Analysis of the Gravity Movement and Decoupling State of China’s CO 2 Emission Embodied in Fixed Capital Formation

: Investment is an essential engine of economic growth and a major source of China’s CO 2 emission. It is therefore crucial to explore the gravity movement and decoupling state of China’s CO 2 emission embodied in ﬁxed capital formation (FCF). This study aims to estimate China’s CO 2 emissions embodied in various categories of FCF by using input–output tables. The gravity model and Shapley decomposition method are used to explore the gravity movement and regional contributions for China’s CO 2 emissions embodied in FCF. Then, the Tapio decoupling model and logarithmic mean Divisia index (LMDI) method are combined to uncover the decoupling relationship between CO 2 emissions and economic growth embodied in FCF and the corresponding driving factors. The results show that China’s CO 2 emissions embodied in FCF experienced a rapid increase during 2002–2012 and remained almost stable during 2012–2017. The gravity center for CO 2 emissions embodied in FCF moved toward northwest during 2002–2015, with the northwestern region and middle Yellow River region being the main engine regions. The relations between CO 2 emissions and added values embodied in various categories of FCF were weak decoupling during 2002–2017. Investment scale was the major factor inhibiting the decoupling, while embodied energy intensity was the major factor promoting the decoupling. Finally, several policy recommendations are proposed based on these ﬁndings.


Introduction
Climate change has become a global challenge during the last couple of decades. In order to address this issue, energy saving and emission reduction have been promoted globally [1]. Carbon dioxide (CO 2 ) is one of the main greenhouse gases and occupies the largest part of the total greenhouse gas emission [2]. China has surpassed the United States as the world's largest CO 2 emitter since 2006 [3]. According to the International Energy Agency [4], China's CO 2 emissions increased from 3552 million tons (Mt) in 2002 to 9257 Mt in 2017, with an average annual growth rate of 6.6% [4]. China has initiated several mitigation policies and set up its own emission-reduction targets. In particular, China's rapid development focuses on supporting various manufacturing sectors, which is based upon consuming a large amount of fossil fuels. Therefore, it is critical to investigate the relationship between engines of economic growth and corresponding CO 2 emissions so that feasible and effective emission-reduction measures can be proposed.
Investment, consumption, and import-export trade are regarded as three engines of economic growth [5]. China's economic growth has heavily relied on investment for decades. The share of investment in gross domestic production (GDP) in China was maintained at 40-50% over 2002-2017 [6]. After the 2008 financial crisis, the Chinese government implemented special investment policies to rescue the market, such as the Four-Trillion RMB (Chinese currency, 1USD = 6.6 RMB) Investment Plan. Most investment funds were used to build up infrastructure and improve the life quality of the Chinese citizens. As a result, the accumulated capital, including newly formed capital and stock, provided the production capacities of goods and services in various economic sectors [7]. In terms of statistical indicators, the gross capital formation is comprised of fixed capital (excluding those disposed) and inventory change, namely fixed capital formation (FCF) and inventory increase [8]. FCF accounted for the vast majority, while inventory occupied less than 2% in China's gross capital formation over the past years [9,10]. Considering that the negative value of inventory implies the CO 2 emissions caused by capital formation in the previous period, and given the important role of FCF in gross capital formation, this study mainly focuses on the effect of FCF on the CO 2 emissions.
