China’s low-carbon economic growth: an empirical analysis based on the combination of parametric and nonparametric methods

As the world’s most populous developing country and the world’s largest carbon emitter, China has already completed its 2020 Intended National Determined Contribution set out in the Paris Agreement. It achieved this result by adopting a dual-goal strategy of economic growth and reducing carbon emission, that is, low-carbon economic growth. Based on both parametric and nonparametric methods, quantitative and qualitative conclusions about China’s low-carbon economic growth are presented. It is found that since the beginning of this century, China has maintained an annual growth efficiency of 1% in low-carbon total factor productivity (TFP) and low-carbon technological progress rate. The Eastern region has leading advantages in low-carbon TFP, low-carbon technology advancement, low-carbon efficiency, and low-carbon technology revolution. It has the potential to be the first to reach its CO2 turning point. The inefficiency ratio of labor and CO2 is higher at the national level and in the Eastern region, with the two accounting for about seven tenths and eight to nine tenths, respectively. The difference is that at the national level, the input–output inefficiency is similar, and the inefficiency in the Eastern region is more from the input side, about eight tenths. At the present stage, China is still lenient in the implementation of low-carbon environmental regulations. In the future, the adjustment of low-carbon policy should pay attention to regional heterogeneity, focus on reducing labor and CO2 inefficiency, and be more stringent in policy implementation.


Introduction
China is a developing country with the largest population in the world. For many years, the government has been improving its economic growth and industrialization level. While largely eradicating poverty, this effort has had the same unintended consequence as other countries' industrialization -massive carbon emissions, of which China is now the world's largest emitter. Since the beginning of the twenty-first century, after the economy has developed to a certain extent, it has begun to adjust the country's development strategy and introduced a series of policies, from focusing on economic construction to gradually adjusting to the dual goals of pursuing economic growth and mitigating carbon emissions. To achieve carbon turning point in development, it is necessary to improve lowcarbon economic growth efficiency. As we all know, China has fulfilled the 2020 goal in the Paris Agreement ahead of schedule. Recently, President Xi Jinping solemnly announced that China's Intended Nationally Determined Contributions would be increased. More effective policies and measures will be adopted, and carbon dioxide emissions will strive to the turning point in 2030. 1 The 14th Five-Year Plan for The National Economic and Social Development of The People's Republic of China, adopted on March 2021, calls for reducing carbon emission intensity, supports local governments to take the lead in achieving carbon emission turning point, and makes an action plan for achieving carbon emission turning point by 2030. This is the first time China has included a carbon turning point target in its economic and social development plan. At present, Guangdong, Jiangsu, Shanghai, Fujian, Hainan, and other Eastern provinces have proposed to strive to be the first in China to achieve a turning point in carbon emissions. There are gaps in China's regional resource endowments, economic development level, industrial layout, and energy structure. Therefore, the regional distribution of carbon summit in China should be arranged according to the economic basis and carbon emissions.
According to Porter hypothesis, strict environmental regulations can promote green technological innovation in microenterprises (Porter and van der Linde 1995). Technological innovation affects macroeconomic growth through improvements in total factor productivity (TFP). Therefore, low-carbon environmental regulations can promote the progress of low-carbon technologies and ultimately improve the efficiency of low-carbon growth. Heggelund (2021) examines China's climate and energy policies over the past 30 years and believes that the most significant policy change after the Paris Agreement is technological innovation in the power and transportation fields.
As is well known, climate change is a global common problem. Moreover, the climate change problem is challenging to address for developing countries. This is because developing countries need to consider how to achieve carbon emission reduction in a climate change era, promote economic development, and thus eliminate poverty. Developing countries often set dual goals, designing a low-carbon development strategy with coordinated consideration of economic growth and carbon emission reduction at an operational level. From this point of view, there has been little empirical research done on evaluating the degree of low-carbon economic growth in developing countries. This paper analyzes the economic efficiency of low-carbon economic growth in China, incorporating China's actual economic situation. In this regard, our specific research questions include (i) what is the status of China's low-carbon economic growth efficiency; (ii) which region has the potential to be the first to reach the turning point; (iii) what are the sources of inefficiencies that affect low-carbon economic growth; and (iv) how can one evaluate the implementation of existing low-carbon regulation policies?
This paper makes both methodological and empirical contributions. Methodologically, we combine parametric and nonparametric approaches, which allow for both quantitative and qualitative analyses. First, from the perspective of low-carbon economic growth, combined with China's actual situation, this article adds the undesirable output of carbon emissions to the nonparametric DEA, constructing a slack-based global Malmquist-Luenberger (ML) Index that includes dual goals of economic growth and carbon emission reduction. It can meet the requirements of cyclicality and transitivity. Thus, it avoids an infeasible solution problem of linear programming and analyzes the sources of inefficiency. As such, it can better analyze the economic efficiency of low-carbon growth. Second, the parametric SFA method adjusted the undesirable nonparametric output (CO 2 ). The two extreme states of the most stringent and the least strict implementation of China's inter-provincial environmental regulations were simulated. In addition, low-carbon global ML Index (LGML) was calculated separately. Finally, based on the above quantitative analysis, the adjusted results are compared with the actual LGML through nonparametric tests to confirm China's overall regulatory implementation status, thus qualitatively judging the strictness of China's low-carbon environmental regulations. Empirically, we also add to the existing literature by focusing on China's low-carbon economic growth efficiency. From an empirical point of view, there are relatively a few studies on low-carbon economic growth in Asia. Given that China is a major carbon emitter, the empirical results of China's low-carbon economic growth are of interest to its neighboring countries and other countries worldwide.

