How to Set the Proper CO 2 Reduction Targets for the Provincial Building Sector of China?

: The improvement of the energy and carbon emission e ﬃ ciency of activities in the building sector is the key to China’s realization of the Paris Agreement. We can explore e ﬀ ective emission abatement approaches for the building sector by evaluating the carbon emissions and energy e ﬃ ciency of construction activities, measuring the emission abatement potential of construction activities across the country and regions, and measuring the marginal abatement cost (MAC) of China and various regions. This study calculates the energy and carbon emissions performance of the building sector of 30 provinces and regions in China from 2005 to 2015, measures the dynamic changes in the energy-saving potential and carbon emission performance of the building sector, conducts relevant veriﬁcation, and estimates the MAC of the building sector by using the slacks-based measure-directional distance function. The level of energy consumption per unit of the building sector of China has been decreasing yearly, but the energy structure has changed minimally (considering that clean energy is used). The total factor technical e ﬃ ciency of the building sector of various provinces, cities, and regions is generally low, as veriﬁed in the evaluation of the energy-saving and emission abatement potential of the building sector of China. The energy saving and emission abatement of the building sector of China have great potential—that is, in approximately 50% of the total emissions of the building sector of China. In particular, Northeast and North China account for more than 50% of the total energy-saving and emission abatement potential. The study of the CO 2 emissions and MAC of the building sector indicates that the larger the CO 2 emissions are, the smaller MAC will be. The emission abatement e ﬃ ciency is proportional to MAC. Based on this research, it can be more equitable and e ﬀ ective in formulating provincial emission reduction policy targets at the national level, and can maximize the contribution of the building sector of various provinces to the national carbon emission reduction.