Academically, a number of studies have examined the CO 2 emissions embodied in China's various economic activities from the final demand-based perspective. Several studies pay attention to the trend of embodied CO 2 emission caused by household consumption. For instance, Zhang et al. [11] explored the indirect energy consumption and CO 2 emission from household consumption using the input-output method, and uncovered the influencing factors of the indirect CO 2 emission. Wu et al. [12] calculated the direct and indirect CO 2 emissions from household consumption at the provincial level in China and explored the interprovincial transfer of such CO 2 emissions. Similar studies have been performed by Wang et al. [13], Wiedenhofer et al. [14], and Li et al. [15]. Other studies pay attention to CO 2 emission embodied in international trade. For instance, Mi et al. [16] explored the patterns and driving forces of China's export-embodied CO 2 emission in the New Normal economy. Wu et al. [17] quantified the potential economic and CO 2 emission impacts of export restructuring under various export structure patterns and climate policies scenarios. Similar studies have also been performed by Liu et al. [18], Xu et al. [19], and Huang et al. [20]. In addition, several studies pay attention to CO 2 emission induced by investment, although studies on embodied CO 2 emissions in FCF are less sufficient. For instance, Li et al. [21] calculated China's provincial CO 2 emissions from investment demand and interprovincial transfer of CO 2 emission caused by investment demand. Gao et al. [8] measured China's CO 2 emissions embodied in FCF from 2007 to 2017. However, these existing studies do not investigate the CO 2 emissions driven by various categories of fixed capital formation in China. Syngros et al. [22] investigated the embodied CO 2 emissions in building construction and pointed out that this process constitutes a large part of global CO 2 emissions. In addition to construction, there are several other types of fixed capital formation which are also worth studying. Besides, in order to achieve the national and regional CO 2 emission reduction targets, it is critical to explore the dynamic variation trace of the gravity center of CO 2 emissions embodied in FCF, as well as the decoupling state between CO 2 emissions embodied in FCF and economic growth embodied in FCF.
To fill the above research gaps, this study aims to estimate the CO 2 emissions embodied in various sub-categories of FCF from economic sectors' perspectives in China's 30 provinces. FCF can be divided into tangible capital formation and intangible capital formation. Grouped by composition of funds, Energies 2020, 13, 6655 3 of 20 tangible capital formation can be divided into construction and installation, purchase of equipment and instruments, and others. Grouped by type of construction, tangible capital formation can be divided into new construction, expansion, and reconstruction and technical transformation. These kinds of FCF and the corresponding embodied CO 2 emissions in the years 2002,2007,2012,2015, and 2017 will be accounted by using the input-output method. Then, the gravity theory will be applied to explore the gravity movement of CO 2 emissions embodied in FCF among different Chinese provinces during 2002-2015, and the Shapley decomposition method will be used to uncover regional contributions to the movement of the gravity center of CO 2 emissions embodied in FCF. In addition, the Tapio decoupling method and the logarithmic mean Divisia index (LMDI) method are combined to examine the decoupling state between CO 2 emissions embodied in FCF and economic growth embodied in FCF during 2002-2017, and uncover the driving forces of the decoupling relationship in China. Due to data unavailability, this study has limitations in estimating the CO 2 emissions embodied in FCF in different Chinese provinces in the year 2017, and thus is unable to examine the gravity center of CO 2 emissions embodied in FCF in the year 2017. Another limitation is the estimation of added value embodied in FCF in different provinces. The added values and taxation duty of some large companies are counted in such places where they are headquartered (like Shanghai and Beijing), although they may have business operations in many other provinces. This may have a marginal effect on the data accuracy of added value embodied in FCF in Chinese provinces.
The rest of this paper is structured as follows. Section 2 introduces research methods and data. Section 3 presents research results. Finally, Section 4 draws research conclusions and proposes several policy suggestions.

Gravity Theory and Shapley Decomposition Method
The gravity theory originally derived from the physical concept proposed by Isaac Newton. It was used to describe the mutual attraction between two objects [23]. Then, Jan Tinbergen introduced the gravity theory into economics research. This theory has been widely applied to study the geographic distributions of research objects in many fields, such as population [24], economic growth [25], land utilization [26], immigration [27], energy consumption [28], and CO 2 emission [29].
In this study, we use the gravity theory to explore the changes in the spatiotemporal centers of gravity for CO 2 emissions embodied in FCF in China. The gravity center of CO 2 emission embodied in FCF in year t is calculated as: where (x i , y i ) represents the coordinate of the ith province, xi and yi respectively represent the longitude and latitude of the ith province, M t i represents the attribute value (CO 2 emission embodied in FCF) of the ith province in year t, n represents the total number of provinces, and X t and Y t represent the longitude and latitude of the gravity center for the attribute value in year t, respectively. The longitude and latitude coordinates are determined for each province, along with their corresponding attribute values.