Literature review
The relevant literature mainly includes climate policy, lowcarbon technology, and input-output efficiency evaluation methods.

Research on climate policy and low-carbon economic development
With the evolution of human, human civilization has experienced many development stages ranging from ancient civilization to industrial economic development and to sustainable development. China's industrial economic development is based on electricity consumption and fossil energy use. However, this caused problems such as resource exhaustion, ecological environment destruction, and nonsustainable economic growth. It even could contribute to global warming and affect ecosystem in an undesirable way. Lowcarbon economy is a new concept generated in response to global warming. It promotes green and low-carbon technological progress and sustainable development. Low-carbon economy can be understood as reducing the consumption of natural resources and pollution; thus, it allows more economic outputs through human capital, resources, and technological progress (Chen and Golley 2014;Li et al. 2015;Chen et al. 2014).
Climate policies such as carbon taxes and carbon emission trading have been introduced in developed countries such as USA, Germany, and Japan (Franks et al. 2021;Li et al. 2015). Finland began to levy carbon tax in 1990. Finland is the earliest country in the world to implement carbon tax. Objects to be taxed include different types of oil, coal, and natural gas (Vehmas 2005). Due to differences in resource endowment, energy, and population structure of countries, various scholars evaluate the effectiveness of climate policies from carbon pricing, carbon emission trading, renewable energy subsidies, etc., with the objective of seeking sustainable development of mankind to cope with climate change (Gugler et al. 2021). Yeh et al. (2016) studied low-carbon fuel standard (LCFS) policies and provided the following three points: first, they compared the economic efficiency of transportation fuel carbon policy, fuel price impact, greenhouse gas emission reduction, and innovation incentive measures; second, they discussed the main regulatory design features of low-carbon fuel carbon emission policies; and third, they introduced the latest status of the implementation of low-carbon fuel carbon emission policies in California, the European Union, British Columbia, and Oregon. Cheng et al. (2016) used the regional Computable General Equilibrium (CGE) model to analyze the impact of Guangdong's energy industry's low-carbon policies on Guangdong's 2020 energy and carbon emission targets and low-carbon policies on Guangdong's 2020 energy and carbon emissions, the costs, and co-benefits of the target. Yang et al. (2018) believe that social carbon cost is an important indicator to measure the social and economic impacts of carbon dioxide emissions, which has been used by the US government to formulate emission reduction policies from 2010 to 2016 and has generated about $1 trillion in policy benefits by 2017.

Research on low-carbon technology
Low-carbon technology is kind of renewable and new energy technologies; it includes climate change mitigation technologies such as solar power, wind power, water power, biomass energy, nonfossil energy generation, and hydrogen and nuclear energy. Low-carbon technologies also include combustion technologies and emission reduction technologies or indirect emission reduction technologies, transportation fuel technologies, and energy efficiency or conservation technologies (Chen et al. 2015). , based on the data of Chinese cement companies, estimated the effect of using carbon pricing to promote the diffusion of low-carbon technology, clarified the diffusion of low-carbon technologies, and provided implications of climate countermeasures for the target sector.  used data collected from steel companies in China to estimate how carbon prices affect the diffusion of low-carbon technologies. They found that the industry is familiar with relevant key energy-saving and low-carbon technologies and has made significant progress in energy conservation. However, its efforts in carbon management still need to be improved. Niu et al. (2016) used data from 1990 to 2013 and found that the emission reduction effects of China's technological progress far outweigh the emission reduction effects of structural changes. The study by Xiu et al. (2019) found that China's technological progress is biased towards energy use and carbon emissions, but this bias is weakening.

Research on input-output efficiency evaluation methods
Since Cobb and Douglas (1928) jointly proposed the production function theory, researchers have begun a quantitative study of the role of productivity in economic growth. At present, there are three main types of quantitative methods for efficiency evaluation of input-output: parametric stochastic frontier production (SFA) models, nonparametric data envelopment analysis (DEA), and semi-parametric Olley and Pakes (OP) and Levinsohn and Petrin (LP).