Introduction
The rapid economic development of China has made its energy consumption and carbon emissions among the major contributors to the global greenhouse effect. The energy consumption, which has been growing at an average annual growth rate of 6% since 1991 [1] The scenario of high energy consumption and carbon emission in China will continue [3,4]. In the Paris Agreement in 2015, the commitment of China to achieve carbon peaks by 2030 or earlier means that China will face enormous pressure to reduce emissions [5,6]. The building sector is one of the three major high-energy-consuming sectors in China [7]. Its carbon emissions have reached 36%, second only to those of the industrial sector [8,9]. With the continuous advancement of the urbanization process in China, urban population and building area continue to grow, and the energy demand and carbon emissions of buildings will further increase [10]. Relevant scholars have found that the construction industry has great emission abatement potential in the study of energy reshaping and low-carbon scenarios [7,11]. Effective mitigation of building carbon emissions in the provinces and regions of China is crucial to the realization of the Paris Agreement. Therefore, the question is, are the energy use and carbon emissions of the building sector efficient? Improving the energy efficiency of the building sector and reducing the carbon emissions of buildings contribute to environmental protection, but the potential of emission abatement and economic costs have not received much attention [12,13]. The development level (or stage) of each province differs. How are emission abatement targets distributed, and what are their effects on economic development? What is the marginal carbon abatement cost? These related issues have not received effective attention and solutions [14,15].
In the face of increasing energy consumption in the building sector and its growing contributions to the greenhouse gas emissions of the world, the Chinese government has adopted a series of environmental protection policies over the past two decades [16]. The energy-saving and emission abatement goals of the building sector of China are reflected in a five-year plan in three stages (2006-2010, 2011-2015, and 2016-2020). The "11th Five-Year Plan" (11thFYP, 2006-2010) has achieved the planning goals. The energy saving of the building sector of China is 67. 5 Mtce, which means carbon emission abatement of 185 Mt-CO 2 [17]. The "12th Five-Year Plan" (2011-2015) emphasized that the national energy and carbon intensity targets were reduced by 16% and 17%, respectively. In accordance with the overall energy-saving and emission abatement targets of China, the building sector has achieved the planning goal of energy saving of 116 Mtce-that is, carbon emission abatement of 317 Mt-CO 2 [18]. Compared with the carbon intensity in 2011, the carbon intensity had decreased by 20% at the end of 2015. The "13th Five-Year Plan" (2016-2020) emphasizes that the national energy and carbon intensity targets will be reduced by 15% and 18%, respectively; the energy-saving and emission abatement targets of the building sector of China will be 123 Mtce and 336 Mt-CO 2 [18], respectively. Faced with these ambitious emission abatement targets, policymakers in the building sector of China are facing great challenges. In this scenario, the assessment of the energy and carbon emission efficiency of the building sector of various provinces and regions in China, the estimation of their energy-saving and emission abatement potential, and the calculation of the marginal cost of their current emission abatement can not only lay the foundation for achieving the overall carbon emission abatement planning goals-they can also support the establishment of carbon pricing for the national building sector to achieve carbon emission trading (the carbon-trading system for the national power sector was implemented in 2017) and the "Porter hypothesis" of carbon emission abatement and economic growth.
Research on energy utilization efficiency and carbon emission abatement efficiency in the building sector and other fields mostly uses the efficiency index method, which is divided into parametric and nonparametric methods. In earlier studies, energy intensity was used to reflect energy efficiency (energy consumption per unit of GDP) [19,20] or carbon emission efficiency (carbon emission per unit of GDP) [21,22]. However, the single selection of influencing factors (factors such as capital, energy consumption, labor, economic output, and Huang Jing's influence should be considered) in efficiency analysis leads to a one-sided result, and the energy intensity or carbon emission efficiency cannot reflect the comprehensive impact on economic growth, energy saving, and emission abatement [23,24]. The influence of multiple factors should be considered in the framework of all factors because an increase in energy input may lead to economic growth [25,26]. These problems cannot be solved in the abovementioned research [27,28]. The nonparametric method of data envelopment analysis (DEA) is applied to various fields to study energy and carbon emission efficiency issues because it can handle multiple input-output variables simultaneously [29]. Song et al. (2012) reviewed the research on environmental efficiency and determined that the DEA method can expand the research field [30]. Mardani et al. (2017) also reviewed 144 articles on the application of the DEA model in 45 advanced journals from 2006 to 2015 to study energy efficiency [31]. The article types, application Sustainability 2020, 12, 10432 3 of 22 fields, research purposes, and results were sorted out. They found that the DEA model has a good application prospect in analyzing energy efficiency.
Since Charnes established the DEA method in 1978, various DEA methods have been derived after more than 30 years of development and application [32]. For example, Chambers et al. proposed the directional distance function (DDF) to apply multifactor mixed guidance and compensate for the problem of single-factor orientation (CCR or BCC) in the DEA method (the calculation result is biased because only one aspect of input or output is considered) [33,34]. Compared with the traditional DEA model, DDF can simultaneously consider multifactor and multidirection vectors for efficiency analysis. The DEA model and DDF efficiency evaluation measure the distance from DMU to the effective frontier [35,36]; the greater the distance is, the lower the DMU efficiency value will be [37]. Nevertheless, a "hyperplane" exists in the effective frontier due to the multidimensional nature of input-output. For DEA or DDF, the distance measured in the model is the point-to-plane distance (nonpoint-to-point distance), which has countless directions. Although the direction in which DMU reaches the reference front is defined in the DDF model as the distance measured by the DDF, countless possible directions remain (because the DMU can obtain high efficiency values by increasing output or reducing input [38,39]). The nonuniqueness of the DDF vector leads to the lack of robustness in the evaluation of DDF [35,38].
To obtain a robust evaluation result of total factor efficiency, this study aims to innovate in the direction of DDF. The use of the DDF model based on slacks-based measure (SBM)-DDF can not only solve the local optimal solution (nonglobal optimal solution) caused by DDF nonlinear programming by transforming a nonlinear problem into a linear problem, but the weighted sum of slack variables (inefficiency degree) can also be used to solve the problem of different calculation results caused by DDF assigning different weights to various distances due to the weighting of relative distances. Addressing the two shortcomings can make this study obtain effective evaluation results, the SBM-DDF value obtained using the weighted sum of slack variables is the inefficiency degree; thus, total factor technical efficiency (TTE) = 1 − inefficiency degree value (SBM-DDF value) can also be obtained. We can further decompose TTE to obtain total factor input efficiency (TIE), total factor economic output efficiency (TYE), and total factor bad output efficiency (TBE). From the relaxation degree of each variable, we can obtain total factor energy efficiency (TEE) = target energy input/actual energy input [31] (Hu and Wang 2006) [40] and total factor carbon emission efficiency (TCE) = target emissions/actual emissions [41].
However, few studies have been conducted on the carbon emission abatement costs of the building sector of China. For example, Choi et al. (2012) used the SBM-DDF model to analyze the provincial panel data of China from 2001 to 2010 and discussed the efficiency and potential of carbon emission abatement in China and the marginal cost of emission abatement; the results are helpful for relevant decisions to obtain the basis for policy making [42]. Wang and Wei (2014) discussed the energy utilization efficiency, carbon emission abatement efficiency, and potential of regional industries of 30 cities of China from 2006 to 2010 by using the SBM-DEA model. They also conducted relevant studies on the marginal cost of emission abatement of regional industries. The research results can support the carbon-pricing basis of the national carbon-trading system [43]. Pang et al. (2015) not only used the SBM-DDF model to discuss the energy and emission abatement efficiency and marginal abatement cost (MAC) of 87 countries from 2004 to 2010, but also studied the impact of clean energy on total factor productivity [44]. The current paper introduces the concept and theory of MAC, uses the SBM-DDF dual solution to obtain the shadow price of carbon emissions, and discusses the MAC of the building sector of various provinces, cities, and regions in China. The objectives are to pay considerable attention to the economic development of the building sector of China (the pillar industry of the economic development of China) and to obtain the economic cost of carbon emission abatement in the building sector.
The main innovations of this paper are as follows: to adopt an SBM-DDF model that can compensate for the direction-oriented defects of DEA and DDF to obtain effective and robust total factor efficiency values; to discuss the emission abatement potential of the building sector of various provinces; to achieve the "Porter effect" (a win-win model of economic development and carbon emission abatement) for the development of various provinces and regions; to estimate the carbon emission reduction potential and the marginal cost of carbon emission abatement in the building sector of each province; and to establish the basis for the carbon pricing of the carbon-trading system of the national building sector. The rest of this paper is organized as follows. Section 2 presents the method for the evaluation of total factor efficiency and the estimation of marginal emission abatement cost. Section 3 indicates the variables and data sources required for the solution of total factor efficiency and discusses the energy and emission efficiency, the potential of energy saving and emission abatement, and the marginal cost of carbon emission in the building sector of each province in China. Section 4 provides related research results and prospects.

Methodology
Chambers et al. established the classic DDF model in 1996 [26], and the idea of the DEA model was used in the construction of the DDF model; hence, economists believe that the DDF model also belongs to DEA. The traditional DEA-CCR/BCC model is only a special form of DDF in different directions-that is, DDF is a general expression of the DEA model. The DDF model can not only compensate for the deficiency of DEA in direction orientation, but can also identify and distinguish between desirable and undesirable outputs. However, the nonunique effective evaluation path, the lack of consideration of input and output slack variables, and the adoption of the same scale treatment for the increase in desirable output and the decrease in undesirable output lead to the deviation of evaluation results. Although the pure SBM model solves the problem of the traditional DEA/DDF model that does not consider the slack variable in inefficiency measurement, the point furthest from the effective frontier is used in DMU efficiency evaluation, which is contrary to the expectation (i.e., to reach the effective frontier with the shortest path). Therefore, this study improves the corresponding method when evaluating the total factor efficiency and marginal cost of emission abatement of the building sector of various provinces and regions of China.

