The role of sectoral coverage in emission abatement costs: evidence from marginal cost savings

In keeping with China's NDCs of carbon intensity reduction by 2030, we follow Mi et al (2017) and Fang et al (2021) who assume an exponential decline in carbon intensity. The historical trend in China's carbon intensity that decreases from 2.96 tons per 10 thousand RMB in 2005 to 1.61 tons per 10 thousand RMB in 2017 fits well with our exponential model. Moreover, considering the uncertainty of China's economic growth in a post-COVID-19 'new normal' (Song and Zhou 2020), we set three scenarios for future economic growth rate (i.e.3%, 4% and 5%) until 2030. Note that this is generally in line with the China's latest economic plan that requires the average annual GDP growth rate to be 4.7% consistently in the next 15 years in achieving the goal of becoming a moderately developed country by 2035 (Asian Development Bank 2021, National Development and orm Commission of China 2021). The measurement of China's ERQs can be done as:

$$\begin{equation}m = 1 - \sqrt[{13}]{{\frac{{{\text{C}}{{\text{I}}_{2030}}}}{{{\text{C}}{{\text{I}}_{2017}}}}}} = 1 - \sqrt[{13}]{{\frac{{{\text{C}}{{\text{I}}_{2005}} \times \left( {1 - 65{{\% }}} \right)}}{{{\text{C}}{{\text{I}}_{2017}}}}}}\end{equation} \tag{ 1 }$$

$$\begin{equation}{\text{C}}{{\text{I}}_t} = {\text{C}}{{\text{I}}_{2017}} \times {\left( {1 - m} \right)^{t - 2017}}\end{equation} \tag{ 2 }$$

$$\begin{equation}{\text{ERQ}}{{\text{s}}_t} = {\text{GD}}{{\text{P}}_t} \times \left( {{\text{C}}{{\text{I}}_{t - 1}} - {\text{C}}{{\text{I}}_t}} \right)\end{equation} \tag{ 3 }$$

$$\begin{equation}{\text{GD}}{{\text{P}}_t} = {\text{GD}}{{\text{P}}_{2017}} \times {\left( {1 + \alpha } \right)^{t - 2017}}\end{equation} \tag{ 4 }$$

where m is the mitigation rate (%) of China's carbon intensity from 2018 to 2030. Given China's updated NDCs, we presume a 65% reduction of carbon intensity in 2030 against the 2005 levels. CI_t is China's carbon intensity (tons CO₂ per 10 thousand RMB) in year t, ERQs_t is China's emission reduction quotas (million tons, Mt) in year t, GDP_t is China's gross domestic product (100 million RMB) in year t, and α is China's economic growth rate (%) from 2018 to 2030.

The total ERQs by 2030 will be allocated to ETS-covered sectors through a top-down approach. Admittedly, there are different schemes for ERQs allocation at the sectoral scale (e.g. grandfathering scheme, output-based scheme), and a consensus on the most appropriate one has not been reached (Fang et al 2019, Lucas et al 2020). However, the cost-effectiveness of ETS can be independent from the allocation process (Zhou et al 2013, Chang et al 2016). In this article, we adopt the grandfathering scheme that allocates ERQs proportionally to the sectoral historical emissions, since it makes the allocation more implementable than other schemes, particularly at the early stage of ETS (Cramton and Kerr 2002, Wang et al 2019). The ERQs allocation based on the grandfathering scheme can be done as:

$$\begin{equation}{\text{CEA}}_t^i = \left( {\sum\limits_i {\text{CE}}_t^i - {\text{ERQ}}{{\text{s}}_t}} \right) \cdot \frac{{{\text{CE}}_t^i}}{{{{\mathop \sum \nolimits }}_i{\text{CE}}_t^i}}\end{equation} \tag{ 5 }$$

$$\begin{equation}{\text{ERQs}}_t^i = {\text{CE}}_t^i - {\text{CEA}}_t^i\end{equation} \tag{ 6 }$$

$$\begin{equation}{\text{ERQs}}_t^i = {\text{ERQ}}{{\text{s}}_t} \cdot \frac{{{\text{CE}}_{{t_0}}^i}}{{{{\mathop \sum \nolimits }}_i{\text{CE}}_{{t_0}}^i}}\end{equation} \tag{ 7 }$$