Parametric SFA method
The stochastic SFA method proposed by Aigner et al. (1977) and Meeusen and van Den Broeck (1977) quantitatively calculate input and output performance and isolate the influence of random error terms. Since then, the stochastic frontier production function method has become one of the mainstream methods for evaluating macroefficiency and microefficiency, and many articles have emerged. The stochastic frontier analysis is used to calculate the technical efficiency in apple production.  used a unique cross-sectional data set covering food production farmers to study the impact of Internet use on the technical efficiency of apple production in China. They found that 52% of the sample farmers use the internet to obtain technical information. On average, the sample farmers' technical efficiency in food production was only 0.6, indicating that there is still room for further improvement. Hasan et al. (2021) estimated total factor productivity growth and its components for the overall manufacturing sector in West Bengal and India from 1980-1981 to 2016-2017 using a stochastic frontier approach. After considering the self-selection bias, if internet users do not use the Internet to obtain technical information, the technical efficiency will be reduced by 30%. Liu et al. (2021) measured industrial land-use efficiency in China and used stochastic frontier analysis to explore its spatial and temporal characteristics and influencing factors. Xie et al. (2021)

Nonparametric DEA method
Since the first data envelopment analysis model -CCR (Charnes et al. 1978) -was proposed, a lot of progress has been made in this line of research, including models such as BCC (Banker et al. 1984), ADD (Farrell 1957), a neighborhood-based approach (Chavas and Kim, 2015), and slack-based measures of efficiency (Tone 2001;Fare and Grosskopf 2010). DEA has gradually become one of the main methods of efficiency or performance evaluation, and many studies have emerged. Since the determinants of carbon emissions may be affected by both temporal and spatial heterogeneity, an extended production-theoretical decomposition analysis (PDA) method based on global meta-frontier data envelopment analysis (DEA) is proposed to solve this issue (Ding et al. 2021).  proposed a cross-regional multi-objective programming model combined with data envelopment analysis to identify a reasonable industrial layout. The representative results selected from different preferred solutions reflect the harmony between economic development and the environment. Yang and Chen (2021) evaluated the energy efficiency of urban sewage treatment plants in China using data envelopment analysis. To assess the performance of the electricity distribution system and sources of in-efficiency since the introduction of deregulation, Lee et al. (2021) employ Simar and Wilson's double-bootstrap data envelopment analysis truncated regression approach. Lu et al. (2021) estimated the national dynamic energy efficiency of countries from 2007 to 2016 using a dynamic data envelopment analysis model. Sekitani and Zhao (2021) incorporate a fitting data technique of medal prediction using ordinary least squares regression in input multiplier restrictions of the conventional DEA model. Based on the super-efficiency data envelopment analysis (DEA), Veiga et al. (2021) proposed and test a process to measure, assess, and address improvements in manufacturing performance by operation strategy. Mwambo et al. (2021) developed emergy-data envelopment analysis approach to determine the resource use efficiency and sustainability.
Both SFA and DEA belong to the frontier production functions, which generally do not require too many behavioral assumptions and can analyze inefficient behaviors in the production process. And they are widely used in the macro and micro input-output efficiency or performance evaluation. The advantage of SFA is that it can separate the influence of uncontrollable factors on input and output, while DEA cannot. DEA can deal with multi-output scenarios more directly, and more DEA methods will be used to analyze green, low-carbon, and sustainable development-related issues. It can be seen that the two methods have their advantages. Over the years, researchers have been trying to combine parametric SFA with nonparametric methods to measure input-output efficiency or performance in a more in-depth and detailed way. By combining the two methods, a study done by Fried et al. (1999) analyzed the influence of external factors on input-output efficiency, the study of Fried et al. (2002) further separates the influence of random noise on input-output performance, and the study of Andor et al. (2019) used a model which combines SFA and DEA methods.
In addition, there are semi-parametric OP method, LP method, and so on. When estimating the production function of telecommunication enterprises, Olley and Pakes (1996) proposed a semi-parametric estimation method to solve the simultaneity problem under the assumption that enterprises can make instantaneous adjustment to input under the impact of productivity. This method came to be known as the OP method. Based on the above OP method, Levinsohn and Petrin (2003) proposed that introducing intermediate inputs can help solve the simultaneity problem. They show how to use the investment to control for correlation between input levels and the unobserved firm-specific productivity process. This method came to be known as the LP method. Ackerberg et al. (2015) further improved the above two methods, called the ACF method. OP and LP and their modified estimation methods are essential for micro input-output efficiency or performance evaluation.
Unlike the frontier production function method, the semiparametric OP and LP methods assume that enterprises can make cost-free immediate adjustments to inputs in the face of productivity shocks. There is no inefficiency in the production process, so they are more often applied in microanalysis. Since the macroproductivity level cannot be understood as the linear sum of the microproductivity, the OP and LP methods are generally not used in the macroresearch. Table 1 below summarizes and compares the major efficiency evaluation approaches.
As shown, it is found that the existing literature covers related issues of climate policy, low-carbon technology, and input-output efficiency evaluation methods.
The rest of this paper includes two sections: "Empirical analysis" and "Conclusions and policy implications" sections. The "Empirical analysis" section consists of two subsections: "Evaluation of low-carbon growth based on a nonparametric method" section and the "The implementation status of low-carbon environmental regulation based on the adjustment of the parametric method" section. In the "Evaluation of low-carbon growth based on a nonparametric method" section, this paper uses LGML to measure the efficiency of China's low-carbon growth. The "Evaluation of low-carbon growth based on a nonparametric method" section can be divided into four sub-subsections: first is the "Slack-based global DEA with carbon emissions" section; second is the "Overall status of low-carbon economic growth efficiency" section; third is the "Screening of region with the potential to first turning point carbon emissions" section; and finally, the "Inefficient sources of low-carbon growth" section. The "The implementation status of lowcarbon environmental regulation based on the adjustment of the parametric method" section is based on the nonparametric calculation of the "Evaluation of low-carbon growth based on a nonparametric method" section. Using a parametric SFA approach, the provincial undesirable output (CO 2 ) data are adjusted to the two extreme states of the most stringent and the most lenient implementation of low-carbon environmental regulation. Then, the nonparametric DEA is used to calculate the low-carbon productivity index under the most strict state (SLGML) and the low-carbon productivity index under the most lenient state (LLGML). Finally, the two LGMLs were compared with the actual LGML through nonparametric tests to determine the current status of China's low-carbon environmental regulations (strict or loose), and qualitatively analyze the overall implementation of China's low-carbon environmental regulations. The "Conclusions and policy implications" section gives research conclusions based on the empirical analysis of the previous one and proposes appropriate suggestions for China's low-carbon growth.