Directional Distance Function
The DDF model (1) established by Chambers must satisfy the following conditions: the input index can be arranged at will; no limit is set to the desirable output, and it can be arbitrarily controlled; undesirable output is weakly dominated; and no direct correlation exists between undesirable and desirable outputs.
In Equation (1), an assumption is that the direction vector satisfies (g x , g y ) = (x, y). When Chambers constructed the model, the relevant theoretical basis of the hypothesis was not sorted out. When all distances are assumed to be equal in the case of input and output, not only will the part of redundancy that leads to input and output be minimized, but also the efficiency will be overestimated if the DMU distance is short, which is contrary to the fact. Equation (1) also does not determine the direction vector selection problem. The direction vector (g) or distance (β) should be adjusted to solve the aforementioned problems. If the direction vector (g) is adjusted loosely, the environmental impact factors are considered, and bad output is introduced. The general expression of DDF is After the introduction of bad output into Equation (2), multiple options may be available for the production possibility set. The weak disposability and variable scale returns of bad output must be Sustainability 2020, 12, 10432 5 of 22 considered to be consistent with the actual situation. The production possible set T that is consistent with the actual situation is constructed as follows [45]: Equation (3) shows that the production possibility set T will perform differently in different time periods. DMUs in different periods cannot be compared; only DMUs in the same period can be compared with one another. From the ideas of continuous DEA and total factor production efficiency index (Malmquist [46]), the production possibility set T is transformed into a multi-period DMU comparable production possibility set, as shown as follows: After the production possibility set for evaluation is established, under the selection of generalization direction (g x , g y , g b , the definition of the objective function should not be β to ensure that the relative distance rather than the absolute distance is considered in the evaluation of DMU efficiency. Equation (2) should be reconstructed into Equation (5) contains distance functions in all directions, and the direction vector (g x , g y , g b becomes an endogenous decision variable instead of a given direction vector, thus solving the problem that input-output redundancy cannot be minimized. The direction vector of Equation (5) can be regarded as (1, 1, 1). The absolute distance (βg x , βg y , βg b and the relative distance (βg x /x, βg y /y,βg b /b) are given. Distance variability exists in different dimensions, which solves the problem of overestimating the efficiency of DMU due to the short distance from the production frontier. Nevertheless, Equation (5) still has some defects, such as local optimization caused by nonlinearity. The result of relative distance calculation leads to different weight distribution results due to varying distances. The introduction of the SBM method can solve the abovementioned problems.

Slacks-Based Measure-Directional Distance Function
A generalized nonradial, nonangular SBM-DDF (6) can be constructed by combining the SBM model and DDF. It can solve the problem of conversion from nonlinear to linear and different weight distribution results due to varying distances.
where g = (g x , g y , g b ) is the direction vector of input and output; z x n , z y m , and z b i are the external weights of input, the desirable output, and the undesirable output, respectively; and n z x n + m z y m + i z b i = 1. The SBM-DDF value is the weighted sum of slack variables during the solution-that is, the degree of DMU inefficiency. On this basis, we can also calculate and decompose TTE and obtain TIE, TYE, and TBE, as shown as follows: The input variables are divided into capital stock, labor, and energy; the desirable output is the total output value of the building sector; the undesirable output is the carbon emission of the building sector [8]. For the objectives of this study, Equations (6) and (7) can be integrated into Equations (8) and (9) to obtain TEE, TYE, and TCE.
The reduction in labor and capital stock is not considered in Equation (8). The main reason for this is that for countries, provinces, or regions, increasing economic output and employment rates is the foundation and the expectation of the development of each region or country. The economic output of DMU should be increased while reducing energy use and carbon emissions. The SBM-DDF used in this study can comprehensively analyze the efficiency values of all aspects of DMU. After the efficiency of all aspects is obtained, the overall technical efficiency of DMU can be obtained through the arithmetic average. How we set the values of z 1 , z 2 , z 3 depends on the local environmental pressure.
If the values of z 1 , z 3 are larger, then energy saving and emission abatement are more important; if the value of z 2 is relatively larger, then economic development is more important.

Marginal Abatement Cost
This study adopts the nonparametric shadow price model to measure the MAC in each province. Compared with the solution of parametric shadow price models, the solution of nonparametric shadow price models does not require any a priori hypothesis about the SBM-DDF model. The shadow price of carbon emissions, namely MAC, can be solved through the dual programming of the SBM-DDF model. The dual programming of Equation (6) leads to The selection of weight and direction vectors is the same as mentioned above. The dual variables ν n , σ m , and ω i are the virtual prices of input, desirable output, and undesirable output, respectively. When the shadow price of undesirable output is assumed to be equal to the market price, the shadow price of undesirable output is p b i = ω i /σ m . The equation shows that the shadow price of undesirable output can be expressed as the marginal conversion rate between undesirable and desirable outputs-that is, the MAC of undesirable output.

