Introduction

Over the past decade, China’s rapid economic development has consumed a large amount of fossil energy and exacerbated carbon emissions1. As China enters the new phase of the “Fifteenth Five-Year Plan,” it faces challenges of slowing GDP growth and urgent carbon reduction2, To address the environmental issues caused by an extensive economic model and fulfill its commitment to peak carbon emissions by 20303, the Chinese government has proposed a high-quality economic development strategy, which in turn has given rise to the concept of “new-quality productivity.” The aim of new-quality productivity is to break away from traditional economic growth methods and productivity development paths. It can be viewed as an intensive model that relies on technological advancements and the improvement of labor quality to promote economic growth4. The core of new-quality productivity is to enhance total factor productivity (TFP), which is closely related to high-quality economic development5,6. Under this intensive growth model, GDP growth no longer relies on resource-intensive expansion but is achieved through efficiency improvements, while technological advancements can indirectly reduce carbon emissions.

Economic growth is closely related to carbon emissions7. Under the extensive growth model, the country achieves high GDP growth while being accompanied by significant carbon emissions8, However, improving technological levels can effectively reduce emissions and promote green economic development9. However, under high economic growth, improving technological levels can effectively reduce emissions and promote green economic development10. It is necessary to formulate optimal emission reduction pathways tailored to the specific needs of different industries.

Currently, many studies on China’s sectoral carbon emission pathways focus primarily on the peak years and peak values for various industries under the constraints of China’s carbon peaking and carbon neutrality goals. For instance, the power, transportation, construction, and industrial sectors are projected to peak before 2030, in 2030, in 2036, and in 2025, respectively, with peak values of 4.5 Gt, 7.04–8.41 Gt, 2.99 Gt, and 8 Gt, respectively11,12,13,14. However, fewer studies simulate the carbon emission pathways of different industries from the perspective of carbon emission efficiency. It is necessary to allocate quotas based on optimal carbon emission efficiency for each sector at the national level to develop effective carbon emission pathways.

Fairness and efficiency are the guiding principles in current carbon quota allocation. At the national and provincial levels, distribution often prioritizes fairness, emphasizing common but differentiated responsibilities. In contrast, the efficiency principle focuses on production efficiency and emission reduction potential, with lower fairness requirements in inter-industry distribution compared to provincial or municipal allocations. The literature on efficiency allocation methods primarily focuses on the Data Envelopment Analysis (DEA) model. The zero-sum gains data envelopment analysis (ZSG-DEA) is an optimization method that maximizes resource allocation efficiency under a fixed total quota. Many studies now use the ZSG-DEA model for the allocation of carbon quotas at the national, provincial, regional, or industry level. For example, research has been conducted on quota allocation at the national level for Chinese provinces15,16,17 and among EU member states18. At the industry level, studies have allocated quotas top-down from industries such as power19, transportation15, steel20, and construction21 to provinces, though fewer studies have focused on specific industries at the national level. Environmental pollution caused by energy consumption is increasingly prominent. It is urgent and necessary to clarify emission reduction targets and share carbon reduction responsibilities, considering industry-specific differences. Each industry bears common but differentiated responsibilities22. allocated China’s 2030 carbon quotas to 41 industries using a combination of entropy and input-output methods, showing that power and heat production and distribution accounted for the largest share23. allocated carbon quotas to 39 industrial sectors in China for 2020, with 6 sectors receiving over 500 million tons of carbon quotas, accounting for 91.77% of total industrial emissions.

Based on the above research, we found that most studies focus on the overall carbon emission allocation from the national level to provinces or from specific industries to provinces or cities, with few studies emphasizing the allocation from China to specific industries. This is a necessary step before allocating from an industry to a province. Secondly, most existing methods for initial carbon quota allocation rely on entropy methods, grey forecasting, or simple backward deduction, without considering that carbon emission outcomes are dynamically changing with market mechanism fluctuations. Finally, in reallocation, the decision-making units selected in the DEA model often fail to adequately reflect fairness. To address the gaps in previous studies, this paper first develops a dynamic recursive CGE model with 2020 as the base year and various emission reduction targets as constraints, simulating the production and emission processes of each industry. Next, it simulates scenarios for both extensive and intensive economic growth models, obtaining the initial carbon quota values for each industry for the peak year 2029 and post-peak year 2035, along with data on energy consumption, added value, and employment in each industry. Finally, the ZSG-DEA model incorporates industry employment as a fairness factor. Industry employment reflects the average number of individuals engaged in production and daily activities within each sector. Each person should have reasonable employment needs throughout the process of carbon peaking and carbon neutrality. After calculating the carbon emission efficiency for each sector, the changes in carbon quotas after each iteration are observed to determine the optimal carbon quota for each industry.

