Research on carbon emission efficiency in the Chinese construction industry based on a three-stage DEA-Tobit model

The traditional data envelopment analysis (DEA) model usually ignores the influence of external environmental factors and random interference. This can easily lead to deviations in efficiency estimates. In order to solve this problem, a three-stage DEA model was used to better reflect the carbon emission efficiency of Chinese construction industry (CEECI) (2006–2017) from the perspective of non-management factors. The internal influencing factors of CEECI are analyzed by the Tobit model, which provides a more accurate basis for formulating policies. It is found that the CEECI is significantly affected by the GDP, the level of industrialization, the degree of opening-up, technological innovation, and energy structure. After excluding environmental factors and random interference, the average CEECI increased by 16%. The resulting calculations are noteworthy in three aspects. First, there are significant regional differences in the CEECI. Both the multi-polarization phenomenon of CEECI and regional differences also reduced gradually over time. Second, the CEECI can be decomposed into pure carbon emission efficiency (PCEE) and scale efficiency (SE), which is mainly caused by SE. Excluding external environmental factors and random interference will have a specific impact on the CEECI. All the 30 provinces are divided into four categories to analyze the reasons and solutions of the differences in the CEECI in provinces. Third, many factors had inhibitory effects on the CEECI, PCEE, and SE; these included energy structure optimization, labor force number, total power of construct ion equipment, and construction intensity in the construction industry. Nevertheless, the development level of the construction industry did have a significant positive effect.


Introduction
As a pillar industry of China's economy, the supply chain of construction industry covers a wide range. In the construction operation stage, it not only consumes fossil energy directly to generate a large amount of carbon emissions but also consumes more than half of the world's construction cement and steel, which is closely related to the indirect carbon emissions caused by upstream industries (such as cement, steel, and wood industries) (Huo et al. 2018). Base on the latest data from the National Bureau of Statistics, the energy consumption of the construction industry was 8555 ten thousand tons of standard coal, accounting for about 30% of the total energy consumption in 2017 (Huo et al. 2020). The carbon emissions from construction industry account for 30%-40% of the total carbon emissions in China . It far exceeded other industries such as agriculture and transportation and has become the main sector of energy consumption and carbon emissions. At the same time, from the perspective of cross-regional linkage, the production line of the industrial sector is fixed and capable of mass production, and the products can be sold all over the world. On the contrary, the buildings produced by the construction industry are fixed, but the production lines are mobile which could undertake construction projects in various places. This special attribute may lead to spatial differences in carbon emission efficiency (CEE) (Huo et al. 2018).
It is worth noting that the total output value of Chinese construction industry has accounted for more than 20% of the gross national product (GNP) since 2009. The reason is that the rapid development of industrialization and urbanization in China has promoted the rapid expansion of the construction industry. Besides, the steady and rapid development of Chinese economy has benefited from the stimulation of real estate investment (Yan et al. 2017a). However, the rapid development of construction industry may lead to environmental problems, especially carbon emissions. Historical experience shows that the economic rise of big countries has been at the expense of ecological environment for a long time, which violates the Chinese concept of coordinated and green development.
The Chinese government attaches great importance to environmental issues. The 13th Five-Year Plan emphasizes that CEE should be improved by promoting green and intelligent buildings. For the construction industry, do these environmental policies improve the CEECI effectively? What are the factors to improve the CEECI? It is still unknown what adjustments should be made to relevant policies in the 14th Five-Year Plan to better enhance the CEECI. Therefore, it is necessary to identify the growth structure of CEECI accurately, evaluate its efficiency and influencing factors scientifically, and then improve the scientific basis for local governments to formulate differentiated carbon emission reduction policies.
At present, the evaluation methods of CEECI mainly include data envelopment analysis (DEA) and stochastic frontier analysis (SFA). Because SFA is highly dependent on the form of function, the efficiency results of fitting based on different influencing factors must be biased. Relatively speaking, the DEA can avoid this problem better (Cheng et al. 2020). However, most scholars ignore the influence of environmental factors and random noise on the efficiency evaluation of decision-making units (DMUs) when using DEA to evaluate CEE. This refers to the traditional DEA model that is mostly used. In fact, aiming at this problem, Fried et al. (2002) have discussed how to introduce environmental factors and random noise into DEA model. Besides, around the analysis of CEECI, most scholars only pay attention to the measurement of efficiency, ignoring the analysis of internal influencing factors of CEECI. Based on this, this paper firstly adopts the three-stage DEA model from the perspective of nonmanagement factors, which could solve the problem of the unreal efficiency evaluation due to the difference of external environment. Secondly, based on the multi-input-multi-output system, the total factor index is constructed, and the growth structure of CEECI is decomposed to provide reference for policy making. Finally, from the perspective of crossregional linkage, this paper examines the spatial differences, temporal evolution trends, and driving forces of CEECI.
The marginal contribution of this paper can be summarized as the following two points: (1) Using three-stage DEA to evaluate the CEECI not only avoids the measurement bias of SFA but also overcomes the influence of traditional DEA model ignoring environmental factors and random noise on efficiency evaluation and then minimizing the measurement bias caused by external environmental differences. (2) From the perspective of management factors, the influences of energy structure, labor force, total power of machinery and equipment, and construction intensity on CEECI are analyzed, which makes up for the deficiency of focusing only on efficiency measurement but ignoring its influencing factors.
The rest of this study is arranged as follows. The next part is a literature review. The third part introduces the models and variables used in this study. The fourth part calculates the CEECI. The fifth part gives the result analysis and enlightenment. Finally, it provides some conclusions and suggestions for the administrative department.

