages 231-255, March.
    4. Wang, Ailun & Hu, Shuo & Li, Jianglong, 2022. "Using machine learning to model technological heterogeneity in carbon emission efficiency evaluation: The case of China's cities," Energy Economics, Elsevier, vol. 114(C).
    5. Toba Stephen Olasehinde & Fangbin Qiao & Shiping Mao, 2023. "Impact of Improved Maize Varieties on Production Efficiency in Nigeria: Separating Technology from Managerial Gaps," Agriculture, MDPI, vol. 13(3), pages 1-14, March.
    6. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
    7. Qingshan Ma & Yuanmeng Zhang & Kexin Yang & Lingyun He, 2021. "Have China’s Pilot Free Trade Zones Improved Green Total Factor Productivity?," IJERPH, MDPI, vol. 18(21), pages 1-20, November.
    8. George Battese & D. Rao & Christopher O'Donnell, 2004. "A Metafrontier Production Function for Estimation of Technical Efficiencies and Technology Gaps for Firms Operating Under Different Technologies," Journal of Productivity Analysis, Springer, vol. 21(1), pages 91-103, January.
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