The contributions of this paper are as follows: (1) It considers the adjustment of carbon emission quotas across 33 subsectors in China, providing a reference for policymakers to adjust the intensity of industry-level carbon reduction efforts at the national level and for the potential inclusion of more sectors into China’s carbon market in the future. (2) It simulates the impact of different economic growth models on quota distribution. (3) Compared to existing literature, this paper’s initial carbon quota allocation method incorporates market factors and includes the employed population as a fairness indicator in the evaluation of carbon efficiency.

The remainder of this paper is organized as follows: Sect. “Modeling methods” introduces the mechanisms of the CGE model and the ZSG-DEA model. Section “Scenario and parameter settings” details the research scenarios and data sources. Section “Results and Discussion” presents the simulation results. Finally, Sect. “Conclusion” provides the conclusions and policy recommendations.

Modeling methods

To better simulate the two types of economic growth, this paper represents extensive economic growth by directly increasing the investment growth rate (investment-driven) and represents intensive economic growth by enhancing new quality productivity (innovation-driven). The ultimate goal of both economic growth models is to promote macroeconomic GDP development.

The development of new quality productivity arises from improvements in labor, labor resources, and other transformations, and it is a bottom-up process that gradually develops within industries. In contrast, increasing investment, as a primary means of stimulating investment growth, involves a top-down approach that increases industry investment from a macro perspective, driving technological progress and the renewal of production resources. Both approaches can contribute to an increase in gross national product, but they differ in their focus on stimulating industries.

Figure 1 illustrates the framework of this study. The CGE model is used to simulate two types of economic growth and calculate the initial carbon quotas for each industry. Industry carbon emissions, added value, energy consumption, and employment figures are then input into the ZSG-DEA model. Finally, through iterative processes, the optimal economic growth scenarios are determined, along with adjustments to the carbon quotas for different industry sectors at various time points under these scenarios.

Fig. 1
figure 1

Research framework diagram.

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CGE model

The neoclassical economic growth theory is one of the core economic theories underlying the CGE model. From the neoclassical economics perspective, increases in labor and capital accumulation play a decisive role in short-term economic growth, while technological progress is the main driver of economic growth in the long run. Thus, employing this theory allows for a realistic simulation of both increased investment and technological advancement in the economic growth process.

The CGE model consists of four main modules: production, income, expenditure, and markets.

Production module

The structure of the production module is shown in Fig. 2. It consists of four layers. The first layer’s output is synthesized using the Leontief production function, incorporating resources, composite inputs, greenhouse gases, and intermediate inputs. The second layer synthesizes composite inputs using a CES function, which mainly includes value-added inputs and energy inputs, while intermediate inputs comprise domestic and imported products. The third layer’s value-added inputs are synthesized using a CES function, incorporating capital, labor, and land, while energy inputs include electricity and fossil fuels. The fourth layer consists of fossil fuels, which are synthesized using a CES function from coal, oil products, natural gas, and greenhouse gas emissions.

Fig. 2
figure 2

Production function structure of the basic sectors.

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Income module

The income module primarily represents the cyclical flow of funds among the government, households, and businesses. Households receive income from businesses through their labor and transfer payments from the government. Government revenue mainly comes from taxes, including personal income taxes from households and corporate taxes. Business income consists of government transfer payments and capital income.

Expenditure module

Households earn income from businesses, which is used for taxes, personal savings, and consumption. In the model, utility maximization for consumers is achieved through product prices and production functions. Business expenditures are distributed to households and the government through transfer payments and taxes, respectively. The government, in turn, establishes a cycle from households to businesses through transfer payments.