Shapley decomposition method is combined with the gravity theory to uncover regional contributions to the gravity movement of CO 2 emissions embodied in FCF in China. To date, three decomposition methods have been developed for exploring the driving forces of gravity movement, including variance decomposition method, differential decomposition method, and Shapley Energies 2020, 13, 6655 4 of 20 decomposition method. Compared with variance decomposition method and differential decomposition method, Shapley decomposition method can incorporate both direct and indirect regional contributions and is more suitable for the target variable with obvious changes [30]. Moreover, Shapley decomposition method is regarded as a symmetric and perfect decomposition method [31]. Each variable is fully decomposed, and the impacts are completely allocated to each factor with no residuals [32]. Given these advantages, Shapley decomposition method is adopted in this study.
Assume a large region consists of n regions, set K= {1, 2, . . . , k, . . . , n}. The marginal contribution of region k to the gravity movement is defined as: where ∆X and ∆Y represent the changes of longitude and latitude of the gravity center, respectively, and MC k,X and MC k,Y represent the marginal contributions of region k to the changes of longitude and latitude of gravity center, respectively. Considering the order σ= (σ 1 , σ 2 , . . . , σ n ) of all regions and assuming region k at the rth position, then there is σ= (σ 1 , σ 2 , . . . , σ r−1 , σ r = k, . . . , σ n ). Defining the set of regions listed before region k as Pre k (σ)= (σ 1 , σ 2 , . . . , σ r−1 ), then the marginal contribution of region k to the gravity movement is calculated as: To eliminate path dependence, we consider all permutation cases Π(n), and then the Shapley contribution of region k to the gravity movement of CO 2 emissions embodied in FCF in China is calculated as: where CX k and CY k represent the Shapley decomposition results of the contributions of region k to the changes of longitude and latitude of the gravity center, respectively.

Decoupling Decomposition Model
Decoupling theory was introduced to the research field of energy and environment at the beginning of the 2000s [33]. To date, two main decoupling models have been proposed, i.e., the OECD decoupling model and Tapio decoupling model. Compared with the OECD decoupling model, the Tapio decoupling model offers a finer distinction of decoupling states and overcomes the high sensitivity in the choice of benchmark years [34]. Here, we choose the Tapio decoupling model to judge the decoupling state between CO 2 emissions embodied in FCF and added value embodied in FCF. The expression of the Tapio decoupling model is presented as below: where subscript t refers to the target year, θ refers to the decoupling indicator, BC denotes CO 2 emissions embodied in FCF, and EV denotes added value embodied in FCF. According to the value of θ, the decoupling state can be classified into eight categories, as shown in Figure 1.   (9) where subscript t refers to the target year,  refers to the decoupling indicator, BC denotes CO2 emissions embodied in FCF, and EV denotes added value embodied in FCF. According to the value of  , the decoupling state can be classified into eight categories, as shown in Figure 1.

BC 
) into several drivers. The LMDI method has been recognized as the most popular method for the decomposition of energy consumption and environmental emissions. Based on the Kaya identity, CO2 emission embodied in FCF can be disaggregated into the following factors: where r refers to economic sectors, s refers to the total number of economic sectors, BE denotes energy consumption embodied in FCF, I denotes the amount of FCF, T denotes the embodied carbon intensity, S denotes the embodied energy intensity, and X denotes the embodied investment efficiency. According to the rationale of LMDI, the change of CO2 emissions embodied in FCF during the period [ 1 t  , t ] can be decomposed into the following form: The determinants on the right hand of Equation (11) are calculated as follows: Next, we use the LMDI method to decompose the change of CO 2 emissions embodied in FCF (∆BC) into several drivers. The LMDI method has been recognized as the most popular method for the decomposition of energy consumption and environmental emissions. Based on the Kaya identity, CO 2 emission embodied in FCF can be disaggregated into the following factors: where r refers to economic sectors, s refers to the total number of economic sectors, BE denotes energy consumption embodied in FCF, I denotes the amount of FCF, T denotes the embodied carbon intensity, S denotes the embodied energy intensity, and X denotes the embodied investment efficiency. According to the rationale of LMDI, the change of CO 2 emissions embodied in FCF during the period [t − 1, t] can be decomposed into the following form: The determinants on the right hand of Equation (11) are calculated as follows: Energies 2020, 13, 6655 6 of 20 Four effects of the changes of CO 2 emission embodied in FCF are entitled as embodied carbon intensity effect (∆BC T ), embodied energy intensity effect (∆BC S ), embodied investment efficiency effect (∆BC X ), and investment scale effect (∆BC I ).