Empirical analysis
The input-output data used in this paper are mainly from China Energy Statistical Yearbook, Provincial Statistical Yearbook, and the National Bureau of Statistics of China website. The capital shall be calculated by the perpetual inventory method. Labor is represented by the number of employees. Carbon emission data are derived from Shan et al.  Table 2 below. The data are from 2000 to 2017 in 30 provinces, totaling 540.

Evaluation of low-carbon growth based on a nonparametric method
The efficiency of low-carbon economic growth can be characterized by the growth of low-carbon TFP and the progress of low-carbon technology. Through comparative analysis, regions with the potential to reach the turning point first can be identified. Further decomposition of low-carbon TFP can analyze the sources of inefficiency of low-carbon growth performance. The following introduces the nonparametric method of evaluating low-carbon economic growth efficiency in this article.

Slack-based global DEA with carbon emissions
A slack-based global ML Index is suitable for the purpose of our study. This is because it can add the undesirable output of carbon emissions, which meets the requirements of circularity and transitivity, avoids the situation that linear programming has no feasible solution, and allows us to analyze the sources of inefficiency.
Assuming that the nonzero input vector set of DMU is According to the method of Pastor and Lovell (2005), the production possibility set of the global DEA can be expressed as where 1, 2, 3… T stands for times; P is the production possibility set; and P G is the global production possibility set.
According to the literature (Fukuyama and Weber 2009;Färe and Grosskopf 2010;Wang and Feng 2015), the directional distance function, including carbon emission, can be expressed as where the directional vector is g = (x, y, b) and CRS indicates constant returns to scale.
Then the global efficiency can be expressed as The global low-carbon ML Index can be expressed as (1) Under constant returns to scale, total factor productivity can be decomposed into two parts: technological efficiency and technological progress (Oh 2010;Fare, Färe, Fèare, Grosskopf, & Lovell, 1994). Let LGEC denote low-carbon global technological efficiency, and LGTC denote low-carbon global technological progress; then, The slacks in the model represent the inefficiency of lowcarbon productivity, in which the inefficiency of input side can be expressed as The inefficiency of desirable output (i.e., GDP) can be expressed as follows: The inefficiency of undesirable output (i.e., CO 2 ) can be expressed as follows: LGML t+1 When the slack is 0, it means that the DMU is the most efficient in the current period and is at the production frontier.