Market module

The market module connects the production and expenditure modules. It uses the CET function to divide total output into export goods and domestic sales goods in varying proportions. The Armington assumption is then employed to use a CES function to combine imported goods and local goods into a composite good for demand allocation. This process represents the price changes of goods as they move from the production module to the expenditure module in the market. In the model, all functions are formulated with the objective of individual producers maximizing their own profits.

Model sectoral division

Table 1 below shows the sectoral classification in the CGE model, which includes 7 energy sectors and 26 production sectors. The classification is based on the 153 sectors from the “2020 China Non-Competitive Input-Output Table,” with sector merging and splitting resulting in the 33 sectors used in this model.

To align with the major industry categories used in existing research, the numbers in the table represent: 1 for agriculture, 2–25 for industry, 26 for construction, 27–32 for transportation, and 33 for services.

Table 1 Model sectoral division.
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Simulation of economic growth modes

The dynamic CGE model uses a one-year step length for recursive calculations, with each year’s process based on the changes from the previous year. The total investment for the next period is jointly calculated based on capital stock, new investments, labor, efficiency parameters, etc. Among these, new investment and total factor productivity are key components of total investment, and any change in either factor will lead to an adjustment in total investment.

The parameters for economic growth models differ across the simulated scenarios. Changes in exogenous parameters set by each scenario lead to variations in total investment and value-added across industries, ultimately resulting in different industry carbon emission efficiencies in each scenario.

ZSG-DEA model

This paper employs the ZSG-DEA model with undesirable outputs to study carbon quota allocation under different economic growth patterns. Industry carbon emissions are treated as the sole undesirable input variable. Given the significant variation in industry scale, the ZSG-DEA model with variable returns to scale is selected. The output variables include industry energy consumption, industry value-added, and industry employment, as these three indicators are strongly manageable with respect to carbon emissions24.

Figure 3 illustrates the process of iteratively adjusting quotas among the four decision units in the model, with all decision units ultimately achieving the highest efficiency on the same frontier. The formula for the ZSG-DEA model is:

$$\left\{ {\begin{array}{*{20}l} {min\varphi _{0} } \hfill \\ {\mathop \sum \limits_{{i = 1}}^{N} \lambda _{i} y_{{ij}} \ge y_{{oj}} ,j = 1,2,3, \ldots ,M} \hfill \\ {\mathop \sum \limits_{{i = 1}}^{N} \lambda _{i} x_{{ik}} \left[ {1 + \frac{{x_{{ok}} \left( {1 - \varphi _{0} } \right)}}{{\mathop \sum \nolimits_{{i \ne 0}} x_{{ik}} }}} \right] \le \varphi _{0} x_{{ok}} ,k = 1,2,3, \ldots ,R} \hfill \\ {\mathop \sum \limits_{{i = 1}}^{N} \lambda _{i} = 1,i = 1,2,3, \ldots ,N} \hfill \\ {\lambda _{i} \ge 0,i = 1,2,3, \ldots ,N} \hfill \\ \end{array} } \right.$$
(1)

In the equation: \(\:x\) represents the carbon emission quota for each industry; \(\:y\) denotes the values of industry energy consumption, industry value-added, and industry employment; \(\:N\) is the number of \(\:DMU\)s (Decision Making Units); \(\:R\) represents the number of input factors; \(\:M\) represents the number of output factors; \(\:{\phi\:}_{0}\) is the relative efficiency of \(\:{DMU}_{0}\), indicating the highest relative efficiency value; \(\:{\lambda\:}_{i}\) is the proportion of the \(\:i\)th \(\:DMU\), which represents the carbon emission proportion of each industry; \(\:{x}_{ik}\) is the input quantity of \(\:{DMU}_{i}\); \(\:{x}_{ok}\) is the input quantity of \(\:{DUM}_{0}\); and\(\:{y}_{oj}\) is the output quantity of \(\:{DMU}_{0}\).

Fig. 3
figure 3

Adjustment path of decision-making units in ZSG-DEA.