Then, Equation (9) can be extended into the following decomposition form: Based on Equation (16), there are four decoupling sub-indicators (θ sub = θ T , θ S , θ X , θ I ). Table 1 illustrates the classifications of effects from decoupling sub-indicators [35]. Table 1. Classifications of effects from decoupling sub-indicators.

∆EV
θ sub Effects Negative effect

Data Sources
Based on the data availability, we collect the  [9,10], and the table for 2015 is derived from the Carbon Dioxide Information Analysis Center [37].
For the year 2017, only the Single Region Input-Output (SRIO) table was issued, and thus we collect it from the National Bureau of Statistics of China [38]. The amounts of gross FCF are derived from the input-output tables. As for the amounts of sub-categories of FCF, the data are estimated according to the constitutions of fixed asset investment. The data for CO 2 emission, energy consumption, and added value embodied in FCF are estimated according to the process of MRIO and SRIO models in Gao et al. [8]. The data for FCF and added value embodied in FCF are deflated at 2010 prices.
Due to the data availability, we exclude Tibet, Hong Kong, Macao, and Taiwan in our analysis. According to the report by the Development Research Center of the State Council of China [39], China's 30 provinces could be classified into eight regions, as shown in Table A1. Since sectoral classifications of CO 2 emission inventory vary in MRIO and SRIO tables, we aggregated all the sectors into eight categories according to the Standard of Industrial Classification for National Economic Activities (GB/T 4754-2011) [38], including: Agriculture (ARG), mining and quarrying industry (MQI), manufacturing industry (MFI), electricity, gas, and water production, and supply (EGW), construction (CON), wholesale, retail trade and hotel (WRH), transportation, storage and post (TSP), and other service industries (OTH).  Figure 3 shows sectoral flows of CO2 emissions embodied in FCF from the supply side to the demand side. Among these sectors, ARG refers to the sector of farming, forestry, animal husbandry, and fishery products and services; MQI refers to the sector of coal mining and dressing, petroleum and natural gas extraction, metals mining and dressing, and nonmetal and other minerals mining and dressing; MFI refers to the sector of manufacture of foods, textiles, paper products, chemical materials and products, nonmetal mineral products, metal products, ordinary and special equipment, transportation equipment, electric equipment and machinery, etc.; EGW refers to the sector of production and supply of electric power, gas, steam, and hot water; CON refers to the sector of construction; WRH refers to the sector of wholesale, retail trade, catering services, and hotels; TSP refers to the sector of transportation, storage, post, and telecommunication; OTH refers to the sector  dressing; MFI refers to the sector of manufacture of foods, textiles, paper products, chemical materials and products, nonmetal mineral products, metal products, ordinary and special equipment, transportation equipment, electric equipment and machinery, etc.; EGW refers to the sector of production and supply of electric power, gas, steam, and hot water; CON refers to the sector of construction; WRH refers to the sector of wholesale, retail trade, catering services, and hotels; TSP refers to the sector of transportation, storage, post, and telecommunication; OTH refers to the sector of other service industries. From a supply-side perspective, MFI and EGW were two major sectors generating CO 2 emissions embodied in FCF, which totally occupied above 85 percent of CO 2 emissions embodied in FCF. The CO 2 emission embodied in MFI was larger than that in EGW in 2002, 2007, and 2017, but the situation was opposite in 2012 and 2015. Among other sectors, TSP and MQI generated relatively more CO 2 emission embodied in FCF, both of which accounted for 3-6% of the total CO 2 emissions embodied in FCF. They were followed by CON (1-2%), WRH (0.8-1.5%) and OTH (0.4-1.1%), while ARG had the least portion of CO 2 emissions embodied in FCF (0.3-0.9%). From a demand-side perspective, CON generated the largest part of CO 2 emissions embodied in FCF (60-80%), and such a proportion