Overall status of low-carbon economic growth efficiency
Using Eqs. (4) and (5), we calculated China's low-carbon total factor productivity index and the degree of low-carbon technological progress. In summary, we found that during the sample period the mean value of LGML in China is 1.01, indicating that China's low-carbon total factor productivity has been increasing since the beginning of the twentyfirst century, with an annual growth rate of 1%. The average LGTCH during the sample period is also 1.01, achieving an average annual positive growth of 1%. This implies that the goal of coordinating economic growth with carbon emission reduction has been well realized. It is also found that the core factor that really drives the improvement of TFP is technological progress. The average annual growth rate of technological progress in the Eastern region is 2%, 1% higher than the national level. This shows that the Eastern region has a relatively high level of low-carbon technological innovation.
Traditionally, the 30 provinces with data are divided into four regions: Eastern, Central, Western, and Northeast. 2 There are obvious gaps in China's regional resource endowments, economic development levels, industrial layouts, and energy structures, so each province's low-carbon total factor productivity is expected to show different efficiency. Figure 1 shows a Radar chart of LGML growth rate among provinces. As shown in Fig. 1, seven provinces with the top 10 growth rates come from the East. It shows that while the Eastern region of China is striving to achieve economic growth, it also achieves better carbon emission reduction and has a high efficiency of low-carbon growth. Figure 2 below is a Radar chart ranking the growth status of lowcarbon technological progress at the provincial level. The chart shows that eight of the top 10 provinces are from the East, similar to the low-carbon TFP situation.
We found that China's low-carbon total factor productivity and low-carbon technological progress showed an average annual growth rate of 1% during the sample period. This indicates that the balance between economic growth and carbon emission mitigation can be achieved with a satisfactory performance. At the same time, we also found that the efficiency of low-carbon economic growth shows obvious regional heterogeneity; only Beijing, Shanghai, Hubei, and Jiangsu have shown that two indices of LGML and LGTC 's growth rate are in equilibrium. The other provinces showed an imbalance (see Fig. 3). In the provincial ranking  of low-carbon total factor productivity and low-carbon technological progress, seven and eight of the top 10 provinces are from the Eastern region. So, does the Eastern region have a big low-carbon economic growth advantage and can be selected as the first region to achieve carbon emission turning point? We investigate these questions below.

Screening of region with the potential to first turning point carbon emissions
The global efficiency shown in Eq. (3) is an intuitive way to compare the input and output effects of different DMUs, and the relative efficiency of DMUs in the same period can be compared. Production possibility frontier promoters refer to the DMUs in T + 1 stage with the highest input-output efficiency and at the same time the technological progress is in a state of improvement. Intuitively, it is the leader of technological innovation that promotes the outward expansion of the production possibility frontier through technological innovation. Therefore, to analyze whether the Eastern region has the potential to be the first to reach the turning point, we need to focus on the global relative efficiency of low-carbon production and the upgrader of the possibility frontier of low-carbon production. Figure 4 below is a regional map of low-carbon overall relative efficiency. As shown in Fig. 3, in terms of low-carbon overall relative efficiency ranking, the Eastern region ranks first, followed by the Northeast, then the Central, and finally the West. The overall low-carbon relative efficiency measured in this paper contains the dual meaning of economic growth and carbon emission reduction. Thus, it reflects a degree of coordination among economic development and carbon reduction in the region's development process. It can be seen that, relatively speaking, the Eastern region has the best coordination between economic development and carbon emission reduction among the four regions.
According to the relevant literature (Cooper et al. 2007;Fare et al. 2008), low-carbon growth production potential frontier promoters (technology innovators) can be selected by the following two indicators: first, the low-carbon global relative efficiency of DMU is at the forefront, so as to ensure that it has reached the optimal relative efficiency, that is: Secondly, the DMU has a technological progress rate of more than 1, so as to ensure that it can expand the front edge of technology outward and promote the progress of technology, namely:   LGML growth rate % LGTC growth rate % Based on the above two indicators, we screened out the provinces as shown in Table 3 below. All the provinces in Table 3 are from the Eastern region. This indicates that the engine of China's low-carbon growth and its low-carbon environmental regulations may have a leading advantage in promoting technological innovation or innovation compensation (Porter and van der Linde 1995).
Based on the analysis of low-carbon total factor productivity growth, low-carbon technology progress, low-carbon overall relative efficiency, and low-carbon technology innovators, the Eastern region is ahead of the other three regions and has the potential to be the first to reach its turning point.

