Research on spatial and temporal differences of carbon emissions and influencing factors in eight economic regions of China based on LMDI model

With the gradual increase of international willingness to reach the carbon peak and carbon neutrality, this paper decomposes the influencing factors of China’s carbon emission changes from 2008 to 2019 using the Logarithmic Mean Divisia Index model (LMDI), and analyzes the contribution amount and rate of each influencing factor. The results found that: for the whole country, the cumulative growth of carbon emissions during the study period is about 416,484.47 (104 tons), among which the economic growth effect plays a major role in promoting, with a cumulative contribution rate of 284.16%; The increase in regulation intensity and the optimization of industrial structure, however, suppress carbon emissions well, with a cumulative contribution rate of about – 199.21% and − 64.75%, respectively, during the study period. For economic regions, the cumulative influence direction of each driver is the same as that of the whole country, while the population size effect in the northeast economic region and the regulation input effect in the eastern coastal economic region act in the opposite direction from other economic regions, and the carbon emission reduction direction of the energy intensity effect varies from one economic region to another. Accordingly, this paper proposes policy recommendations to enhance regulatory intensity, optimize industrial and energy consumption structure, implement localized emission reduction strategies, and promote synergistic emission reduction in economic zones.

www.nature.com/scientificreports/ With China's increasing willingness to achieve a carbon peak by 2030, scholars at home and abroad have conducted a lot of research on China's carbon emissions, focusing on the feasibility extrapolation and realization path of China's 3060 plan, carbon emission efficiency analysis 10 , carbon emission peak projection 11 , carbon emission impact factor decomposition 12,13 , carbon emission research and emission reduction strategies by industry and region 13 . For carbon emissions research, scholars have mainly used the DEA model, IPAT model, Kaya constant equation, LMDI decomposition method, environmental Kuznets curve, etc. 14 . Compared with the extended Kaya constant equation, the LMDI decomposition model can decompose each influence factor into data without residual terms 15 , which has the advantages of strong interpretability, unique results, easy-to-use and mature technology, and is often applied to carbon The relevant studies have revealed that the factors influencing the level of carbon emissions in China are mainly economic growth level, energy consumption, technological progress, urbanization rate, and industrial structure 16,17 . However, little research has been done on the impact of environmental regulation, which is an institutional arrangement that uses new concepts, systems and institutions to restrain the behavior of the public to conserve resources and protect the environment, and plays a very important role in the process of environmental governance 18 . Therefore, this paper also uses the LMDI model as a basis when mining the factors influencing carbon emissions, and innovatively introduces environmental regulation indicators for driving analysis. To remedy the shortcomings of previous studies, we aim to identify carbon emission drivers more scientifically and precisely, and to provide a scientific basis for the formulation of sensible badlands policies to reduce CO 2 emissions and promote low-carbon green development.
This study also fills a research gap by extending environmental regulation to a decomposition analysis of the main drivers of CO 2 emissions in terms of China and economic regions. The rest of the study is organized as follows: Chapter 2 literature review, a brief compilation, and analysis method. Chapter 3 describes the methodology and data sources. Chapter 4 provides an analysis and discussion of the results; Chapter 5 concludes and policy recommendations.

Literature review
In the 1990s, Grossman and Panayotou proposed the Environmental Kuznets Curve (EKC) 19,20 . The theory suggests that in the early stages of economic development, the level of environmental pollution increases with the growth of per capita income, and when economic growth exceeds a critical level, environmental pollution decreases, i.e. there is an inverted "U" shaped relationship between economic growth and environmental pollution 21 . Since then, scholars have argued for the EKC in terms of national policies 22 , value chains 23 , and participating actors 24 . However, most of these studies treat the relationship between economic growth and environmental pollution as a "black box" 25 , and only use economic output data and environmental data to explore the degree of mutual influence between the two, without explaining the specific mechanisms of influence between specific economic factors such as industrial structure and technology level and environmental factors such as resource inputs and environmental pollution emissions. The mechanism of interaction between specific economic factors such as industrial structure and technology level and environmental factors such as resource inputs and environmental pollution emissions is not explained. However, it is more important to dissect the "black box" to explore the mechanisms behind the EKC 26 . In this context, factor decomposition models have been introduced into the study of the EKC. Due to their ability to break down indicators into components and assess the contribution of each component 27 , factor decomposition models are widely used to explore the mechanisms underlying environmental issues such as energy consumption and carbon emissions 28 .