where ${\text{CEA}}_t^i$ is the carbon emission allowance (CEA) (Mt) of sector i in year t, ${\text{CE}}_t^i$ is the carbon emissions (Mt) of sector i in year t, ${\text{ERQs}}_t^i$ is the emission reduction quotas (Mt) of sector i in year t, and t₀ is the baseline year. As seen in formula 5, we allocate the CEA to each sector by multiplying China's total CEA and the proportion of sectoral emissions in each year t. Then to simulate the ETS in terms of MACs, we translate CEA to ERQs as previous studies (Zhou et al 2013, Fang et al 2021). In theory, CEA represents the emissions that agents must comply with, and ERQs represent the emissions that should be reduced to meet the caps. In this sense, the translation will have no impacts on the EACs and carbon price. Specifically, the sectoral ERQs then can be calculated by subtracting the allocated CEA from its future carbon emissions (formula 6). We assume that the proportion of carbon emissions by each sector keeps unchanged from 2018 to 2030 for brevity. While this probably increases the uncertainty of the estimated ERQs by sector, it has nothing related to our simulation on the impacts of sectoral coverage on the total EACs. In doing so, formulas 5 and 6 can be converted to formula 7 that accounts for the sectoral ERQs proportional to the historical emissions of each sector. Here the historical emissions refer to the annual average carbon emissions between 2015 and 2017.

The MAC curves depict how the EACs of a sector increase due to an additional unit of CER. Given the growing MACs when CER increases, we adopt a second-order polynomial function as a basis for estimating the MAC curves for sectors, as suggested by previous studies (Zhou et al 2013, Cui et al 2014, Fan et al 2016). Specifically, we follow Zhou et al (2013) and use accumulative carbon emission reduction (defined in this paper as the CER added up between 2000 and the specific year) as a proxy for the emission reduction potential. To account for the MACs, we introduce the potential economic loss proposed by Fang et al (2021) as a substitute for the investment on clean development mechanism. Potential economic loss that calculates the economic loss due to the production inefficiency and accounts for the direct and indirect costs of CER is expected to correct the serious distortion in the MACs estimation given the phaseout of clean development mechanism since 2008 (World Bank 2012, Maraseni 2013). The MAC curves for sectors are estimated as:

$$\begin{equation}{\text{PEL}}_t^i = {a^i} \cdot {({\text{ACER}}_t^i)^2} + {b^i} \cdot {\text{ACER}}_t^i + {c^{\,i}}\end{equation} \tag{ 8 }$$

$$\begin{equation}{\text{PEL}}_t^i = \left( {{\text{EP}}_{t + 1}^i - {\text{EP}}_t^i} \right) \cdot {\text{CE}}_t^i\end{equation} \tag{ 9 }$$

$$\begin{equation}{\text{ACER}}_t^i = \sum\limits_{{t_0}}^t {\text{CER}}_t^i = \sum\limits_{{t_0}}^t ({\text{CI}}_{t - 1}^i - {\text{CI}}_t^i) \cdot {\text{GDP}}_t^i\end{equation} \tag{ 10 }$$

where ${\text{PEL}}_t^i$ is the potential economic loss (100 million RMB) of sector i in year t, ${\text{ACER}}_t^i$ is the accumulative carbon emission reduction (Mt) of sector i in year t while ${\text{CER}}_t^i$ is the carbon emission reduction (Mt) of sector i in the single year t. In this study, we set 2000 as the starting year for measuring the cumulative value. ${\text{EP}}_t^i$ is the emission productivity (10 thousand RMB per ton CO₂) of sector i in year t, expressed as the inverse of carbon intensity, and a_i, b_i and c_i are parameters to be estimated. Specifically, to account for the three parameters for each sector, we calculate potential economic loss and accumulative CER for all the sectors from 2000 to 2017 by formulas 9 and 10. As shown in formula 9, the potential economic loss of sectors is calculated by multiplying the difference in emission productivity and carbon emissions between adjacent years.

In the ETS regime, the sectors with higher MACs tend to transfer their ERQs to those that have lower MACs. By reallocating the ERQs to sectors with lower MACs, the ETS enables the rigorous and cost-effective achievement of climate targets. We develop a non-linear programming model to simulate China's inter-sectoral ETS, and estimate China's EACs under different sectoral coverages, following the formulas:

$$\begin{equation}\min {\text{TAC}} = \sum\limits_i \int\limits_{{\text{ACER}}_{2018}^i}^{{\text{ACER}}_{2030}^i} {\text{PEL}}_t^id{\text{ACER}}_t^i\end{equation} \tag{ 11 }$$

$$\begin{equation}{\text{ACER}}_{2030}^i - {\text{ACER}}_{2017}^i - {\text{Trad}}{{\text{e}}_i} \ge \sum\limits_{t = 2018}^{2030} {\text{ERQs}}_t^i\end{equation} \tag{ 12 }$$

