###### Abstract  
At present, China implements a quota-based trading mechanism to achieve carbon emission reduction, in which the allocation of carbon emission quotas among different provinces is short of considering the influence of unbalanced provincial development. Heterogeneity among the provincial-level three major industries, namely, agriculture, manufacturing and mining, and service industries, is a case in point. To address this insufficiency, this paper proposes a novel parallel data envelopment analysis (DEA) based method for carbon emission quota allocation. The method models each province as a decision-making unit (DMU) and the provincial-level three major industries as parallel sub-decision-making units (SDMUs). A distinguished feature of the method is that it makes explicit tradeoffs between efficiency and equality considerations for policymakers in allocating the carbon quotas among three heterogeneous provincial-level major industries. The empirical results show that the proposed method effectively improves the overall provincial gross domestic product (GDP) potentials through the reallocation of carbon quotas among industries while the equality level is not worse off. This work is helpful for policymakers to achieve a long-term emission reduction target and provides suggestions for improving the initial allocation mechanism of a national carbon trading market. data envelopment analysis (DEA); parallel structure; allocation of carbon emission quotas; Gini coefficient; three major industries 202315  
China introduced a quota-based national carbon market in 2011 and carried out trading pilot work in seven regions successively (i.e., Beijing, Shanghai, Tianjin, Chongqing, Hubei, Guangdong, and Shenzhen). By the end of 2021, the cumulative volume of carbon quotas traded in the national carbon market achieved 140 million tons. In addition to the development of the national carbon market, some provinces have created local carbon emission trading markets as an indispensable part of China's carbon market. For example, Zhejiang province has established the first local carbon-inclusive market in the city of Yueqing, where both enterprises and individuals can participate in carbon trading independently [3]. The carbon emissions from China are among the highest in the world, which means China needs more efforts to reduce carbon emissions. According to statistics from British Petroleum (BP) [4], the carbon emissions of China in 2021 were 10,398 tons, far exceeding the shares of other countries. In the meantime, China has set up an ambitious national plan to actively control carbon emissions. For example, to achieve the Intended Nationally Determined Contribution (INDC) target specified in 2015 for addressing climate change, the Chinese Government Work Report proposed a binding constraint for the carbon emission intensity to decline by 18% compared with that of 2020 during the \"14 th Five-Year\" Plan period, i.e., 2021-2025. Allocation of carbon quotas is a fundamental issue in implementing a carbon trading mechanism [5]. The current carbon quota allocation mechanism in China is facing challenges. Presently, China allocates national carbon reduction targets on a provincial basis. However, this method has called into question the viability of allocation results. For example, the economic development of industrial provinces such as Hebei, Shanxi, and Inner Mongolia heavily depends on high energy-consuming sectors. Under the allocation method, these provinces are in huge carbon emission deficits, i.e., their actual carbon emissions are much larger than their carbon quotas. In the meantime, service industry-oriented regions such as Beijing and Shanghai, where the tertiary industry accounts for a larger share, are found in a \"low emission, high quota\" situation [6]. In this case, the allocation method is short of considerations of differences in regional industrial structures.