There are two main types of common carbon emission factor decomposition models, Structural Decomposition Analysis (SDA) and Index Decomposition Analysis (IDA). Since researchers first used it to analyze industrial electricity consumption in the early 1980s, Index Decomposition Analysis (IDA) has been widely used in energy and emissions studies 29 . In 2001, the LMDI-I (Additive Model) and LMDI-II (Multiplication model) were formally introduced 30 . Logarithmic Mean Divisia Index (LMDI) has become the most popular IDA method because of its residual-free, complete decomposition, ease of operation, and applicability 31 . The Japanese scholar Yoichi Kaya, who linked CO 2 emissions to economic, energy and demographic factors, proposed the Kaya identity to examine the degree of influence of each driver on CO 2 emissions 32,33 . Since then, scholars have continued to expand on the Kaya-LMDI. Xue Wang included the industrial structure and investment efficiency in the Kaya-LMDI 34 , while Xiaojun Ma expanded the Kaya-LMDI to include six drivers: carbon emission factor, energy structure, energy intensity, industrial structure, economic output and population size 35 . In recent years, Python-LMDI developed based on Python tools has appeared, which simplifies the calculation process of LMDI, and extends the range of applications of LMDI with its advantages of convenience, speed, and efficiency 36 . Table 1 lists the research results for the last 5 years. Current research trends indicate that LMDI is expected to continue to play an important role in future research on our carbon emissions.
As a vast country, China faces significant differences in terms of energy endowments, natural conditions and regional economic development 45 . Therefore, it is necessary to differentiate the analysis according to the regional characteristics. Throughout the existing regional studies of China's carbon emissions, there is a large body of literature on on the division of many regions according to the geographical location in the east-central-west region or the traditional seven geographic regions 46 . While this classification is easy to apply, it cannot be directly used to find targeted strategies, as the same measures do not necessarily apply to provinces in close geographical proximity 47 . And, as China's economy enters a phase of high-quality development, the internal differences within the traditional regional analysis are coming to the fore. Literature is emerging that uses urban agglomerations 14 www.nature.com/scientificreports/ industrial restructuring directions and "carbon peak and carbon neutrality goals" action plans for each region according to the characteristics of carbon emissions in different regions 50 .
In summary, scholars have conducted in-depth studies on the factors that influence China's regional carbon emissions, but it is rare to see environmental regulation factors included in the LMDI decomposition models when decomposing carbon emission factors; and there is also little literature on comparative analysis of China's eight economic regions when analyzing regional carbon emissions. Therefore, based on the existing studies, this paper uses data from 30 Chinese provinces and cities from 2008 to 2019, establishes an LMDI-I additive decomposition model based on the Kaya identity, analyses the factors influencing carbon emissions including environmental regulation factors, explores the spatial and temporal differences in the factors influencing carbon emissions between the whole country and the eight economic regions, and proposes a reasonable evolutionary path for low-carbon development based on the LMDI decomposition results, so as to provide lessons for the low-carbon development of other regions. The analysis will also provide a reasonable path for low-carbon development and lessons for other regions to learn.

Data and methods
Data source. This paper takes the eight comprehensive economic zones delineated in the report "Strategies and Policies for Coordinated Regional Development" by the Development Research Center of the State Council as the research object and conducts a study on carbon emissions in China as a whole and in the eight economic zones based on relevant data from 2008 to 2019 (Tibet, Hong Kong, Macao, and Taiwan are not included in the sample set due to missing data), and the specific regional scope is shown in Table 2.
The data for measurement analysis were mainly obtained from IPCC (2006) Table 3.
Model building. In this paper, we decompose the factors influencing CO 2 emissions based on the modified equation of Kaya's 32,51 identity as: Energy Carbon Emission Intensity effect (ECEI), Regulatory input effect(RIE), Regulatory strength effect(RSE), Industry Structure Effect(ISE), Economic growth effect(EGE) and Population size effect(PSE) 11,52 , show as Eqs. (1) and (2): Table 1. Literature on the decomposition of China's regional carbon emission factors in the past 5 years. www.nature.com/scientificreports/ where, C is the total CO 2 emissions, data from CSMAR, refer to IPCC (2006). E is the total energy consumption, I is the amount of investment completed in industrial pollution control for the year, V is the value added of secondary industry, GDP is the gross regional product for the year, and P is the year-end resident population. In summary, Eq. (2) can be derived: Additive and decomposition theory based on LMDI model 29  The contribution of each factor change to the change in CO 2 emissions is calculated as Eq. (4): The contribution of changes in each factor to the change in CO 2 emissions is expressed as Eq. (5): X represents different drivers of CO 2 emissions.