$$\begin{equation}\sum\limits_i {\text{Trad}}{{\text{e}}_i} = 0\end{equation} \tag{ 13 }$$

where TAC is China's total abatement (100 million RMB) after trading, and ${\text{Trad}}{{\text{e}}_i}$ is the trading ERQs (Mt) of sector i from 2018 to 2030. Note that this study concerns the ERQs trade between sectors instead of CEA trade, whereby the positive Trade_i refers to additional emissions reduced by Sector i for others, and vice versa. Formula 11 sets the objective function of minimizing China's EACs in 2018–2030. Formula 12 implies that the emissions reduced by each sector in 2018–2030 and the trading ERQs should not be fewer than its initially assigned climate targets. Formula 13 suggests a market clearing of ETS in this period.

As shown in table 1, Chinese economy is classified into 29 sectors, of which 24 are sub-sectors in the manufacturing industry. Because there is no official carbon intensity published at national and sectoral scales, we calculate these values by dividing the carbon emissions by the corresponding GDP. The emission data for China and all the sectors in 2000–2017 come from the China Emission Accounts and Datasets. Since this is an emission inventory of 45 sectors from 1997 to 2017, we aggregate these data according to our sectoral classification. The GDP data for China and all the sectors in 2000–2017 are derived from the Chinese Statistical Yearbooks, all of which have been converted to the 2005 prices for comparability. Due to the lack of access to GDP of sub-sectors in the manufacturing industry, we use the data on value added of industrial enterprises above designed size to estimate the GDP of each sub-sector.

Based on the sectoral potential economic loss and accumulative CER from 2000 to 2017, we estimate the MAC curves for 29 sectors using the quadratic function as displayed in figure 2. In general, the MACs experience an exponential rise as the sectoral CER increases. Specifically, GenMac, Whol&Ret and ElecEqp have high MACs irrespective of CER, as they are less carbon-intensive and thus have little potential of CER. By contrast, for those large emitters (e.g. E&W Prod, Metl, NonmetlProd), the MACs always remain at a low level regardless of the CER. In addition, the MACs of Tran&Stor, ChemInd, CoalMin start at the bottom but experience a sharp increase in MACs in response to the deep emission reduction. For instance, when the CER is assumed at 50 Mt, Tran&Stor, ChemInd and CoalMin have their MACs at 22.44, 25.22 and 53.42 RMB per ton. But when the CER increases to 250 Mt, an additional unit of CER of these three sectors will cost 161.32, 504.94 and 829.16 RMB. In addition to the varying MAC curves for sectors, the difference in the historical CER between sectors is pronounced. For instance, NonmetlProd, E&W Prod, and Metl with relatively flat MAC curves have historical CER over 500 Mt, while the majority of the sectors (e.g. Whol&Ret, Petr&Coking, CoalMin) have their historical CER less than 100 Mt.

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In theory, the varying sectoral MACs provide a basis for implementing the ETS across sectors. However, despite the considerable divergence of sectoral MACs, we notice some sectors that have similar MAC curves, e.g. Metl and NonmetlProd, Tran&Stor and Petr&Coking, Petr&Gas and ChemInd. Covering the sectors resembling in their MAC curves might contribute little to the potential cost savings of ETS while leading to a substantial increase in the administrative and transaction costs. With the aim of reducing more EACs with a relatively small sectoral coverage, there is a great need to identify the prioritized sectors that have large MCSs.

Figure 3 shows that China's carbon intensity has reduced from 2.96 tons per 10 thousand RMB in 2005 to 1.61 tons per 10 thousand RMB in 2017, and will continuously decline to 1.04 tons per 10 thousand RMB in 2030 at a mitigation rate of 3.3% according to our exponential model. After projecting China's future GDP in the three scenarios for economic growth (i.e. 3%, 4% and 5%), we measure China's total ERQs from 2018 to 2030 that amount to 4217.78, 4513.30 and 4832.60 Mt, respectively. As seen, enhancing the economic growth will moderately lead to more ERQs in the next decade.

