The importance and urgency of improving energy and carbon emissions efficiency in mitigating climate change and achieving carbon neutrality have become an increasingly relentless focus in recent years. Assessing the performance of energy saving and carbon emissions reduction is a significant necessity to achieve sustainable economic development. Therefore, from the perspective of production economics, this paper presents a review of the definition, models, and input-output variables for measuring total-factor energy efficiency and total-factor carbon emissions efficiency. Relevant literature in this field, published between 2006 and 2021, has been systematically analyzed using CiteSpace software, which includes a quantitative and visual review of a large body of published literature. This review found that the current definitions of total-factor energy efficiency and total-factor carbon emissions efficiency are confusing and misleading. Furthermore, future research on energy saving and carbon emissions reduction should incorporate subject areas such as economics, energy, and ecology.

Energy efficiency is crucial to the 2030 UN Sustainable Development Goals (SDGs), but its widely measured indicator, energy intensity, is still insufficient. For this reason, in 2006, total factor energy efficiency (TFEE) was proposed with capital, labor, and energy as inputs and GDP as the desirable output. The later TFEE approach further incorporated pollution as the undesirable output. However, it is problematic to regard GDP (the total value of final products) as the desirable output, because GDP does not include the intermediate consumption, which accounts for a large part of the production activities and may even be larger than the value of GDP. GDP is more suitable for measuring distribution, while VO (value of output) is more appropriate for sustainable production analysis. Therefore, we propose a VO TFEE approach that takes VO as the desirable output instead and correspondingly incorporates the other intermediate materials and services except energy into inputs. Finally, the empirical analysis of the textile industry of EU member states during 2011–2017 indicates that the VO TFEE approach is more stable and convergent in measuring energy efficiency, and is more suitable for helping policymakers achieve the SDGs of energy saving, emissions reduction, and sustainable economic development.

This paper introduces an improved slack-based game cross-efficiency measurement model that enhances the existing cross-efficiency framework and integrates it with the Data Envelopment Analysis (DEA) game cross-efficiency. The model ensures the fairness of its results through the implementation of a more stringent selection of frontier face weights. It accounts for the competitive relationships among Decision Making Units (DMUs), achieving a Nash equilibrium solution through continuous iterations. Furthermore, the model accounts for undesirable outputs and various strategic orientations, enhancing its applicability. The model’s effectiveness is validated through comparative analyses of diverse case studies. Additionally, the model’s practical utility is demonstrated through the analysis of industrial data from various Chinese provinces between 2010 and 2019. Analysis results show that the proposed model measures production efficiency with greater precision and comparability than alternative models.