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In the ZSG-DEA model, if the relative efficiency \(\:{\phi\:}_{0}\) of \(\:{DMU}_{0}\) has excessive input, the excess part will be proportionally allocated to other DMUs according to the ratio \(\left[ {\frac{{x_{{ik}} }}{{\sum\nolimits_{{i \ne 0}} {x_{{ik}} } }}.\left( {1 - \varphi _{0} } \right)} \right]\). The amount \(\:{DMU}_{i}\) receives from \(\:{DMU}_{0}\) is \(\:\left[\frac{{x}_{ik}}{{\sum\:}_{i\ne\:0}{x}_{ik}}(1-{\phi\:}_{0}){x}_{ok}\right]\). Since all DMUs simultaneously reduce their inputs proportionally, after this reallocation, the redistributed amount of input \(\:k\) to \(\:{DMU}_{i}\) is:

$$\:{x}_{ik}=\left[\frac{{x}_{ik}}{\sum\:_{i\ne\:0}{x}_{ik}}\times\:{x}_{ok}\left(1-{\phi\:}_{o}\right)\right]-{x}_{ik}\left(1-{\phi\:}_{i}\right),\:i=\text{1,2},3,\ldots,N$$
(2)

Through multiple iterations, input variables are allocated rationally, ultimately achieving DEA effectiveness and arriving at the most efficient allocation scheme.

Scenario and parameter settings

Scenario settings

Total factor productivity (TFP) growth is not directly driven by capital and labor, but rather attributed to technological progress and other non-capital and non-labor factors of production, effectively removing the growth contributed by capital and labor. This differs from economic development driven by direct increases in investment. According to the “Suggestions of the Central Committee of the Communist Party of China on Formulating the 14th Five-Year Plan for National Economic and Social Development and Long-Range Objectives Through the Year 2035,” the goal is to achieve “per capita GDP reaching the level of moderately developed countries by 2035.” To achieve this vision, in March 2021, the Fourth Session of the 13th National People’s Congress proposed in the “14th Five-Year Plan for National Economic and Social Development and the 2035 Vision Goals” that the basic approach is for “labor productivity growth to exceed GDP growth.”

When labor productivity growth exceeds GDP growth, it indicates healthy economic development. The following Eq. (3) can be derived:

$$\:\frac{d{\theta\:}^{T}}{d{\Omega\:}}=\frac{{n}^{L}}{(1+{\Omega\:})}>0$$
(3)

Where:

\(\:{\theta\:}^{T}\) represents China’s macro TFP that changes over time;

\(\:\varOmega\:\) is the GDP growth rate;

\(\:{n}^{L}\) is the proportion of income from labor factor growth relative to the overall increase in economic value.

With the goal of achieving a per capita GDP at the level of middle-income developed countries by 2035, China aims to increase its per capita GDP from $12,600 in 2020 to $35,000–45,000 by 2035. This requires an average annual growth rate of approximately 5.4–7.2% from 2020 to 2035. Consequently, using Eq. (6), the average annual growth rate of China’s macroeconomic TFP is calculated to be greater than 3.4–4.6%.

Table 2 shows the model scenarios:

Baseline Scenario (BASE): TFP and investment growth rates meet current development needs and follow this trend through 2035.

New Quality Productivity Improvement Scenario (PRD): From 2021 to 2035, TFP increases by 1%, 1.5%, and 2% relative to the baseline scenario in three five-year periods, with total carbon emissions set according to the baseline scenario.

Increased Investment Scenario (INV): From 2021 to 2035, investment growth rates increase by 1%, 1.5%, and 2% in three five-year periods, with total carbon emissions consistent with the baseline scenario.

High-Quality Development Scenario (HQD): Combines the TFP and investment growth rates of PRD and INV scenarios, with total carbon emissions matching the baseline scenario.

Table 2 Scenario settings.
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Parameter settings

SAM table

The data input into the model is the Social Accounting Matrix (SAM), which is the data foundation for the CGE model.

The SAM describes the supply and usage flows of various accounts in the national economic accounting system and their balancing relationships in matrix form. In the SAM, rows represent income, and columns represent expenditure. According to the balance of receipts and payments, the sum of each row equals the sum of each column.

In the CGE model, each sector is represented by value quantities, while actual energy consumption and carbon emissions require corresponding physical quantities. By using the ratio of physical quantities in the energy balance table to value quantities in the input-output table, various energy prices are determined, and physical quantities for future periods are calculated.

