The environmental problems caused by global warming have seriously affected the ecological environment and the sustainable development of society. From 2000 to 2019, global carbon dioxide emissions increased by 40%. Therefore, reducing carbon emissions and other harmful gases has become a common goal for all countries to combat climate change ^[1]. As the world’s largest CO₂ emitter, China’s emission reduction initiatives have attracted widespread global attention ^[2]. China has implemented a series of action plans for the prevention and control of air pollution, resolutely fought the battle against pollution, won the battle to protect the blue sky, and concentrated on overcoming prominent ecological and environmental problems. Among a range of environmental policies, the carbon emissions trading Scheme (CETs) is the most influential. The plan is a major institutional innovation that uses market mechanisms to regulate greenhouse gas emissions and reduce air pollution while facilitating the transition to a green and low-carbon economic development model, contributing to the realization of sustainable environmental goals, and fighting for blue skies [3,4]^[3][4].

In 2013, the Chinese government initiated carbon emission trading pilot programs in key regions, including Beijing, Shanghai, Tianjin, Chongqing, Hubei, Guangdong, and Shenzhen. These programs successfully established carbon emission trading markets in the pilot areas and began online trading activities. Subsequently, in December 2016, Fujian Province launched its carbon trading market, marking the country’s eighth carbon trading pilot initiative. From 2017 onwards, the carbon emission trading market has gradually expanded its coverage from pilot areas to encompass the entire nation, with a particular focus on the power generation industry as an entry point for market expansion. By August 2020, the carbon emission market in pilot provinces and cities has expanded to encompass nearly 3000 enterprises across more than 20 industries, including steel, electricity, and cement ^[5]. Notably, the national carbon emission trading market was officially launched in July 2021 ^[6]. By July 2022, this market had facilitated the trading of 194 million tons of carbon emission allowances, equivalent to a total value of nearly 8.5 billion yuan. Consequently, the CETs have emerged as an indispensable tool in the government’s efforts to regulate and mitigate overall greenhouse gas emissions in China.

As a typical market-based environmental governance policy, the CETs can effectively reduce carbon emissions through market incentives and technological innovation based on the theory of property rights [7,8]^[7][8]. Previous literature focused on the construction of DID models to study the effects of CETs on improving energy efficiency ^[9], reducing carbon emissions ^[10], promoting technological innovation [11^[11][12],12], and controlling air pollution [13,14]^[13][14]. However, few studies have explored the spatial effects of CETs on carbon efficiency. Carbon efficiency, which represents the level of productivity achieved at a given level of carbon emissions, serves as a crucial indicator for assessing carbon emission performance. The implementation of the CETs not only influences the carbon emission efficiency within the pilot areas but also has spillover effects on the carbon emissions of neighboring cities, thereby generating spatial dependencies ^[15]. This spatial spillover effect manifests itself in the transmission of the promotion or inhibition effect of the CETs on carbon efficiency from one local region to its neighboring regions. However, the traditional Difference-in-Differences (DID) model fails to account for this spatial aspect, potentially resulting in estimation bias. To address this limitation, this study employs a multi-period Spatial Difference-in-Differences (SDID) approach to comprehensively analyze the spatial effects of the CETs and provide a more nuanced understanding of their impact.

The existing literature mainly explores the emission reduction effect of CETs at the provincial level, while there is little literature focusing on the influencing factors of carbon emission efficiency at the city level. More importantly, the second batch of pilot implementation in Fujian in 2016 was taken into account in the model, and there might be deviations in policy evaluation if a single-period DID was adopted. For example, Shao and Zhang (2022) ^[16] analyzed the emission reduction effect of CETs based on China’s provincial panel data rather than the city level. Zhang et al. (2020) ^[10] tested the effect of CETs on energy and environmental efficiency by using the single-period DID instead of taking the pilot in Fujian in 2016 as the second batch and using the multi-period DID analysis model. 