Data
The main objective of this study is to investigate the total factor efficiency, energy-saving potential, and MAC of the building sector by exploring the expected output value and the unexpected output caused by the building sector activities (construction and operation stage) of each province of China. The research scopes are mainly the construction and operation stages of buildings, which account for more than 80% of the energy consumption of the building sector [47]. Relevant data are primarily Building activity capital stock (BCS-billion yuan), labor force (L-104 employees), and energy consumption (E-104 tons of coal equivalent) are selected as input indicators; the total output value of building activities (BTV-billion yuan) serves as the desirable output indicator; carbon emissions from building activities (CO 2 -104 tons) are used as undesirable output indicators [48]. Table 1 shows the summarized statistics of the five variables.
The perpetual inventory method is used to estimate the actual capital stock (k) of the building sector of each province over the years.
where K t i represents the actual capital stock of the construction industry in the t-th year of the i-th province, and I t i represents the investment of the building sector in the t-th year of the i-th province. This paper regards the fixed assets of the building sector in the current year (the fixed assets of the entire society in the building sector: sum of fixed asset investment in construction and operation stages) as the investment of the building sector. δ represents the capital depreciation rate. According to Ji and Zhou (2020), the depreciation rate of fixed assets in each province is 10.8%. We calculate the capital stock of the building sector of each province in each year on the basis of 2005 data [49]. The fixed asset investment price index of the building sector of each province and city is used in the calculation, and the actual capital stock of the building sector of each province and city in each year (constant price in 2005) is obtained to eliminate the influence of price factors. The sum of the number of employees (l) in the construction industry (building construction stage) and the building operation stage at the end of each year in various provinces and cities is used as the labor force input for the activities of the building sector. The number of employees in the construction industry cannot be obtained directly. To ensure the availability and reliability of the data, the sum of the number of urban unit employees, private enterprise employees, and individual employees of the construction industry at the end of the year in each province is used to estimate the number of construction industry employees. The data come from "China Statistical Yearbook 2006-2017".
This study uses the method of the energy balance table to estimate the final energy consumption of the building sector (converted into standard coal) as the energy consumption of the building sector (including renewable energy) in consideration of the lack of energy consumption data for the building sector of various provinces and cities. It combines the energy balance sheet and the carbon emission intensity method to estimate the undesirable output carbon emissions of the building sector and eliminate the double calculation of energy consumption when eliminating carbon emissions from the building sector. The specific method can be found in the paper of Shi et al. (2020) [50]. The total output value of building sector activities (the sum of the values of building products, commercial building operation, and the living consumption of residents) serves as the desirable output of the building sector, which refers to the sum of the output value of the construction industry (the value of building products) and the output value of building activities in the operation stage. The main reasons for using the total output value of the building sector as the desirable output of the building sector are that the building sector involves multiple industries, the intermediate input is relatively large, and the influence of intermediate input factors cannot be ignored. The total output value of the building sector is the sum of the output of all input factors, which can comprehensively reflect the overall development status of the building sector. The statistical caliber of the energy consumption of the building sector is the same as the total output value of the building sector, which ensures the reliability and effectiveness of obtaining relevant data.
As shown in Figure 1, the statistical data show that the unit economic energy consumption and carbon emissions of the building sector have shown a downward trend over time, while the CO 2 emissions per unit energy consumption have not changed significantly. The proportion of renewable energy can reflect the energy structure. The downward trend of unit economic energy consumption and carbon emissions shows that the energy-saving and emission abatement policies or technologies adopted by the building sector have achieved some results. However, the use of renewable energy in the building sector has not been effectively promoted, and the promotion and application of renewable energy policies and technologies in the building sector should be further strengthened. emissions per unit energy consumption have not changed significantly. The proportion of renewable energy can reflect the energy structure. The downward trend of unit economic energy consumption and carbon emissions shows that the energy-saving and emission abatement policies or technologies adopted by the building sector have achieved some results. However, the use of renewable energy in the building sector has not been effectively promoted, and the promotion and application of renewable energy policies and technologies in the building sector should be further strengthened.

Analysis of the Total Factor Efficiency of the Building Sector of China
This study uses models (6)-(9) to calculate the total factor efficiency and the efficiency of technology, energy, carbon emission, and economic output of 30 provinces and cities of China (excluding Tibet, Taiwan, Hong Kong, and Macao due to the lack of data) from 2005 to 2015. The evaluation results are shown in Table 2.  TTE  TYE  TEE  TCE  TTE  TYE  TEE  TCE  TTE  TYE  TEE

Analysis of the Total Factor Efficiency of the Building Sector of China
This study uses models (6)-(9) to calculate the total factor efficiency and the efficiency of technology, energy, carbon emission, and economic output of 30 provinces and cities of China (excluding Tibet, Taiwan, Hong Kong, and Macao due to the lack of data) from 2005 to 2015. The evaluation results are shown in Table 2.
From the calculation results in Table 2, the provinces with high TTE are mainly those dominated by tertiary industry, and several developed municipalities are also among them. This trend did not change significantly from 2005 to 2015. The regions with high TTE value include Beijing, Tianjin, Shanghai, Jiangsu, Zhejiang, and Hainan. In Tianjin and Shanghai, the mean value of TTE is greater than 0.8. The value of TYE in Tianjin, Shanghai, and Hainan is always greater than 0.8 from 2005 to 2015, which means that the relevant policies and strategies of these provinces and cities for promoting economic growth are highly efficient. They are followed by Beijing, Jiangsu, and Zhejiang. Except for a few provinces and regions, the TYE of most provinces and regions is greater than TTE. For example, in 2010, the TYE of 29 provinces and regions was greater than TTE. This finding can indirectly explain that the low efficiency of total factor technology in most provinces and regions is mainly caused by the low efficiency of energy use and emission abatement.
For the energy efficiency of the building sector of 30 provinces of China, the overall energy efficiency was relatively low, especially from 2005 to 2010. With the rapid development of the economy of China, the energy structure has become irrational. Consequently, the building sector of China maintains high energy intensity (0.56 kt/mYuan). Nevertheless, with the transformation of the economic structure of China, the energy efficiency of the building sector improved from 2011 to 2015. The energy intensity (0.36 kt/mYuan) also declined significantly, although it is still relatively large. This phenomenon proves the effectiveness of the economic transformation strategy of China in terms of energy saving. Compared with energy efficiency, the emission abatement capacity of the building sector of various provinces, cities, and regions is relatively better. Although the carbon emission abatement efficiency of most provinces and cities is not high, after a series of efforts by the Chinese government, the emission abatement efficiency of Tianjin, Shanghai, Hainan, and Chongqing was close to or equal to 1 in 2015, followed by that of Anhui, Fujian, Jiangxi, Hubei, Hunan, Sichuan, and other places. The emission abatement efficiency is greater than 0.6, which is far from that achieved in 2005-2010. Since China joined the Paris Agreement in 2015, it has imposed relevant requirements regarding the emission abatement targets and energy intensity of each province, which will increase the contribution of the building sector of China to reducing emissions further.   Figure 2 shows that the energy consumption per unit building area has a linear relationship with TEE and TCE, which is consistent with the actual situation. The economic efficiency value and the energy consumption per unit building area show an M-shaped change curve, which conforms to the theoretical hypothesis of the environmental Kuznets curve (EKC). An inverted U-shaped relationship exists between the energy consumption and economic development levels. Total factor technical efficiency is based on the product of economic efficiency, energy efficiency, and carbon emission efficiency, and its change trend and the value of economic efficiency show the same direction. This result indicates that energy consumption per unit building area is the main factor affecting the total factor technical efficiency, economic efficiency, and carbon emission abatement efficiency, especially the carbon emission abatement efficiency of the building sector. The development of the relevant trend line in 2015 is obvious. and high energy efficiency value, means that the utilization rate of coal (or high-carbon energy) in the building sector in the region is higher than that of clean (or renewable) energy. The double lowefficiency group-that is, low energy efficiency and low carbon emission abatement efficiency values-is located in the North of Qinling Mountains-Huaihe River Line and the western region of China. Its energy structure is irrational, and relevant emission abatement policies have not been implemented. In accordance with the 11-year (2005-2015) average scores of TEE and total factor carbon emission abatement efficiency of the building sector of China, the building sector of 30 provinces and cities in China is divided into four datasets (high/low energy/carbon emission abatement efficiency datasets), as shown in Figure 3. Tianjin and Shanghai are the only two provinces with double high efficiency. Beijing, Guangdong, Zhejiang, Jiangsu, Chongqing, and Hainan, which have a relatively developed economy, belong to the high-low (or low-high)-efficiency group. They do not perform well in terms of energy use and carbon emissions. The meaning of high-low is high carbon emission abatement rate and low energy efficiency index values. Provinces and cities that belong to the high-low-efficiency group, such as Hainan, Zhejiang, and Jiangsu, display minimal energy consumed with high carbon intensity, and the energy structure is relatively reasonable (the proportion of clean or renewable energy is relatively large). Low-high, namely low carbon emission abatement efficiency and high energy efficiency value, means that the utilization rate of coal (or high-carbon energy) in the building sector in the region is higher than that of clean (or renewable) energy. The double low-efficiency group-that is, low energy efficiency and low carbon emission abatement efficiency values-is located in the North of Qinling Mountains-Huaihe River Line and the western region of China. Its energy structure is irrational, and relevant emission abatement policies have not been implemented.