Socio-economic parameter settings

The Socio-economic Settings settings are shown in the table. According to the United Nations “2022 World Population Prospects” report, and combined with related studies and the results of the Seventh National Census, the elderly population in China is expected to peak in the middle of the 21st century. Before 2030, China’s population is projected to peak and begin to decline. To achieve the goal of doubling per capita GDP by 2035 compared to 2020, if the GDP growth rate during the “14th Five-Year Plan” is 5% and the proportion of non-fossil energy is 23% or higher, China can reach its peak before 2030.

This study takes into account the current national fertility policies and economic development. The study focuses on three five-year periods: the “14th Five-Year Plan,” the “15th Five-Year Plan,” and the “16th Five-Year Plan.”

Table 3 Socio-economic parameter settings.
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Electricity generation growth rate settings

According to the “14th Five-Year Plan for Modern Energy System” and the “14th Five-Year Plan for Renewable Energy Development,” by 2025, non-fossil energy consumption is expected to account for around 20%.The annual electricity generation from renewable energy is projected to reach 3.3 trillion kWh, with wind and solar power generation expected to double. Additionally, hydropower installed capacity is targeted to reach 380 million kW, nuclear power capacity to 7,000 MW, and by 2025, a cumulative 200 million kW of coal-fired units will be upgraded, with oil-fired power gradually phased out. In this study, the growth rate of installed capacity is set according to the scenarios outlined in Table 4.

Table 4 Model power generation growth rate settings for 2020–2035.
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Employment by industry

The employment numbers for each industry (Table 5) are primarily sourced from the “China Population and Employment Statistics Yearbook” (referred to as the Employment Yearbook) and the “China Industrial Statistics Yearbook” (referred to as the Industrial Yearbook). The total employment figures by industry from the Employment Yearbook are allocated to specific sub-sectors based on the employment shares provided in the Industrial Yearbook.

Table 5 Employment by industry.
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Results and discussion

Carbon emissions

To better study the allocation of carbon quotas at the industry level under different economic growth models, this paper employs the control variable method, setting each scenario with the same total carbon emissions. To reflect the “plateau period” of carbon emissions in actual production and the necessity of reaching the peak earlier, this study uses 2029 and 2035 as the time nodes, rather than China’s pledged year (2030). Figure 4 shows the total carbon emissions across all industries for each scenario, with emissions peaking in 2029 at 11,729 million tons, and reaching 9,165 million tons by 2035.

Fig. 4
figure 4

Total carbon emissions by scenario.

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Initial carbon efficiency and initial carbon quotas by industry

This study uses the ZSG-DEA model, with Tables 6 and 7 showing the initial carbon emission efficiency and initial carbon quotas for 33 industries in China for 2029 and 2035, respectively. Only the agriculture, chemicals, steel, electronic equipment, water supply, and service industries achieved an initial efficiency of 1, while all other industries had efficiencies below 0.7.

For 2029, the average initial efficiencies for the four scenarios are 0.5011, 0.5132, 0.4943, and 0.4365, respectively. Under the same carbon constraints, technological progress increases the input-output ratio of industries, leading to reduced carbon emissions from greater inputs and thus improving carbon emission efficiency. Increasing investment only raises the amount of capital input without improving the input-output ratio, which results in a further decrease in carbon emission efficiency. The HQD scenario, which increases the investment growth rate over the PRD scenario while maintaining the same carbon constraints, will further reduce carbon emission efficiency due to the technological development constraints.

Table 6 Initial carbon emission efficiency and initial carbon quotas by scenario for 2029.
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By 2035, the average efficiencies for the four scenarios are 0.4556, 0.4919, 0.4874, and 0.4018, respectively. Both the technological progress and increased investment scenarios show improved carbon emission efficiency relative to the baseline scenario, while only the HQD scenario experiences a decrease.

Table 7 Initial carbon emission efficiency and initial carbon quotas by scenario for 2035.
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Figure 5 shows the changes in initial carbon emission efficiency relative to the baseline scenario for different scenarios in 2029 and 2035. The PRD scenario has higher efficiency compared to the INV and HQD scenarios, indicating that technological progress can maintain stable initial carbon efficiency before and after the peak when altering the economic growth model from the baseline scenario.