increased in recent years. The CO 2 emissions embodied in CON were mainly from MFI and EGW. MFI also generated a large amount of CO 2 emissions embodied in FCF (18-30%), which also mainly resulted from MFI and EGW. Among other sectors, OTH generated relatively more CO 2 emissions embodied in FCF, followed by ARG, TSP, and WRH, while EGW had the least amount of CO 2 emission embodied in FCF. Further, Figure 4 shows the compositions of CO2 emissions embodied in FCF in main sectors from both supply-side and demand-side perspectives. MFI and EGW were two major supply-side sectors, while CON and MFI were two major demand-side sectors generating CO2 emissions embodied in FCF. From a supply-side perspective, the CO2 emissions embodied in new construction occupied the largest proportion among three types of FCF grouped by different types of construction Further, Figure 4 shows the compositions of CO 2 emissions embodied in FCF in main sectors from both supply-side and demand-side perspectives. MFI and EGW were two major supply-side sectors, while CON and MFI were two major demand-side sectors generating CO 2 emissions embodied in FCF. From a supply-side perspective, the CO 2 emissions embodied in new construction occupied the largest proportion among three types of FCF grouped by different types of construction in MFI and EGW, which were above 50%, and the proportions gradually increased with time.   Regarding FCF grouped by compositions of funds, the CO 2 emissions embodied in construction and installation accounted for the largest part in the overall CO 2 emissions embodied in FCF, both in supply-side and demand-side sectors. From a supply-side perspective, the CO 2 emissions embodied in construction and installation decreased during 2002-2007, but increased during 2007-2017 in MFI and EGW. In contrast, the CO 2 emissions embodied in purchase of equipment and instruments and CO 2 emissions embodied in others increased during 2002-2007, but decreased during 2007-2017 in MFI and EGW. From a demand-side perspective, the CO 2 emissions embodied in construction and installation firstly decreased and then increased in CON, while they were more volatile in MFI. The CO 2 emissions embodied in the purchase of equipment and instruments firstly increased and then decreased in CON, while they were more volatile in MFI. The CO 2 emissions embodied in others firstly increased, and then decreased in CON and MFI.

Analysis of CO 2 Emission Embodied in FCF
The CO 2 emissions embodied in intangible capital formation were much smaller, and they mainly existed in MFI and EGW from a supply-side perspective, and in OTH from a demand-side perspective. The percentage of the CO 2 emissions embodied in intangible capital formation to the CO 2 emissions embodied in FCF in these sectors increased with time.   Figure 6 further shows regional contributions to the movements of gravity centers for China's CO 2 emissions embodied in FCF. The region that drives the gravity movement along the gravity shift direction is named as an engine region, while the region that prevents the gravity movement along the gravity shift direction is called as an inverse engine region. During the period 2002-2015, the northwestern region and middle Yellow River region were the main engine regions for the gravity shift of CO 2 emissions embodied in FCF. Among other regions, the eastern coast and northern coast had essential effects on promoting the gravity shift to the west, while the eastern coast and southern coast exerted significant positive effects on the northward movement of the gravity center. On the contrary, the southwestern region and middle Yangtze River region were inverse engine regions both along the longitude and latitude.

Analysis of Gravity Movement and Its Drivers
Regarding the gravity movement of CO 2 emissions embodied in intangible capital formation, the southwestern region and southern coast were the main engine regions. Among other regions, the northwestern region had essential effects on promoting the gravity shift to the west, while the northern coast exerted significant positive effects on the southward movement of the gravity center. On the contrary, the northeastern region was the only inverse engine region both along the longitude and latitude.