Results analysis
National level analysis. Based on the time series data of China from 2008 to 2019, the effects of energy intensity, regulatory inputs, regulatory intensity, industrial structure, economic growth, and population size on carbon emissions in China are empirically analyzed by combining the decomposition results of the Python-LMDI model. The combined effect of the influencing factors over the study period is shown in Fig. 1 (Drawn through ArcGIS 10.7: https:// www. esri. com/ zh-cn/ arcgis/ produ cts/ arcgis-deskt op/ overv iew and PowerPoint 365: https:// www. micro soft. com/ zh-cn/ micro soft-365/ power point).
(1)  Except for 2015, the impact curve of the environmental regulation input effect on carbon emission change generally shows an inverted "U" shape, with the critical value point or "inflection point" in 2013. On the contrary, except for 2015, the impact curve of environmental regulation intensity effect on carbon emission change has an overall "U" shape, but the critical point or "inflection point" is also in 2013. The possible reasons for this are that in February 2013, the Chinese Ministry of Environmental Protection issued the "12th Five-Year Plan for the Development of National Environmental Protection Standards", which revised environmental standards and increased environmental investment; in September of the same year, the State Council issued the "Notice on the Action Plan for the Prevention and Control of Air Pollution", referred to as the "Ten Measures for Air Pollution". In September of the same year, the State Council issued the Circular on the Action Plan for the Prevention and Control of Atmospheric Pollution, referred to as the "Ten Atmospheric Articles", which set new goals for air pollution prevention and control by proposing many specific measures to increase comprehensive treatment and reduce emissions of multiple pollutants. The introduction of two consecutive environmental regulation policies has raised awareness and increased investment in environmental protection in all regions of the country, so that the contribution of the environmental protection input effect to carbon emissions reached a maximum value of -80,339.23.
As an inverse indicator, the contribution of the environmental regulation input effect decreases rapidly and the contribution of the environmental regulation intensity effect increases to a maximum value of 685,203.82. 2015, the closing year of the 12th Five-Year Plan, is the year in which the new plan will begin, which will change the original situation. This may be the reason for the outliers in 2015 (Fig. 2).
The level of economic growth is the third most important factor influencing changes in carbon emissions. As the level of the economy improves, GDP per capita increases, and industry and urbanization continue to grow, the demand for carbon emissions will also increase, so economic growth is a positive effect. The contribution value of the economic growth level effect keeps increasing between 2009 and 2011 and then decreases, presumably because since the 2008 economic crisis, there has been an increase in infrastructure construction in places to accelerate the economic recovery, which promotes the growth of carbon emissions. After that, the government continued to increase environmental protection and put the environment and economic development side by side, and the incremental carbon emissions caused by economic growth decreased. The fourth major factor driving changes in carbon emissions is industrial structure. The contribution of industrial structure is negative all year round, although, in 2010 and 2011, the contribution becomes positive, 16,380.02 (10 4 tons) and 3271.06 (10 4 tons) respectively, in general, the effect of industrial structure limits the increase of carbon emissions. This also reflects that the third technological revolution, represented by information technology and new materials www.nature.com/scientificreports/ technologies, has impacted traditional industries, and China's industrial structure, which is dominated by secondary industries, is changing. As a negative indicator, the contribution of energy intensity fluctuated significantly between 2010-2011 and 2012-2013, first from positive to negative and then from negative to positive. The reason for this fluctuation may be that during the 12th Five-Year Plan period, China's energy structure has been optimized, clean energy has been developed rapidly, and the competition and substitution between clean energy represented by hydro, wind, and solar energy and traditional energy represented by coal have become increasingly intense, and the traditional energy structure has been adjusted, thus the contribution of energy intensity effect is unstable. The driving effect of population size on changes in carbon emission has been stable over time and has been small during 2008 to 2019 period, with a contribution rate ranging from 6 to 80% over time, and is the factor with the least impact on carbon emissions. The likely cause is the long-standing family planning policy and the sense of birth control people have developed. Although the population expansion policy was promulgated in 2015, the liberalization of the fertility policy did not trigger a fertility climax, and China's fertility level and the birth population did not get the imagined increase, and China's population did not get a large-scale expansion but tended to be stable in the long term, and it is reasonable to believe that the population size will not increase significantly in the next few years, so the population size has the smallest and most stable impact on carbon emissions.  www.nature.com/scientificreports/ Regional level analysis. Regional carbon emissions patterns.  (Table 4).