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By estimating and comparing the MCSs of sectors, the rankings of ETS-covered sectors can be determined. Figure 4 shows the impacts of each sector on China's EACs when it is involved in the ETS. In general, China's EACs can be largely reduced due to coverage extension. As seen, at an economic growth rate of 3%, 4% and 5%, the total EACs will drop from 0.90–0.35, 1.07–0.44 and 1.27–0.55 trillion RMB, respectively. Meanwhile, we notice a sharp decrease in the MCSs as the sectoral coverage extends. Regardless of the economic growth scenarios, China's EACs can be cut by over 80% with the engagement of six sectors (i.e. E&W Prod, OthrServ, Metl, Tran&Stor, Petr&Gas and NonmetlMin) compared to the engagement of E&W Prod only. Alternatively, the other 23 sectors contribute less than 20% to reducing the total EACs. This intriguing observation that a small sectoral coverage can save large EACs in the ETS conforms with the Pareto principle that 80% of effects arise from 20% of the causes (also referred to as the 80/20 rule).

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Likewise, our simulation of China's MACs (i.e. the equilibrium carbon price) supports the Pareto principle as well (figure 5). By including the first six sectors (i.e. E&W Prod, OthrServ, Metl, Tran&Stor, Petr&Gas and NonmetlMin), China's MACs can be cut by around 80%, from 802.25, 895.13 and 1001.22 RMB per ton to 341.44, 261.41 and 383.49 RMB per ton at an economic growth rate of 3%, 4% and 5%, respectively. Note that the inter-sectoral trading is not allowed until two or more sectors are engaged. While including OthrSev in the ETS might increase China's MACs compared to the case where only E&W Prod is engaged, it can leave the tertiary industry more room for economic growth and reduce the total EACs considerably. Moreover, we elaborate on the reallocation of the ERQs between sectors through ETS, whereas the technical countermeasures of each sector to realize climate targets (e.g. investment on low-carbon technology, transition of energy mix) are out of this study.

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Sectoral coverage plays a critical role in the distribution of initial ERQs. As shown in figure 6, under the grandfathering scheme, more initial ERQs tend to be assigned to the sectors that have large historical emissions, e.g. E&W Prod, Metl, Tran&Stor. Overall, the wider coverage of sectors can lead to a more even distribution of initial ERQs across sectors. For example, including the first four sectors (i.e. E&W Prod, OthrServ, Metl and Tran&Stor) in the ETS considerably reduces the ERQs share assigned to E&W Prod and Metl from 100% and 29.6% to 60.3% and 26.5%, respectively, and this ERQs distribution remains largely steady when more sectors are engaged.

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Figure 7 shows the impacts of sectoral coverage on the ERQs traded between sectors. In general, the total trading volumes of ERQs between sectors experience a notable increase due to coverage extension that improves the market activation of ETS. Our simulation of three economic growth scenarios demonstrates that, on average, covering all the 29 sectors can increase the total trading volumes of ERQs from 289.78 Mt (when E&W Prod and OthrServ are involved) to 1320.41 Mt. However, the impacts of coverage extension on the trading ERQs vary considerably across sectors. For instance, in line with coverage extension, the trading ERQs of E&W Prod exhibit an N-shaped change while those of Metl exhibit a U-shaped change. Despite the benefits of market activation, the involvement of big ERQ traders runs the risk of market manipulatione when the sectoral coverage extends (Deng and Zhang 2019, Bauer et al 2020, Wang et al 2021). As such, we believe that covering the six sectors (i.e. E&W Prod, OthrServ, Metl, Tran&Stor, Petr&Gas, NonmetlMin) in the ETS can reach a balance between ETS market activation and risks especially at its early stage.

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We further calculate the ratio of sectoral EACs to GDP and explore the impacts of sectoral coverage on the EACs of sectors. Although the sectors involved in the ETS still have varying EACs, the differences between sectors can be reduced as the sectoral coverage extends. Specifically, our simulation result of three economic growth scenarios shows that, on average, E&W Prod and Metl will reduce the ratio of sectoral EACs to GDP from 1.3% to 0.1% and from 14.7% to 6.9% in response to the coverage extension, while the ratio for Petr&Gas increases from −2.7% to −1.7%. In other words, the EACs of sectors tend to converge as the sectoral coverage extends. However, covering the first ten sectors (e.g. E&W Prod, OthrServ, Metl) has enabled a convergence of EACs between sectors. Despite the same observation on cost convergence in all the three economic growth scenarios, we find that higher economic growth will increase the deviations of EACs between sectors, but this impact seems moderate because of the little difference between the three economic growth scenarios (figure 8).