Inefficient sources of low-carbon growth
China has made some progress in its low-carbon growth. It has achieved the 2020 target set in the Paris Agreement and is on track to reach a carbon turning point by 2030. To fulfill this commitment, we need a more detailed analysis of the sources of inefficiency in the current low-carbon growth efficiency. It is expected that identifying the sources of inefficiency allows us to introduce targeted low-carbon regulation policies and promote the improvement of low-carbon performance more efficiently. Using Eqs. (6), (7), and (8), we analyzed the sources of inefficiency. In Fig. 4 below, we compare inefficiency sources at both input and output across the country and the Eastern region. The degree of inefficiency of the input and output sides is almost the same in most cases nationwide. This indicates that to improve the efficiency of national low-carbon growth, we should reduce the inefficiency on the input side and reduce the inefficiency on the output side. Low-carbon regulatory policies need to be implemented bilaterally (focusing on both input and output sides). As shown in Fig. 5, when it comes to the sources of inefficiency, the Eastern region is different from the national average level. The inefficiency of the input side accounts for nearly eight tenths, and the inefficiency of the output side only accounts for about two tenths. It can be seen that the inefficiency of the Eastern region comes from the input side, that is, capital and labor. In the future, in the formulation of low-carbon regulatory policies, while taking both sides into account, we should pay more attention to the schemes focusing on the efficiency of the input side.
Next, we will further subdivide the sources of inefficiency from the perspective of components. Figure 6 below shows the inefficiency of components across the country. As shown in the figure, the country's input-side labor and output-side carbon dioxide inefficiency accounted for a relatively high proportion, with the two accounting for about seven tenths. In contrast, the inefficiency of input-side capital and output-side GDP accounted for a relatively low proportion. It can be seen that China's labor input efficiency is relatively unsatisfactory relative to capital, and there is also a high room for improvement in carbon dioxide emission control. Figure 6 also shows that labor and  CO 2 inefficiency generally experienced an inverted "U"-shaped process from the increase of their proportion to decrease, and the maximum value of CO 2 inefficiency appeared in 2011. It also shows that although the proportion of labor and CO 2 inefficiency is declining, the proportion of these two is still very high, suggesting that we should pay more attention to the efficiency of labor and CO 2 in the future adjustment of low-carbon environmental regulations. Figure 7 below shows the inefficiency of the components in the Eastern region. As shown in Fig. 6, the input-side labor and output-side carbon dioxide inefficiency accounted for a relatively high proportion, similar to the whole country. In contrast, the inefficiency of input-side capital and output-side GDP accounted for a relatively low proportion. The difference is that the output-side GDP has a tiny inefficiency ratio compared with other components in the recent decade. After 2002, the proportion of inefficiency is almost negligible. It indicates that the production of GDP in the Eastern region has reached a very high level of efficiency, far ahead of other regions. In addition, since GDP output is basically associated with the Eastern region with the highest performance in China as far as efficiency is concerned, there will be more room for potential adjustment. This implies that more active policies on carbon emission reduction can be introduced. An emphasis should also be placed on labor and CO 2 in designing a future adjustment process of low-carbon environmental regulations.