In summary, total carbon dioxide emissions are increasing in all eight economic regions, and the situation for carbon reduction remains relatively severe. The NEEZ is the smallest in both total volume and magnitude. This is because the NEEZ, as a heavy equipment and equipment manufacturing base, has benefited from the rapid transformation of its industrial structure in recent years and has played a very significant role in carbon reduction. NWEZ, MYtREZ and MYeREZ are in the top three in terms of volume and rate of change. Among them, the two economic zones in the middle reaches of the MYeREZ and the MYtREZ, as China's main grain base and heavy industrial production base, both have the difficulties of low openness to the outside world and the difficult task of industrial restructuring, which in turn leads to an increase in carbon emissions. The NWEZ ranks behind all regions in terms of economic size as a percentage of the country and the NWEZ is also the largest region in China and the fastest growing region in terms of economic growth. It is a key breakthrough direction for the future to use the Belt and Road strategy and modern industrial means to transform the ecological environment in northwest China so that the population can grow rapidly and bring about rapid economic growth.
Regional differentiation analysis. In terms of influencing factors, for all integrated economic zones, the level of economic growth is an important indicator of the contribution to the increase in carbon emissions, with a contribution rate above 100%. Slightly different from the findings of Ding et al. 50 is that the extended analysis of the impact factor indicators reveals that the effect of economic growth level is most prominent in the southwest, with a contribution rate of 726.66%. At the same time, the clean energy resource of the SWEZ endowment and policy support enable it to grow at a high rate while maintaining low incremental carbon emissions due to interactions. The NWEZ, which is also a concentration of energy resources in China, has the smallest contribution of economic growth level to carbon emissions (117.47%). Because most of the provinces in the NWEZ are in the process of moving from agriculture to industrialization, the level of industrialization and urbanization development is low and the growth rate of the economy is slow compared to the rest of the economic zone 53 .
Human life needs to consume energy, and the energy consumption is an important source of carbon dioxide emissions, and more population means more carbon dioxide emissions, and studies have shown that there is a positive relationship between world population size and carbon emissions 54 ; however, on the contrary, the population size effect, except for the Northeast Economic Zone (-45.92%), it can positively contribute to carbon emissions in other economic zones, which may be related to the Northeast Economic Zone with a single industrial structure and weak manufacturing industry, leading to a large labor force loss and negative population size growth 55 , which is consistent with the results shown in the 2019 National Economic and Social Development Statistical Bulletin of Liaoning, Jilin, and Heilongjiang provinces.
The results show that the regulatory input effect can promote the increase of carbon emissions in all economic zones (except the ECEZ), with the largest contribution to the SWEZ (412.44%) and the smallest contribution to the NCEZ (18.75%); the ECEZ, on the other hand, because of the early start of modernization and high intensity of R&D investment, has played a significant role in carbon emissions in recent years with the development of scientific and technological innovation, industrial integration and industrial carbon emission efficiency The continuous improvement of carbon emission has played an obvious inhibiting effect on carbon emission, which is consistent with the findings of Mi et al. 56 .
Among the factors that inhibit the increase of carbon emissions, the changes in the regulation intensity effect and the industrial structure effect during the study period are able to inhibit all the integrated economic zones. As an inverse indicator of the regulatory input, the carbon reduction effect of the regulatory intensity effect in the SWEZ is the largest (− 859.63%), which is 30 times larger than that of the smallest ECEZ (− 28.63%), while the carbon reduction effect of the rest of the economic zones ranges from − 113.90% (NWEZ) to − 511.24% (NEEZ). In terms of industrial structure effects, the NEEZ is the most inhibited (− 208.97%), the two economic zones with the weakest inhibitory effect on carbon emission increase are the MYtREZ (− 27.80%) and the NWEZ (− 30.13%). Overall, stronger regulation and restructuring of industry remain the main ways to reduce carbon emissions. In comparison, the implementation of environmental regulation also indirectly promotes the adjustment of regional industrial structure 57,58 , which in turn suppresses carbon emissions, so the role of environmental regulation is stronger than adjusting industrial structure.
The direction of the energy intensity effect on carbon emission reduction is not consistent across economic regions. There is an inhibitory effect on the SWEZ, NCEZ, ECEZ, and SCEZ, with the strongest inhibitory effect in the SWEZ(-120.27%), which is due to the large proportion of clean energy in the SWEZ as the inland energy base 59 , especially the full utilization of hydro energy and natural gas, which significantly promotes regional carbon emission reduction. In contrast, the energy intensity effect promotes carbon emissions in the remaining four economic regions, but to an overall weaker extent, with the middle reaches of the MYeREZ receiving the strongest promotion effect (18.07%) and the middle reaches of the MYtREZ receiving the weakest promotion effect (9.05%); although China vigorously implements energy conservation and emission reduction policies,  60 , the weak prior foundation, and the slow transformation of energy structures have led to energy intensity a certain rebound occurred (Table 5).