Carbon Emission Abatement Efficiency and Economic Development of the Building Sector
Existing research on the EKC of China shows that the level of economic development has an inverted U-shaped relationship with energy consumption or carbon emission levels. That is, as the level of economic development increases (or the income level increases), the environmental pressure (energy consumption and carbon emission levels) also rises to a certain level, and the environmental

Carbon Emission Abatement Efficiency and Economic Development of the Building Sector
Existing research on the EKC of China shows that the level of economic development has an inverted U-shaped relationship with energy consumption or carbon emission levels. That is, as the level of economic development increases (or the income level increases), the environmental pressure (energy consumption and carbon emission levels) also rises to a certain level, and the environmental pressure begins to decline after reaching a certain level. This finding has been verified in the preceding analysis of total factor economic efficiency and energy consumption per unit building area (as shown in Figure 2, TYE), but the relevant analysis remains insufficient. This study aims to prove that an EKC exists between the CO 2 emission efficiency of the building sector and the economic development level (or income growth level) of each province and city. The EKC regression model for each region is established to study the relationship among the output value of the building sector per capita (BTVPC), GDP per capita (GPDPC), and carbon emission efficiency of each region, as shown as follows: where TCE represents the CO 2 emission abatement efficiency value of the building sector, i represents the provinces and cities, c represents a constant, βrepresents the relevant explanatory variable coefficient, η represents the coefficient of other explanatory variables, and Z represents the vector value of other variables that may affect the total factor carbon emission abatement efficiency of the building sector, and ε represents the stochastic error. The least-squares panel fixed-effect regression method is used to verify the results of Equation (12). The results show that the correlation coefficient of variables is significantly not zero (the significance level is 1%), the coefficients of primary and cubic terms are positive, and the coefficient of quadratic terms is negative. TCE and the per capita output value of buildings show an N-shaped curve relationship, and the goodness-of-fit value R 2 = 0.786 is sufficiently high. The residual results (DW is approximately equal to 2) indicate that they are independent. Therefore, the results prove that an environmental (carbon) Kuznets curve ( Figure 4) exists between TCE and BTVPC in the building sector of China. However, in the calculation results of Equation (13), although the coefficients of the relevant variables are insignificantly zero, the coefficients of the primary and cubic terms are positive, and the coefficient of quadratic terms is negative, the EKC hypothesis cannot be determined between TCE and GDPPC. The main reason for this may be that the proportion of energy consumption in the building sector and the growth rate of GDP have a reverse fluctuation relationship-that is, the smaller the growth rate of GDP is, the greater the proportion of building energy consumption will be, and vice versa. The growth of GDP is closely related to industry development. The energy consumption generated by an industry is highly sensitive to the growth rate of GDP. When the economy develops rapidly, the growth rate of industrial energy consumption is fast, which leads to a reduction in the proportion of building energy consumption. Thus, the EKC hypothesis cannot be determined between TCE and GPDPC in the building sector.
The environmental (carbon) Kuznets curve (Figure 4) between TCE and BTVPC in the building sector of China may be attributed to the following reasons [51]. In the early stages of reform and opening up, with the continuous and stable economic development and the acceleration of the urbanization process in China, the level of energy use efficiency has also continued to increase, resulting in the growth of the added value of the building sector faster than its energy consumption and related CO 2 emissions. Subsequently, the policy of citizenization was implemented continuously, China entered a period of prosperity in the real estate market (national real estate), and a large number of real estate projects were constructed, resulting in a significant increase in the energy consumption and carbon emissions in the building sector. Consequently, the energy efficiency improvement of the building sector becomes slow. However, with the continuous implementation of the sustainable goals and policies of global cooperation, all countries and regions have implemented relatively strict environmental regulations and carbon emission abatement goals (such as building energy efficiency standards in the building sector). This phenomenon has prompted the continuous increase in energy and carbon emission abatement efficiency. consumption generated by an industry is highly sensitive to the growth rate of GDP. When the economy develops rapidly, the growth rate of industrial energy consumption is fast, which leads to a reduction in the proportion of building energy consumption. Thus, the EKC hypothesis cannot be determined between TCE and GPDPC in the building sector. The environmental (carbon) Kuznets curve ( Figure 4) between TCE and BTVPC in the building sector of China may be attributed to the following reasons [51]. In the early stages of reform and opening up, with the continuous and stable economic development and the acceleration of the urbanization process in China, the level of energy use efficiency has also continued to increase, resulting in the growth of the added value of the building sector faster than its energy consumption and related CO2 emissions. Subsequently, the policy of citizenization was implemented continuously, China entered a period of prosperity in the real estate market (national real estate), and a large number of real estate projects were constructed, resulting in a significant increase in the energy consumption and carbon emissions in the building sector. Consequently, the energy efficiency improvement of the building sector becomes slow. However, with the continuous implementation of the sustainable goals and policies of global cooperation, all countries and regions have implemented relatively strict environmental regulations and carbon emission abatement goals (such as building energy efficiency standards in the building sector). This phenomenon has prompted the continuous increase in energy and carbon emission abatement efficiency.