The implementation status of low-carbon environmental regulation based on the adjustment of the parametric method
Stringent regulation can produce greater innovation and innovation offsets (Porter and van der Linde 1995). If follows that low-carbon economic growth efficiency needs to depend on strict low-carbon environmental regulations. China's environmental regulations reduce carbon intensity, improve carbon emission efficiency, and enhance the ability of economic transformation through a variety of measures. These measures include reducing energy density, increasing the proportion of tertiary industry, and accelerating the use of new energy. Adjusting energy density is a means, not the ultimate goal of environmental regulation. The ultimate goal is to improve the carbon emission efficiency, and then improve LGML in general, so as to achieve low-carbon economic growth. Since the decision to implement the lowcarbon transition, the Chinese government has carefully analyzed the factors affecting China's carbon emissions, and introduced a series of targeted regulatory policies to reduce carbon emissions. An important part of these policies is the factors affecting carbon emissions, such as adjusting the industrial structure and energy structure.
China is a vast country, and although China's central and local governments have enacted various laws and regulations related to low-carbon development, the rigor and effectiveness of enforcement varies across regions for various reasons. In this regard, investigating the effectiveness of implementing China's low-carbon environmental regulations across regions is of interest. China's current economic development stage and the reality of energy factor endowment make the economy in a state of high-energy and high-carbon emissions. On the side of low-carbon growth is the market failure, and the third hand failed to adjust the economy spontaneously. Therefore, it is necessary for the government to formulate corresponding environmental regulation policies to internalize the cost of carbon reduction and form a better market environment. Since the decision to implement the low-carbon transition, the Chinese government has carefully analyzed the factors affecting China's carbon emissions and introduced a series of targeted regulatory policies to reduce carbon emissions. The important parts of these policies are factors that affect carbon emissions, such as adjusting the industrial structure and energy structure. At present, the government's environmental regulation policy is the leading factor affecting the industrial structure, energy structure, and so on, which are the results of environmental regulation. However, these are not the final goal. The final goal of environmental regulation is still to improve the carbon efficiency, and then improve the carbon efficiency, so as to achieve low-carbon economic growth. This section adjusts the above nonparametric undesirable output (CO 2 ) through the use of a parametric SFA approach to determine the overall implementation of low-carbon environmental regulations. Specifically, we use a parametric SFA approach: (1) to design the stringency of low-carbon environmental regulation implementation as an undesirable output affects production activities, (2) to set the implementation of lowcarbon environmental regulation in China's provinces into the most stringent and the most lenient scenarios, (3) to adjust the level of CO 2 emissions among provinces, (4) to recalculate the LGML, and (5) to compare the results before and after the adjustment. As a result, it reveals the effects of the strictness of China's overall low-carbon environmental regulations on China's economy.
China's energy structure is dominated by fossil fuels, so low-carbon environmental regulations mainly reduce carbon emissions by reducing energy intensity (energy consumption per unit of GDP). Energy intensity can effectively measure the cost of low-carbon environmental regulations in China, also reveal (1) which provinces have adopted specific and effective low-carbon environmental regulation measures and (2) which provinces have adopted low-carbon environmental policies and regulations but failed to be effective in restraining production. From the empirical study of the former subsection, we found that the efficiency of low-carbon economic growth in the Eastern region is different from that of the other three regions. In addition to energy intensity, we include the Eastern region as a dummy variable to adjust CO 2 data and analyze the degree of implementation of lowcarbon environmental regulations.
The slack of CO 2 in the above nonparametric DEA can be expressed as SFA was used to adjust the slack of Eq. (11). Then the regression equation becomes where N is the energy intensity; E is a dummy variable indicating the Eastern region; α, , and are the parameters to be estimated; and = v + , v ∼ N 0, 2 2 , and ∼ N + 0, 2 2 . The estimation results of Eq. (12) are presented in the Appendix (Table 4), where we found a negative relationship between the slack of CO 2 and energy intensity (and the Eastern region dummy variable). This indicates that the Eastern region's economic growth model has been transformed from an old growth model that relies on energy consumption and carbon emissions to a new growth model which incorporates both energy-and CO 2 -saving technologies, thus demonstrating that there is decoupling between energy intensity and carbon emissions; low-carbon technology is contributing to its low-carbon economic growth.
Hypothetical scenario 1: Under the current low-carbon regulatory policy conditions, all provinces are at a state of most lenient implementation. As we all know, when the implementation of low-carbon environmental regulations is relatively lenient, companies will emit more CO 2 following a profit maximization rule. Among them, the provinces with the most lenient implementation have the worst CO 2 emission control efficiency and the largest output slack, which is max ( Ŝ b ) . The gap between the slack in CO 2 output in other provinces and the province with the most lenient implementation is max ( Ŝ b ) − S b . Then, using Eq. (12), the provincial CO 2 under the most lenient state of low-carbon environmental regulation can be adjusted with the following formula: Hypothetical scenario 2: Under the current low-carbon regulatory policy conditions, all provinces are at a state of most stringent implementation. When the implementation of low-carbon environmental regulations is relatively stringent, companies have to reduce CO 2 emissions in the face of emission costs. Among them, the most stringent provinces have the highest CO 2 emission control efficiency and the smallest output slack, which is min ( Ŝ b ) . The gap between the slack in CO 2 output in other provinces and the province with the most stringent enforcement is S b − min ( Ŝ b ) . Then, in the most stringent state of low-carbon environmental regulation, the provincial CO 2 can be adjusted by the following formula: Finally, the adjusted CO 2 is re-substituted into Eq. (4) to calculate the low-carbon global DEA, and the low-carbon productivity index (SLGML) for each province under the strictest state of low-carbon regulation policy implementation and the productivity index (LLGML) for each province under the most lenient state. The actual LGML in China is compared with SLGML and LLGML, respectively, using six nonparametric tests. 3 The SLGML comparison between the actual LGML and the implementation scenario of strict low-carbon environmental regulations shows that all the six nonparametric assumptions significantly reject the null hypothesis of similar distribution, indicating that China's provinces are not a whole at a state of strict implementation of low-carbon environmental regulations. The SLGM comparison between the actual LGML and the implementation scenarios of lenient low-carbon environmental regulations shows that none of the six nonparametric assumptions can significantly reject the null hypothesis of the similar distribution, indicating that the implementation of low-carbon environmental regulations in China's provinces is more likely to be at a relatively lenient state. China has established a series of low-carbon environmental regulation policies, and these were specific to each province. Although there are different degrees of strictness in enforcement, these are turned out to be not rigorous and relatively lenient. Based on this finding, it can be argued that the "stock" policies (the existing policies) should be more rigorously implemented to better leverage their role in promoting low-carbon economic growth efficiency.