The roles of eight regions in the movement of the gravity center for CO 2 emissions embodied in construction and installation were similar to those for CO 2 emissions embodied in FCF. With regard to CO 2 emissions embodied in the purchase of equipment and instruments, the northwestern region and southern coast were the top engine regions driving the gravity shift. The eastern coast and southwestern regions were small engines driving the gravity shift to the west. The Middle Yellow River and eastern coast had much smaller effects on the northward movement of the gravity center. On the contrary, the middle Yangtze River was the inverse engine region both along the longitude and latitude. With regard to CO 2 emissions embodied in others, the Middle Yellow River and the northwestern coast were the top engine regions driving the gravity shift. The eastern coast and northeastern region also had important effects on promoting the gravity shift to the west, while the eastern coast and southwestern region exerted significant positive effects on the northward movement of the gravity center. On the contrary, the southern coast was the only inverse engine region both along the longitude and latitude.
As for the gravity movement of CO 2 emissions embodied in new construction, the northwestern region was the major engine region. Among other regions, the eastern coast had essential effects on promoting the gravity shift to the west, while the middle Yellow River and the southern coast exerted significant positive effects on the northward movement of the gravity center. On the contrary, the northern coast and southwestern region were the main inverse engine regions both along the longitude and latitude. With regard to CO 2 emissions embodied in expansion, the southern coast was the top engine region driving the gravity shift. Besides, the eastern coast, and northwestern and southwestern regions, were essential engines driving the gravity shift to the east. With regard to CO 2 emissions embodied in reconstruction and technical transformation, the northwestern region was the top engine region driving the gravity shift. The southwestern region also had important effects on promoting the gravity shift to the east, while the southern coast exerted significant positive effects on Regarding the gravity movement of CO2 emissions embodied in intangible capital formation, the southwestern region and southern coast were the main engine regions. Among other regions, the northwestern region had essential effects on promoting the gravity shift to the west, while the northern   The CO 2 emissions embodied in new construction had a weak decoupling relation with the embodied added value during all the periods. Investment scale was the major factor inhibiting the decoupling in all periods. Embodied carbon intensity was the key driver for promoting the decoupling during 2002-2007, while embodied energy intensity was the leading driver for promoting the decoupling during 2007-2012, 2012-2017, and the entire period. The effect of embodied investment efficiency on the decoupling was small. This is mainly because that, over the period of 2002-2017, the FCF of new construction increased by 8 times, which was the main promotion factor of embodied CO 2 emissions. In contrast, embodied energy intensity decreased by 50%, which was the main driver for the embodied CO 2 emissions reduction. Embodied carbon intensity and embodied investment efficiency had small variations, with a 10.7% reduction and 10.3% increase, respectively.

Analysis of Decoupling State and Its Drivers
The relation between CO 2 emission and added value embodied in expansion was weak decoupling

Conclusions and Policy Implications
With increasing attention on global climate change, it is crucial for China to reducing CO 2 emissions embodied in various economic activities. Although investment is an essential engine of economic growth, there is a lack of a detailed analysis on the CO 2 emissions embodied in various categories of FCF in China, as well as the related driving forces. Using the input-output tables for 2002, 2007, 2012, 2015m and 2017, this study estimates the CO 2 emissions embodied in various categories of FCF in China. The gravity model and the Shapley decomposition method are employed to explore the gravity movement of CO 2 emissions embodied in various categories of FCF among China's provinces, as well as regional contributions to the gravity movement. Finally, we combine the Tapio decoupling model and the LMDI method to investigate the decoupling relationship between CO 2 emissions embodied in FCF and the economic growth embodied in FCF and uncover the driving factors.
The results show that China's CO 2 emissions embodied in FCF had a rapid increase during 2002-2012 and remained almost flat during 2012-2017. The amount of CO 2 emissions embodied in intangible capital formation was much smaller than that embodied in tangible capital formation. On one hand, the CO 2 emissions embodied in construction and installation played a dominant role among tangible capital formation grouped by compositions of funds. On the other hand, the CO 2 emissions embodied in new construction played a dominant role among tangible capital formation grouped by types of construction. MFI and EGW were two major supply-side sectors generating more CO 2 emissions embodied in FCF, while CON and MFI were two major demand-side sectors.