Energy-Saving Potential
From the definition of energy efficiency calculation in the building sector, the increased value of desirable output and the decreased value of undesirable output are estimated using models (6) and (7). China can be divided into six regions in consideration of the relevant energy-saving potential involving the building sector of 30 provinces (data on Tibet, Macau, Hong Kong, and Taiwan are lacking) and in accordance with the characteristics of economic geography and power supply to describe the energy saving and emission abatement of the regional building sector.

Energy-Saving Potential
From the definition of energy efficiency calculation in the building sector, the increased value of desirable output and the decreased value of undesirable output are estimated using models (6) and (7). China can be divided into six regions in consideration of the relevant energy-saving potential involving the building sector of 30 provinces (data on Tibet, Macau, Hong Kong, and Taiwan are lacking) and in accordance with the characteristics of economic geography and power supply to describe the energy saving and emission abatement of the regional building sector. These six regions are Northeast China As shown in Figure 6, the total potential of the building sector of 30 provinces and regions in China was 197 Mtce in 2005. The value slightly increased to 208 Mtce in 2007, continued to rise from 2010 to 2013, and reached 311 Mtce in 2013. The main reason for this situation is that the investment and construction scale of the real estate industry increased rapidly during this period. From the results, the building sector of NC has the largest energy-saving potential, accounting for approximately 31% of the total energy-saving potential of 30 provinces and cities in China, followed by those of the NEC and SC regions, where the energy-saving potential accounts for 17% of the total energy-saving potential. The energy-saving potential of the three regions (approximately 15 provinces and cities) accounted for approximately 70% of the total energy-saving potential of 30 provinces and by those of the NEC and SC regions, where the energy-saving potential accounts for 17% of the total energy-saving potential. The energy-saving potential of the three regions (approximately 15 provinces and cities) accounted for approximately 70% of the total energy-saving potential of 30 provinces and cities in China from 2005 to 2015. The results of this study indicate that the building sector of NC will take more responsibility and play a key role in future energy saving compared with others.  This finding can be verified using the results of the previous analysis. Figures 6 and 7 show that the energy-saving potential of NEC and NC regions is relatively high. Both regions are located in the central heating area of China and belong to the regions with high energy consumption in the building Figure 6. Energy-saving potential of the regional building sector of China. sector. The energy consumption per unit building area is also relatively high due to the concentration of economic volume and population density in southern and eastern China. Hence, the improvement of energy utilization efficiency in eastern and southern China should be focused on. which was greatly related to the efforts of the Chinese government to implement related emission abatement policies. From the results, the emission abatement potential of the building sector of NEC and NC remained large and showed an upward trend. On the contrary, southern China exhibited decreased total energy-saving potential by 17% and decreased total emission abatement potential by 11%. The difference in the development trends of energy saving and emission abatement between NEC and NC and SC is mainly due to their difference in energy structure. Raw coal accounts for a large proportion in the energy structure of NEC and NC, mainly because the energy consumption of central heating in NC is derived from raw coal. Another reason is that the energy and emission abatement efficiency values of SC are high; consequently, it shows a low value in emission abatement potential. The main reason for this situation is that the investment and construction scale of the real estate industry increased rapidly during this period. From the results, the building sector of NC has the largest energy-saving potential, accounting for approximately 31% of the total energy-saving potential of 30 provinces and cities in China, followed by those of the NEC and SC regions, where the energy-saving potential accounts for 17% of the total energy-saving potential. The energy-saving potential of the three regions (approximately 15 provinces and cities) accounted for approximately 70% of the total energy-saving potential of 30 provinces and cities in China from 2005 to 2015. The results of this study indicate that the building sector of NC will take more responsibility and play a key role in future energy saving compared with others. From the two five-year energy consumption growth rates of 23.86% and 25.01% and the energy-saving potential growth rates of 27.18% and 6.42%, the energy utilization efficiency between 2005 and 2015 did not greatly improve. This finding can be verified using the results of the previous analysis. Figures 6 and 7 show that the energy-saving potential of NEC and NC regions is relatively high. Both regions are located in the central heating area of China and belong to the regions with high energy consumption in the building sector. The energy consumption per unit building area is also relatively high due to the concentration of economic volume and population density in southern and eastern China. Hence, the improvement of energy utilization efficiency in eastern and southern China should be focused on. Potential   Figures 8 and 9 respectively show the emission abatement potential and targets of the six regional building sectors of China. In 2005, the total emission abatement potential of the building sector of 30 provinces and regions in China was 434.38 Mt-CO 2 . Compared with the values in 2005 and 2010, the energy-saving potential slightly increased to 530.67 Mt-CO 2 . From 2010 to 2013, the value continued to rise, reaching 683.37 Mt-CO 2 by 2013. An inverted U-shaped development trend of emission abatement potential occurred from 2005 to 2015, which was greatly related to the efforts of the Chinese government to implement related emission abatement policies. From the results, the emission abatement potential of the building sector of NEC and NC remained large and showed an upward trend. On the contrary, southern China exhibited decreased total energy-saving potential by 17% and decreased total emission abatement potential by 11%. The difference in the development trends of energy saving and emission abatement between NEC and NC and SC is mainly due to their difference in energy structure. Raw coal accounts for a large proportion in the energy structure of NEC and NC, mainly because the energy consumption of central heating in NC is derived from raw coal. Another reason is that the energy and emission abatement efficiency values of SC are high; consequently, it shows a low value in emission abatement potential. On the contrary, southern China exhibited decreased total energy-saving potential by 17% and decreased total emission abatement potential by 11%. The difference in the development trends of energy saving and emission abatement between NEC and NC and SC is mainly due to their difference in energy structure. Raw coal accounts for a large proportion in the energy structure of NEC and NC, mainly because the energy consumption of central heating in NC is derived from raw coal. Another reason is that the energy and emission abatement efficiency values of SC are high; consequently, it shows a low value in emission abatement potential. Figure 8. Emission abatement potential of the regional building sector of China. Figure 8. Emission abatement potential of the regional building sector of China. Figure 9. Emission abatement potential and targets of the regional building sector of China. Figure 9 illustrates the total carbon emission value and carbon emission abatement target value of the building sector of 30 provinces, cities, and regions in China from 2005 to 2015. Compared with the emission abatement potential of the building sector in the 10th Five-Year Plan period, the rising trend of the emission abatement potential in the 11thFYP period decreased significantly from 25.04% to 16.69%. The NEC and NC regions, as the two regions with the largest carbon emission contribution value in China from 2005 to 2015, will play a major role in the future emission abatement work of the building sector of China. Therefore, the carbon emission abatement effectiveness of the building sector of the two regions, including the northwest region (central heating area), may significantly affect the overall emission abatement effect of China.