Different industries not only show significant differences in initial carbon emission efficiency at the same time point but also exhibit variations in efficiency over different time points within the same industry. Figure 6 illustrates the carbon emission pathways of various industries from 2020 to 2035 under the baseline scenario. The peak years for electricity, steel, construction, transportation, and cement are 2029, 2023, 2027, 2035, and 2023, respectively. By comparing the carbon emission efficiency before and after the peak, it is observed that the efficiency after the peak is lower than before and at the peak. After reaching the peak, under tighter carbon constraints, it is necessary to further increase employment, value added, and energy consumption to reduce emissions.

Fig. 5
figure 5

Changes in Industry Initial Efficiency Relative to Baseline Scenario for 2029 and 2035 by Scenario.

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Fig. 6
figure 6

Sectoral Carbon Emission Pathways for the Baseline Scenario (2020–2035).

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Carbon allocation efficiency at peak and post-peak

To make carbon quotas for each industry more effective, initial carbon quotas for each industry are adjusted through iteration. Iteration involves scaling the allocations based on the ZSG-DEA model until each industry’s efficiency value approaches 1, while keeping the total carbon emission quota constant throughout the iteration process. Figure 7 shows the changes in carbon emission efficiency for various industries during the iteration process under the baseline scenario. In the first iteration, 6 industries had efficiency values above 0.99. By the third iteration, 4 industries still had efficiencies below 0.99. After four iterations, the carbon quota distribution for all 33 industries reached an optimal state.

Fig. 7
figure 7

Changes in Industry Carbon Emission Efficiency during the Iterative Process of the Baseline Scenario for 2029 and 2035.

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During the iteration process, the total amount remains unchanged for all industries, with adjustments made between industries to increase or decrease quotas. As shown in Fig. 8, in the peak year 2029, the chemical industry (CRP), steel industry (I_S), and service industry (CCS) received the largest amount of quotas. In the four scenarios, the total quotas received by these three industries were 1325.47 million tons, 1093.38 million tons, 1037.68 million tons, and 1654.38 million tons, respectively. Because these three industries have an initial carbon efficiency of 1, they are prioritized for receiving quotas during the optimization iteration process. Conversely, industries with lower initial carbon efficiency, such as electricity (ELE), coal (coa), and coke (cok), experienced the largest reductions in quotas, with reductions of 944.17 million tons, 796.65 million tons, 745.85 million tons, and 975.11 million tons in the four scenarios, respectively.

Fig. 8
figure 8

Changes in Sectoral Quotas by Scenario for 2029 and 2035.

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Changes in carbon reduction costs and economic impacts

In this study, the other three scenarios all promote economic growth compared to the baseline scenario. As shown in Fig. 9, the GDP values for PRD, INV, and HQD scenarios are higher than the baseline scenario, with HQD being the highest, followed by PRD, and INV being the lowest. Since all four scenarios are subject to the same total carbon emission limit, they incur different additional carbon reduction costs under various economic stimulus scenarios. In Fig. 9, the carbon reduction costs for scenarios other than the baseline follow a similar ranking to GDP, with higher GDP growth leading to increased carbon reduction costs.

The baseline scenario, under the current model, not only has a smaller GDP but also higher carbon emission costs compared to other scenarios, thus highlighting the need to change the current economic growth model. Although the investment-increase scenario has the lowest carbon reduction cost and a higher GDP value, it is challenging to maintain a high GDP growth rate through increased investment alone, given China’s current development model. The PRD scenario addresses the shortcomings of both, offering a higher GDP growth rate with lower carbon reduction costs, and its approach—technological improvement—is easier to achieve compared to the INV and HQD scenarios.

Fig. 9
figure 9

GDP and Carbon Reduction Costs by Scenario.

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Optimal carbon quota allocation

This study performed four iterations to obtain the final distribution results of carbon emission quotas for each industry under the four scenarios for 2029 and 2035. Figures 10 and 11 show the distribution for the PRD scenario at these two time points. The industries receiving the most carbon quotas are Electricity (ELE), Chemicals (CRP), Coal (COA), and Cement (CMT). At both distribution time points, the combined carbon quotas for these four industries account for 54.03% and 51.36% of the total carbon quotas, respectively. Under the constrained total carbon quotas, the quotas for these high-carbon industries are reduced.