Over 2002-2015, the gravity center for CO 2 emission embodied in FCF moved toward the northwest, with the northwestern region and middle Yellow River region being the main engine regions. The situations of CO 2 emissions embodied in construction and installation, new construction, and others were similar with that of CO 2 emissions embodied in FCF. The gravity center for CO 2 emissions embodied in intangible capital formation moved toward the southwest, with the southwestern region and southern coast being the main engine regions. The gravity center for CO 2 emissions embodied in the purchase of equipment and instruments moved toward the northwest, with the northwestern region and southern coast being the main engine regions. The gravity center for CO 2 emissions embodied in expansion moved toward the southeast, with the southern coast being the main engine region. The gravity center for CO 2 emissions embodied in reconstruction and technical transformation moved toward the southeast, with the northwestern region being the main engine region.
Over 2002-2017, the relations between CO 2 emissions and added value embodied in various categories of FCF were a weak decoupling. Investment scale was the major factor inhibiting the decoupling, while embodied energy intensity was the major factor promoting the decoupling during all sub-periods and the whole period. In contrast, embodied carbon intensity and embodied investment efficiency had marginal effects on the decoupling.
Several policy recommendations are proposed based upon the key findings of this study. First, the Chinese government should pay more attention on reducing its CO 2 emissions embodied in construction and installation, as well as new construction. As investment scale was the major driver for the increase of CO 2 emissions in these two projects, China should strengthen the macro-control on fixed capital formation so as to effectively restrain the excessively rapid growth of investment, especially for sectors of MFI, EGW, and CON. Embodied energy intensity largely promoted the decoupling of embodied CO 2 emission, but the effects from embodied carbon intensity and embodied investment efficiency were too small. Therefore, there is a great potential to optimize the carbon intensity and investment efficiency. Coal-type consumption has been playing the dominant role in the production activities due to China's energy endowment [40]. It is therefore necessary to develop low carbon energy sources, such as natural gas, hydropower, solar power, wind power, and geothermal power. For example, the local governments in Yellow River region could promote the application of photovoltaic solar panels on the roofs of local residential buildings due to the abundant solar energy resources in Yellow River region. Financial subsidies should be provided to those residents who have financial pressure to afford solar panels. The marketization reform of energy pricing mechanisms is also one effective incentive measure to optimize energy structure. [41,42]. Besides, the Chinese government should improve the investment efficiency and adjust the capital ratio of investment projects to introduce more environmentally friendly enterprises. All the enterprises should be encouraged to increase their green investment so that cleaner production technologies and energy efficient equipment could be introduced and applied.
Moreover, the northwestern region and middle Yellow River region were two major drivers of the gravity movement of CO 2 emissions embodied in FCF. The Chinese government should focus on reducing the CO 2 emissions in these two regions by optimizing the investment distribution among regions, as well as reducing energy intensity, optimizing energy structure, and improving investment efficiency. With regard to projects of construction and installation as well as new construction, their embodied CO 2 emissions in the northwestern region and middle Yellow River region should also be the focus of emission reduction. With regard to the purchase of equipment and instruments, the embodied CO 2 emissions in the northwestern region and southern coast should be the focus of emission reduction. With regard to project of expansion, the embodied CO 2 emission in the southern coast should be the focus of emission reduction. With regard to project of reconstruction and technical transformation, the embodied CO 2 emission in the northwestern region should be the focus of emission reduction. It is necessary for the local governments in the above regions to adopt effective measures and regulations to mitigate the CO 2 emissions embodied in corresponding FCF categories.
In general, this study can help decision-makers identify the key regions affecting the gravity movement of CO 2 emissions embodied in FCF, as well as the key factors affecting the decoupling effect between CO 2 emissions and added value embodied in FCF. Although this study focuses on China, policy implications from this study can provide valuable insights for other emerging countries facing