Overall, there are differences in the effects of various factors on carbon emissions in different economic zones, especially after the introduction of environmental regulation factors, which significantly change the results compared to previous studies. For different economic zones, the economic growth level effect is the most important factor that inhibits carbon emission reduction, and the regulatory input effect also plays a strong inhibiting role with the increasing energy consumption (except for the ECEZ); the industrial structure effects and the regulatory intensity effects can significantly promote carbon emission reduction; the population size effect and the energy intensity effect have relatively weak effects on carbon emission reduction, and the energy intensity effect has obvious regional The effects of population size and energy intensity on carbon emission reduction are relatively weak, and the energy intensity effect has obvious regional differences (Fig. 3).

Conclusions and recommendations
Conclusions. Based     www.nature.com/scientificreports/ in 2015 may be that it is the closing year of the 12th Five-Year Plan. Meanwhile, the economic growth effect has been declining since the financial crisis. But with the third technological revolution and the development of clean energy industries, the industrial and energy structures have been continuously adjusted and optimized, and the potential for energy saving and emission reduction from the industrial structures and energy carbon emission intensity effect has been increasing. The population size effect, as a negative carbon emission reduction effect, is stable over the long term and has the smallest driving effect, which is closely related to the stable rate of population growth in China. At the economic zone level, the Mid-Yellow River Economic Zone had the largest cumulative increase in carbon emissions during the study period, and the Northwest Economic Zone far exceeds the other economic zones in terms of the magnitude of the change. The Northeast Economic Zone, on the other hand, came bottom in both the amount of carbon emissions growth and the magnitude of the change. For all integrated economic zones, the economic growth effect is the main contributor to the increase in carbon emissions, but there is some regional variation in the contribution to the change in carbon emissions. Cumulatively over the study period, the level of economic growth effect is most pronounced in the Southwest and lowest in the Northwest Economic Zone. The regulatory input effect contributes to the increase in carbon emissions in all economic zones (except the Eastern Coastal Economic Zone), with the largest contribution to the Southwestern and the smallest contribution to the Southwestern Coastal Economic Zone. The population size effect positively contributes to carbon emissions in all economic regions except the Northeast Economic Zone. Among the factors that suppress the increase in carbon emissions, regulatory strength effects and changes in industrial structure effects over the study period inhibit all integrated economic regions. However, the energy carbon emission intensity effect is not consistent across economic regions, with the strongest inhibitory effect in the Southwest and the strongest promoting effect in the middle reaches of the Mid-Yellow River Economic Zone.
Recommendations. Based on the above findings, this paper further proposes the following targeted carbon reduction policy recommendations: (1) The effect of economic growth is the main factor that promotes the increase of regional carbon emissions.
Therefore, it is necessary to change the mode of economic growth, pay attention to the impact of population migration and labor loss, pay attention to the cultivation of talents and the research and development of new technologies, support the development of a digital economy, and develop high-tech industry, vigorously develop a low-carbon economy. (2) Pay attention to the different impacts of various factors on regional carbon emissions. Select key policy measures to reduce carbon emissions based on regional characteristics. It is necessary to pay attention to the role of environmental regulation and implement environmental protection standards and environmental protection laws and regulations. It is also necessary to optimize the industrial structure and energy consumption structure according to the regional industrial characteristics and resource endowments, and promote the upgrading of industrial structure and green development. For example, for old industrial areas, such as the Northeast Economic Zone, adjusting the industrial structure and appropriately shifting the industrial center of gravity will help to rejuvenate new opportunities. (3) When formulating energy conservation and emission reduction policies, the synergistic emission reduction effect between regions should also be considered. It is necessary to make timely adjustments based on the contribution of carbon emission reduction driving factors in each economic zone and also to coordinate with China's "14th Five-Year Plan" for a unified layout. At the same time, we must pay close attention to the promotion of "carbon trading" as a market-based emission reduction method to avoid fragmentation.
As mentioned in the full paper, while this paper innovatively considers the impact of environmental regulation on carbon emissions, it does not include all the influencing factors. In future studies, we can try to consider more influential factors, such as digital technology, digital ubiquity, etc. Financial benefits, etc., to obtain more comprehensive results (Supplementary Information).

Data availability
The datasets generated and analyzed during the current study are not publicly available, but are available from the corresponding author on reasonable request.