Fig. 10
figure 10

Changes in PRD Industry Quota Ratios and Sectoral Carbon Quota Allocation for the Peak Year 2029.

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From the perspective of major industry categories, the carbon quotas for Industry, Transportation, and Construction have decreased. Specifically, the total carbon quota for Industry in 2035 is reduced by 2,387.35 million tons compared to 2029. In contrast, the carbon quotas for Services and Agriculture have increased, with Services gaining an additional 6.48 million tons. Industry will be the primary sector experiencing a reduction in carbon quotas in the future. The sharp decrease in quotas indicates that, post-peak, the input-output ratio in this sector is lower than in other industries, necessitating industrial upgrades or technological improvements to achieve higher economic returns with lower carbon emissions.

Fig. 11
figure 11

Changes in PRD Industry Quota Ratios and Sectoral Carbon Quota Allocation for 2035 Post-Peak.

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Conclusion

This study constructs a dynamic CGE model for China to simulate two economic growth scenarios and determine the initial carbon allocation quotas for China in 2029 and 2035. By using fairness and efficiency indicators, the ZSG-DEA model was employed to allocate carbon quotas among 33 Chinese industries at the highest carbon efficiency levels. The results indicate that:

  1. (1)

    Among the detailed industries in China, only agriculture, chemicals, steel, electronics, water supply, and services achieved an initial efficiency of 1, while other industries had efficiencies below 0.7. The PRD scenario exhibited higher initial efficiencies in 2029 and 2035 compared to other scenarios, indicating that this scenario represents the optimal carbon emission input-output model for various industries. To ensure optimal initial efficiency under the same carbon emissions across different scenarios, at least one of the industry value-added, energy consumption, or employment needs to be greater compared to the values in other scenarios.

  2. (2)

    The allocation of carbon quotas for electricity, chemicals, coal, and cement has decreased, while the quotas for agriculture and services have increased. In 2029 and 2035, the carbon quotas allocated to electricity, chemicals, coal, and cement decreased, but these four industries collectively accounted for over 50% of China’s total carbon emission quotas. Over time, the allocation of quotas to major industries such as industry, construction, and transportation has significantly decreased, whereas the quotas for agriculture and services have increased. Under the tightened carbon emission limits, high-carbon industries face a conflict between increasing energy demand and emission reduction targets.

  3. (3)

    Under the same total carbon emission limit, the scenario focusing on technological progress is superior to the other scenarios in terms of comprehensively enhancing GDP and avoiding additional carbon reduction costs.

Limitations and future directions

This study constructed four scenarios using the CGE model to allocate initial carbon quotas, and then employed the ZSG-DEA model with multiple iterations to derive the carbon quota distribution scheme that maximizes carbon emission efficiency for each industry. It found that the scenario emphasizing technological progress achieves the optimal initial carbon emission efficiency. However, there are still limitations in this study:

First, the technological progress scenario in the initial carbon quota allocation assumes that all industries experience the same proportional increase in total factor productivity, without accounting for the varying difficulties in technological upgrades across industries. Additionally, the investment growth rate and total factor productivity in Eq. (6) consider only the national-level relationship, without differentiating between industries. These issues arise from the differences among industries.

Second, using the employment population of an industry as a “fairness” indicator in the ZSG-DEA model’s decision-making units does not fully represent the carbon emissions of an industry. The model aims for higher employment with lower carbon emissions. To better reflect “fairness,” it is necessary to consider the total number of people in the households supported by the employed individuals. Using the number of households as an indicator would be more reasonable.

Finally, the adjustment of industry carbon quotas for optimal carbon efficiency only considers value-added, energy consumption, and employment. In practice, determining carbon quotas is more complex. Future research should not only incorporate additional indicators but also address industry heterogeneity. It would be beneficial to first allocate quotas among broad industry categories before refining the allocation to sub-sectors within these categories. At the same time, attention should also be given to the correlation between selected indicators and the issue of weak disposability of undesirable outputs.