Conclusions and policy implications
In general, China has maintained an annual growth efficiency of low-carbon TFP and low-carbon technological progress of 1% at the national level since this century. China has already met its 2020 Intended National Determined Contribution Target in the Paris Agreement and has recently committed on seven public occasions to aim for carbon turning point by 2030. Future low-carbon regulatory policies also need to be adjusted in response to this goal. This paper analyzes low-carbon growth in China based on a combination of parametric and nonparametric approaches, giving both quantitative and qualitative conclusions. In this regard, this study provides a detailed empirical analysis of China's low-carbon economic growth in terms of regional heterogeneity, sources of inefficiency, and stringency of low-carbon environmental regulation enforcement to identify specific policy adjustment directions.
Due to China's vast territory, different factor endowments, and varying levels of development, it is inevitable that carbon emission levels in different regions cannot move together to reach to the turning point. Regional heterogeneity needs to be accounted for. From a regional point of view, the Eastern region is the growth engine of China's economy. We found that the Eastern region has a leading edge in TFP, technological progress, relative efficiency, and technological innovation revolution for low-carbon growth. In addition, this region is identified as the best performing region for low-carbon growth in China, with the potential to take the lead in achieving carbon turning point. Therefore, in the future adjustment process of low-carbon environmental regulation, differentiated policy measures need to be introduced to implement a more aggressive low-carbon economic growth strategy in the Eastern region, encouraging it to maintain its economic growth advantage while being more aggressive in carbon emission reduction. One needs to explore advanced development experiences suitable for the mutual coordination of economic growth and carbon emission reduction, thus providing a leading and exemplary role for China's overall carbon turning point.
The further improvement of China's low-carbon economic growth efficiency depends on finding sources of inefficiency in order to make targeted adjustments. From input and output sides, this study found that, in general, the inefficiency of low-carbon TFP in China comes from both the input and output sides, and the difference between the two is not large, with the input side accounting for a slightly higher proportion. Therefore, regarding policy adjustment, we need to exert both sides to introduce a better plan for reducing the production inefficiency of the input and output sides to improve the overall low-carbon economic growth efficiency. Among them, compared with the overall situation of the whole country, the situation of the Eastern region is unique, and its inefficiency comes from its input side, accounting for about eight tenths of the total inefficiency. In the adjustment of low-carbon regulation, identifying the reasons for the slack is necessary. This enables us to introduce measures to improve and reduce the inefficiency of the input side in the Eastern region to improve the efficiency of the input side and improve its efficiency in low-carbon growth efficiency. The further decomposition of ineffective sources shows that there are inefficiencies of both the input and output in China as a whole. The inefficiency rate of labor in the input side is higher, and the inefficiency rate of CO 2 in the output side is higher, accounting for about seven tenths of the total. The Eastern region also has the highest proportion of inefficiency in labor input and CO 2 emissions, with the two accounting for nearly eight tenths to nine tenths. We also found that after 2003, the slack in output GDP in the East is extremely small, basically negligible, and output GDP is the most efficient among all components. Therefore, in the low-carbon regulatory adjustment process, only the labor and capital on the input side and CO 2 on the output side need to be adjusted.
From parametric and nonparametric simulation analysis, we found that although China has introduced a series of regulation policies to promote low-carbon growth, most of the provinces are still in a relatively lenient state of regulation and implementation. According to Porter hypothesis, strict implementation of the stock policy is a reliable way to promote low-carbon growth. In the future, in terms of low-carbon growth, China should issue corresponding "incremental" policies, also pay more attention to the implementation of policies and strictly enforce the law to better play the role of stock policy in promoting the efficiency of low-carbon growth.
All in all, China's provinces are broadly in a state of less stringent and relatively lenient implementation of low-carbon environmental regulation policies. Still, they have also achieved gratifying results, with an average annual low-carbon growth rate of 1%. Based on our empirical findings reflecting regional heterogeneity, China can encourage its Eastern region to implement more active low-carbon environmental regulations and make it the first to reach its turning point. Our empirical findings on the sources of inefficiency reveal that China's input-output inefficiency accounts for the same proportion, among which labor and CO 2 account for the higher inefficiency. The adjustment of low-carbon policy should be carried out on both sides, focusing on labor and CO 2 . The inefficiency in the Eastern region is mainly from the input side, and labor and CO 2 inefficiency account for a relatively high proportion. Thus, the adjustment of low-carbon policy in the Eastern region should focus on the input side, and pay more attention to labor and CO 2 . Going forward, with targeted adaptation and strict implementation of low-carbon economic growth policies, we can remain optimistic that China can reach its carbon turning point by 2030. Author contribution All authors made substantial contributions to the conception and design of the work and have drafted the work and/or substantively revised it. Specifically, material preparation, data collection, and analysis were performed by Jing Xiu, Xiaoqiang Zang, Zhenggang Piao, Liang Li, and Kwansoo Kim. All authors commented on previous versions of the manuscript and approved the submitted version of the manuscript. All authors agreed to be personally accountable for the author's own contributions and to ensure that questions related to the accuracy or integrity of any part of the work. Data availability Data and materials are available from the authors upon request.