Marginal Carbon Emission Abatement Cost
This study further estimates the marginal carbon emission abatement cost of the building sector of 30 provinces, cities, and regions in China on the basis of model (10) to measure the economic impact of carbon emission abatement work on the building sector. The table lists the relative CO 2 shadow prices of 30 provinces and regions in China relative to the output value of the building sector-that is, the opportunity cost of carbon emission abatement in the building sector of China. In terms of the output value of the building sector, the shadow price represents the marginal cost of CO 2 emissions from the building sector of different provinces and regions of China. Table 3 presents that the average shadow price for 11 years from 2005 to 2015 was CNY63.4/t-CO 2 . This result is similar to the research results of Shi [52] and is in line with the development scenario of the current carbon-trading market in China [53]. It is generally equivalent to the average carbon emission-trading price in the EU market. The average carbon emission-trading price from 2010 to 2017 was EUR 8/t-CO 2 . The study of the principles of environmental economics shows that the marginal cost of CO 2 emission abatement is negatively related to the CO 2 emissions in regions. Relevant verifications are also obtained in Table 3. For example, in 2015, the carbon emission and emission abatement potential of the building sector of the northeast region reached 30% and 39% of the national cumulative total, respectively; the marginal carbon emission abatement cost of the building sector was the lowest among the six regions. The average value in 11 years was CNY24.93/t-CO 2 .The highest marginal carbon emission abatement cost existed in EC, with an 11-year average of CNY 137.53/t-CO 2 . The marginal carbon emission abatement costs of the building sector of the four municipalities of China, namely, Beijing, Tianjin, Shanghai, and Chongqing, were higher than those of other regions. The 11-year averages were CNY 152.71/t-CO 2 , CNY 124.59/t-CO 2 , CNY 284.25/t-CO 2 , and CNY 85.5/t-CO 2 . They belong to areas with city-level building carbon emissions, and the cost is thus relatively high. The relatively high efficiency of emission abatement is another reason for this situation. Figure 10 illustrates the average shadow price of CO 2 emissions from the building sector of 30 provinces and cities in China and the relationship between the CO 2 emission abatement costs and CO 2 emission efficiency scores of the building sectors in these provinces and cities. A positive correlation mainly exists between the two variables, which indicates that cities with high industrial CO 2 emission efficiency will also bear high CO 2 emission abatement costs. Among the building sector of 30 provinces and cities in China, that of Shanghai has the highest CO 2 emission abatement costs, whereas that of Heilongjiang has the lowest CO 2 emission abatement cost. The cost of CO 2 reduction in Beijing, Tianjin, Guangdong, Zhejiang, and Jiangsu ranks in the top six of the 30 provinces and regions, with CO 2 per ton higher than 100CNY/t-CO 2 . The cost of CO 2 emission abatement in Jilin and Inner Mongolia ranks in the bottom three of the 30 major cities, all of which are below CNY 20 per ton of CO 2 . Table 3. China's regional CO 2 emissions abatement cost of building sector (CNY/t-CO 2 ).  The large gap in reducing the CO2 emission costs of the building sector among different regions of China implies the necessity and possibility of establishing a regional emission-trading system. With this system, an efficient and cost-effective CO2 emission abatement plan can be realized at the national level. If such a trading system is introduced into the Chinese market among different The large gap in reducing the CO 2 emission costs of the building sector among different regions of China implies the necessity and possibility of establishing a regional emission-trading system. With this system, an efficient and cost-effective CO 2 emission abatement plan can be realized at the national level. If such a trading system is introduced into the Chinese market among different provinces, cities, and regions, the market price of CO 2 emissions in the national building sector of China can be set to approximately CNY 60/t-CO 2 on the basis of the average CO 2 emission abatement costs from 2005 to 2015. The market price of CO 2 emissions of each provincial region can be set between 20 and 290 CNY/t-CO 2 .

