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

Xiaoxia Zhu, Tongyue Feng (), Yuhe Shen, Ning Zhang () and Xu Guo
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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

Mathematics, 2025, vol. 13, issue 9, 1-29

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.

Keywords: three-level meta-frontier; carbon emission efficiency; heterogeneity decomposition; nonradial directional distance function (DDF); technology gap ratio (TGR) (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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