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The discussion over the criteria for sectoral coverage has emerged since the proposal of ETS. In addition to MCSs concerned in this paper, carbon intensity and trade intensity are two commonly adopted criteria focusing on emission reduction potential and carbon leakage, respectively (Wang et al 2017, Qian et al 2018). As said, the former refers to the carbon emissions per unit of GDP, and the latter refers to the ratio of the exports and imports to the total market scale. By estimating the MCSs of ETS-covered sectors under each criterion, we bring together these three criteria into figure 9(a). Note that this comparison is performed at an economic growth rate of 4%, and the detailed sectoral rankings by carbon intensity or trade intensity can be found in tables A1 and A2 in appendix A (available online at stacks.iop.org/ERL/17/045002/mmedia). We show that E&W Prod, Metl, NonmetlProd, and Tran&Stor will be first included in the ETS if sectors are ranked by carbon intensity. However, compared to our study, the potentialcost savings of ETS will remain at lower levels until OthrServ is engaged. While determining the sectoral coverage by trade intensity would allow for soaring cost savings even with fewer ETS-covered sectors (e.g. Clothing, ElenEqp, MetlProd), it leads to excessively high EACs compared to the other two criteria because sectors having less emission reduction potential will be first included in the ETS. In summary, despite the insightful views on sectoral coverage from emission reduction potential and carbon leakage, our COASCO method is more appropriate in the sense that it allows for minimal EACs associated with any sectoral coverages.

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By comparing the MCSs of sectors, our study recommends E&W Prod, OthrServ, Metl, Tran&Stor, Petr&Gas and NonmetlMin to be first included in the ETS. As shown in figure 9(b), these six sectors differ considerably in their MAC curves that basically reflect the overall distribution of the MAC curves for all the 29 sectors. This implies that we should give priority to those sectors that have tremendously diverging MACs if the aim is to embrace the Pareto principle—a remarkable decline in EACs with a relatively small sectoral coverage. In other words, once the typical sectors that have large MCSs are identified, the Pareto principle can arise in terms of sectoral coverage.

We acknowledge that there remain some limitations in the assumptions and methods of our analysis that need to be addressed in future studies. First, the use of macro data (e.g. sectoral carbon emissions, GDP) is likely to trigger an overestimation of the MACs by sector. Even though projecting future carbon price is not what this study mainly concerns, it is still desirable to further conduct a sensitivity analysis of sectoral MAC curves as long as the methodology underlying the MACs simulation becomes more scientifically robust. Second, while we set three scenarios to explore the impacts of economic growth on our empirical results, more socioeconomic factors that go beyond GDP should be considered at the next step. For example, China recently updates its NDCs in terms of carbon intensity reduction. More efforts to understand the impacts of this update on our empirical results would be required. Third, analysis of some highly aggregated sectors (e.g. Agr, OthrServ) in this paper may lead to impractical results. To strengthen the policy relevance of this study, a potential solution might be to present the results at the aggregated and disaggregated levels in keeping with divergent requirements of policy makers and scientists. Fourth, we assume a long time period of carbon market clearing when all the agents are allowed for inter-temporal trading. Although this assumption may breach the reality of China's ETS and raise some uncertainties of the results, many researches have demonstrated that inter-temporal trading can smooth out the demand shocks of CEA and strengthen the resilience of ETS (Fankhauser and Hepburn 2010, Duan et al 2018, Bocklet et al 2019). In practice, recent reform in the ETS of the European Union allows the inter-temporal trading by making use of the market stability reserve (Perino and Willner 2017, Bocklet et al 2019). Nevertheless, further analyses that divide long time period into several intervals can be the next step to examine the differentiated impacts of inter-temporal trading on the various agents. Fifth, in this article, we consider direct emissions of sectors merely and leave aside indirect emissions associated with outsourcing electricity requirements. While the negligence of indirect emissions might substantially increase the costs of electricity production that would be passed on to power consumers ultimately, some research has demonstrated that the double counting that considers both direct and indirect emissions may cause a higher overall cap of ETS, thus leading to a lower emission reduction effect (Xiong et al 2017, Qian et al 2018, Zeng et al 2018). Further analysis related to this issue would therefore be required. Last but not least, this paper focuses exclusively on ETS as a single policy tool for CER. By allocating all the ERQs to the ETS-covered sectors, the remaining sectors are excluded from CER. This may lead to unfairness and inefficiency because unengaged sectors would not reduce their carbon emissions proactively (Mu et al 2018). Mixed policy packages including ETS, carbon tax, renewable energy subsidy, emission standards and sophisticated emission accounting methods like carbon footprinting, remote sensing retrieval, machine learning and big data analysis are expected to respond to this challenge (Duren and Miller 2012, Gouveia and Palma 2019, Liu and Lo 2021, Long et al 2019, Ye et al 2021, Zhao et al 2021).