Region
The relationship between marginal emission abatement cost and carbon emission abatement efficiency is illustrated in Figure 10. When the carbon emission abatement efficiency in 30 provinces and cities in China is less than 0.6, the emission abatement efficiency and the marginal cost of carbon emission abatement have a linear relationship. When the carbon emission abatement efficiency value is greater than 0.6, the carbon emission abatement efficiency and the marginal carbon emission abatement cost show an exponential relationship. Although the emission abatement efficiency of the building sector of Shanghai and Hainan is relatively high (0.92 and 0.97, respectively), the emission abatement costs greatly differ-that is, 284 CNY/t-CO 2 in Shanghai and 85 CNY/t-CO 2 in Hainan. When the emission abatement efficiency is less than 0.6, a linear relationship of emission abatement cost (or carbon market transaction value) should be set; when the emission abatement efficiency value is greater than 0.6, the local actual economic development and emission abatement difficulty value should be considered to establish the carbon emission abatement cost in line with local conditions. Accordingly, an efficient and cost-effective CO 2 emission-trading market in China will be achieved, and a sustainable development system under the "Porter Hypothesis" will be constructed.

Discussions
Although there are many studies on energy efficiency, as mentioned in the introduction, previous scholars mainly focused on industry and the transportation sector. There are relatively few studies on energy efficiency and the marginal cost of carbon emission reduction in the building sector. Related research is more easily explored from the national level, ignoring the differences between regions, resulting in the positive results of energy efficiency research. This is also the main reason why this article differs from other scholars' research results. Secondly, the defects in previous scholars' research methods also cause local optimal solutions (nonglobal optimal solution) and instability of research results. This paper has proven that SBM-DDF solves the two key problems of traditional methods in the methodology section, and also carried out robust analysis in Section 3.2. In addition, the relevant research on carbon emission reduction, without considering the economic impact of carbon emission reduction on regions, just discusses the impact of its carbon emission reduction efficiency on relevant policies, neglecting the development willingness of various regions, which is also the key factor causing local emission reduction policies to fail to achieve the expected goals. At the same time, this paper further explored the possibility of the building sector's carbon emission reduction responsibility in each province, combined with the marginal cost of carbon emission reduction and emission reduction potential of building sector. It has laid a certain foundation for setting emission reduction policy objectives of building sector in various regions.
Although this research has its advantages, it also inevitably has some limitations, which will trigger the potential direction of future research. First, our MAC estimates are limited by the feasibility of the data. The lack of data support at the city level in China, such as in the four major municipalities of China (Beijing, Shanghai, Tianjin, and Chongqing), clearly shows differences from other provinces. Given the availability of data, future empirical studies covering other cities and pollutants are of great significance. Second, the choice of pollutants is insufficiently comprehensive. Although carbon emissions are the main problem in the global greenhouse effect, building health and safety will also be areas that we will continue to explore.

Conclusions
The rapid economic development of China over the past three decades has caused many environmental problems. Chinese stakeholders are becoming increasingly aware of the importance of sustainable development. Considering the balance between economy and environment, this study expands the nonparametric method of production economics, constructs SBM-DDF, and measures the total factor efficiency (TTE, TYE, TEE, and TCE) of 30 provinces and regions in China from 2005 to 2015. It also evaluates the energy-saving and emission abatement potential and estimates the marginal emission abatement cost of each province and city. A comprehensive understanding of the total factor efficiency value, energy saving, and emission abatement capabilities of various provinces and cities and the economic cost of emission abatement in the building sector can provide policy analysts with valuable information on formulating specific emission abatement strategies.
From the efficiency evaluation results, the total factor efficiency values, especially TTE (in consideration of economic growth, energy saving, and emission abatement), of EC and SC are higher than others. On the contrary, the TTE values of NC and NEC are relatively low. The economically developed regions, such as Beijing, Shanghai, Tianjin, Zhejiang, and Hainan, have better total factor efficiency than others. By contrast, less-developed cities, such as in the northeast region, have suffered from worse total factor efficiency. This finding is verified in the evaluation of the energy-saving and emission abatement potential of six regional building sectors of China. The overall emission abatement potential of the building sector of China has reached approximately 50%. This condition means that the high emission abatement potential of the building sector of China has a great impact on the realization of the overall emission abatement plan of China. Relevant government departments should pay further attention and formulate targeted emission reduction strategies and goals. Under the background of the sustainable development of the economy and environment, the economic cost of the marginal emission abatement of the building sector of various provinces, cities, and regions is estimated. The emission abatement cost of the building sector across the country is CNY 63.4/t-CO 2 . The prediction of the economic cost of emission abatement of the building sector of each region and province can help determine the market transaction prices or reasonable carbon tax values under the coordinated development of economy and environment. It provides not only a basis for China to establish a comprehensive carbon market-trading system but also a good data foundation for the emission abatement policies in the building sector.
The policy implications of our research are as follows. First, the total factor efficiency, energy saving, and emission-abatement potential of each province and city and the estimated MAC can be used as the basis for local governments to measure and reduce the overall emission abatement cost. Second, the differences in energy-saving and emission abatement potential and MAC among provinces and cities are significant, indicating a high trade potential among them. A comprehensive limit and trading plan for CO 2 emissions can be introduced to minimize the overall cost of emission abatement. Lastly, the Chinese central government can determine specific cost-effective emission abatement strategies by encouraging emission trading between economically developed and economically undeveloped provinces. The energy-saving and emission abatement potential of each province, city, and region and MAC can also be used as the basis for the initial allocation of emission permits. From a cost-saving perspective, economically developed provinces should allocate more emission permits because they have relatively higher MAC than less economically developed provinces.
Author Contributions: W.C. conceptualized the framework of this study. Q.S. and J.G. contributed to the methodology, data collection, data calculation, and results analysis. H.R. helped to revise the original manuscript (especially the graph). All authors have read and agreed to the published version of the manuscript.

Conflicts of Interest:
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.