2. Carbon Emission Trading Policies in China

Since the European Union established the world’s largest carbon emissions trading market in 2005, scholars have been concerned about its effectiveness in reducing carbon emissions [20]^[17]. Some scholars have proposed that the CETs, as a typical market-oriented environmental governance policy, are more effective than traditional government regulation in carbon reduction. However, due to differences in basic national conditions and technical levels, scholars have yet to reach a unified conclusion on the emission reduction effect of CETs. On the one hand, certain scholars hold the view that the carbon reduction effect resulting from the implementation of CETs is not substantial. For example, Streimikiene and Roos (2009) [21]^[18] studied the carbon emission data of European countries and found that the EU emission trading system has not been able to reduce carbon dioxide emissions at a low cost, and the CETs are not strong in reducing carbon emissions. On the other hand, some scholars believe that the CET policies can effectively achieve carbon emission reduction and improve carbon emission efficiency. For example, Camila et al. (2018) [22]^[19] believe that the CETs have a stronger effect on carbon reduction than the carbon tax and other mechanisms. Zhang and Zhang (2019) [23]^[20] and Shen et al. (2017) [24]^[21] respectively point out at the national and enterprise levels that the implementation of China’s carbon trading pilot policies can effectively promote the emission reduction of the whole country and enterprises. Zhang et al. (2020) ^[10] pointed out that the implementation of CETs significantly reduced industrial CO₂ emissions in pilot areas, and the average carbon emission efficiency of China’s seven CETs increased year by year. Meanwhile, scholars have gradually explored the carbon emission reduction mechanisms of CETs. Lin and Huang (2022) [20]^[17] found that the inhibition effect of carbon emissions is realized through government implementation rather than market mechanisms. Meanwhile, Cai and Ye (2022) ^[2] pointed out that CETs can promote low-carbon development by improving the efficiency of low-carbon technologies. Dong et al. (2022) ^[13] believed that CETs indirectly affect carbon emissions by improving the innovation level of cities and guiding the location choice of local industries. However, this literature ignores the indirect effects of labor resource allocation and green technology innovation on the influence channels of carbon trading pilot policies on carbon emissions. In addition, most scholars use the traditional differential method to explore the economic impact of CETs. For example, Zhang et al. (2020) ^[10] used the DID method to assess the impact on carbon emissions after the implementation of the CETs in pilot cities and found that in all seven pilot regions of the carbon trading policy, the emission reduction effect of the CETs was significant. Shao and Zhang (2022) ^[16] employed the DID method to examine the 31 provinces in China from 2000 to 2015. Their findings indicated that the implementation of CETs in pilot areas effectively led to a reduction in local carbon emissions. However, previous literature focused on the provincial level did not take the two groups of pilot cities into account in the model and ignored the spatial effects of CETs. Since the CETs are implemented gradually in two groups of cities, the traditional DID method is limited in evaluating the policy’s effect. Moreover, the implementation of CETs in a specific region may have spillover effects on the carbon emission intensity of neighboring areas, which the conventional DID model might not adequately capture, leading to potential biases in assessing these effects. To address this limitation, scholars have extensively utilized the Spatial Difference-in-Differences (SDID) model, which combines spatial econometrics with the DID framework, to examine the impacts of various policies. The SDID model allows for the consideration of spatial interactions and dependencies among regions, providing a more comprehensive understanding of the spatial spillover effects of the CETs on carbon emission intensity. The measurement of carbon emission efficiency in previous literature has predominantly relied on single-factor methods, which may introduce measurement deviations [25,26]^[22][23]. To overcome these shortcomings, this study employs the Slack-Based Measure (SBM) model with non-expected outputs to comprehensively evaluate the total factor carbon emission efficiency of 253 prefecture-level cities in China. By incorporating relaxation variables into the objective function, the non-expected SBM model offers a more comprehensive and accurate measurement of carbon emission efficiency. In line with the approach taken by Gao et al. (2022) [27]^[24], this paper extends the SBM model to include carbon dioxide emissions as an undesirable output, thereby capturing a more comprehensive assessment of total factor carbon emission efficiency. In summary, previous literature has laid a certain foundation for studying the economic effect of CETs, but there are some limitations: First, most of the studies used the seven provinces of the first batch of pilots in 2013, without considering the second batch of pilots in Fujian Province in 2016. So, the traditional single-period DID may lead to inaccurate estimates. Secondly, the spatial spillover effect of CETs on carbon emission efficiency has been largely neglected in the existing literature. Although the implementation of CETs in pilot cities may have repercussions on the carbon emissions of neighboring cities, the spatial dimension of CETs has been largely overlooked. Consequently, the understanding of the spatial spillover effect of CETs on carbon emission efficiency remains limited and requires further scholarly attention. Thirdly, the previous studies did not provide a comprehensive analysis of the impact mechanism of CET policies on carbon emission efficiency, ignoring the mediating role of labor resource allocation and green technology innovation. Fourthly, most of the literature uses single-factor methods to measure carbon emissions efficiency, and few have taken environmental factors into account to measure the total factor carbon emission efficiency.