## 6 Conclusions  
From the perspectives of efficiency and equality, this paper considers CO\({}_{2}\) as an undesirable output and proposes a parallel DEA resource allocation model considering industrial structure characteristics of regions, and conducts an empirical study on the allocation of provincial-level carbon quotas for the three major industries in China. The method provided in this study can implement carbon emission quota allocation in pursuit of maximizing macro performance. This is a useful modification to the current carbon emissions trading market in China, which is gradually expanding its coverage. The methodology we provide assesses regional carbon emission efficiencies from a more comprehensive perspective and also facilitates more scientific and precise guidance for local governments to improve carbon emission control and improve environmental sustainability. In addition, the Chinese government has clearly proposed to transit from the dual control of total energy consumption and energy intensity to the dual control of total carbon emissions and carbon intensity. This implies that the scope of inclusion of carbon emission control is expanding from trading enterprises to the whole society. The method provided in this study can be a powerful reference for formulating and decomposing carbon emission control targets by sub-region and industry. The empirical results show that the equality of the resulting allocation scheme is the same as that of the actual carbon emissions allocation scheme, while the total GDP potentials is substantially increased compared to the initial total GDP. The results show the effectiveness and rationality of the proposed method. For example, carbon quotas in Shandong, Inner Mongolia, and other heavy industrial regions are still dominated by secondary industries. Furthermore, the resulting allocation scheme takes into account regional industrial characteristics. In addition, the carbon quotas of Jiangsu, Hainan, and  
Figure 5: The proportion of regional industry quota changes before and after. Shaanxi remain unchanged before and after the allocation. In the meantime, the carbon quotas of Jilin and Heilongjiang have declined disproportionately. Particularly, carbon quota allocations for all three major industries in Jilin have declined significantly after allocation, indicating that it will face greater pressure in the future to purchase carbon quotas from provinces other than emission reduction provinces, while Zhejiang and Gansu obtain more carbon quotas after the allocation and can sell on their carbon quotas. From the regional allocation results, the southern coastal and eastern coastal regions have received more carbon quotas, and government departments will have a more flexible capacity in formulating emission reduction policies for the relevant regions. The Middle Yellow River and northeast regions have seen a disproportionate decline in carbon quotas and face greater pressure to reduce emissions than other regions with lower carbon quotas for a single industry. According to the above empirical results, four policy implications are proposed:  
1. The Gini coefficient for carbon emissions in both primary and tertiary industries was less than 0.3 before the allocation was made, making the allocation scheme relatively equal. The Gini coefficient for carbon emissions in the secondary industry is 0.3835, which is a reasonable allocation scheme, but there is still a large gap from the levels of other industries. Policymakers should further improve the equality level of carbon quota allocation schemes between provinces, which will make it more reasonable for provinces to set carbon quota schemes within industries. 2. Due to the disproportionate emission abatement among and within provinces for the three major industries after carbon quota allocation, the allocation scheme can be implemented through carbon quota trading between provinces.