Literature review
This part summarizes the related literature. Firstly, the literature on CEE is reviewed in the "Research on CEE" section. In the "On the evolution of the three-stage DEA model" section, the instrumental method of measuring efficiency is discussed intensively. The literature on the structure of efficiency growth is combed in the "Research on the CEECI" section. Finally, this literature is briefly summarized and reviewed.

Research on CEE
With the increasingly serious climate and environmental problems in the world, scholars at home and abroad have done a lot of research on carbon productivity and CEE and so on. Yamaji et al. (1993) put forward carbon productivity for the first time. And the CEE indicates the amount of carbon dioxide that needs to be emitted when generating each unit of economic output.
Up to now, the research work mainly focuses on using different measurement methods to evaluate CEE. The measurement methods of CEE are mainly divided into single factor measurement method and total factor measurement method. The single factor measurement method regards energy consumption as the only input, which is convenient and quick to compare the CEE of different regions in specific periods, and is widely used by some scholars (Long et al. 2016;Pretis and Roser 2017;Ferreira et al. 2018;Vujović et al. 2018). However, this method has great limitations. The single factor index only considers the impact of energy consumption on economic outputs, ignoring the internal connection with non-energy resources and other production inputs. It cannot fully reflect the multidimensional characteristics of CEE (Jaraitė and Maria 2012). To remedy these defects, Hu and Wang (2006) introduced an index of total factor for the first time to measure the CEE of an economy. Based on a multiinput and multi-output system, they investigated the relationship between multi-factor input and output, including energy consumption, labor, and capital. It made up for the drawbacks of a single index as it more accurately reflected the efficiency levels of regional economic activity and has since been widely used (Cheng et al. 2018a;Zhou et al. 2020).
In addition, scholars have conducted extensive research on various research objects or scenarios of CEE, including spatial differences (Yan et al. 2017b), dynamic changes (Cheng et al. 2018b), carbon emission reduction potential (Yao et al. 2015), and time effects of economic and energy input on regional productivity (Ding et al. 2019).
On the evolution of the three-stage DEA model How to measure the CEE of a region or industry is also hotly debated in current research. During the analysis of inputoutput efficiency, some scholars have adopted the stochastic frontier analysis (SFA) to quantitatively explore the influence of efficiency differences of DMUs. These were based on economic theories to get more accurate results with a set method model (Dong et al. 2013;Cai et al. 2019;Jin and Kim 2019;Sun and Huang 2020). However, not only does the SFA model need to be set in the form of specific functions, but the assumptions must also be relatively strict. When the model is set with inaccuracies, the results after measurement are likely to be biased. But the data envelopment analysis (DEA) does not need to set the mode of production for input factors and output factors. Instead, it objectively calculates the weight of each index based on input-output data which avoids estimation bias caused by either the wrong settings of the parameter model or subjectivity. These methods have been recognized by most scholars and have been widely applied in research including the energy efficiency, enterprise performance (Yan et al. 2017b;Wu et al. 2018), and thermal power industry CEE (Yan et al. 2017a).
The above research methods have ignored the influence of environmental factors and random interference. When the DMUs are in different external environments, using the traditional DEA model ignores the input-output slack and leads to interference by non-managerial factors. The traditional DEA model may make different environments and luck further affect the authenticity and accuracy of the estimation results due to the difference in selection of research objects (Li et al. 2020). With this in mind, Fried et al. (2002) proposed a three-stage DEA method further based on both the SFA method and the traditional DEA model. The three-stage DEA model puts each DMU in the same environment, overcoming the influence of environmental factors and random interference, all of which makes the measurement results more exact.
At present, the three-stage DEA model had been widely applied in the manufacturing industry (Li and Lin 2016), the iron and steel industry (Xu and Lin 2016), the transportation industry (Cui and Li 2014), and other industries. It displays the superiority and accuracy of efficiency assessment. However, the three-stage DEA model is still seldom used in the construction industry. Based on the above analysis, this paper uses the three-stage DEA method to evaluate the CEECI in 30 Chinese regions from 2006 to 2017.

Research on the CEECI
As for the growth structure of CEE, most scholars think that it is mainly dominated by technological progress, and there are obvious spatial differences. Ding et al. (2019) found that under the constraints of energy, resources, and environment, the performance of regional economic growth was mainly driven by technological progress. Cheng et al. (2018b) found that although upgrading and optimizing industrial structure is beneficial to reducing carbon intensity, the most important thing in China is technological progress. Yan et al. (2017b), based on spatial autocorrelation analysis, think that the CEE has unbalanced spatial distribution, and the efficiency of eastern region is relatively high, which tends to have positive spillover effect on neighboring provinces. It is not known whether the same rule exists in the construction industry.

Summary of literature
Generally speaking, the abovementioned documents provide important reference value for this study, but there is still room for further expansion. First of all, as far as the three-stage DEA and Tobit models are concerned, few scholars in the existing literature have applied these two methods to the construction industry. In addition, no scholars have systematically studied the internal and external factors of CEECI. Secondly, on the application of DEA in construction industry, most of the existing literature focus on the measurement and analysis of CEE, and few scholars consider the growth structure of efficiency and analyze the root causes of the problems. Therefore, this study aims to fill the important gaps in this literature.

Model construction
The three-stage DEA model was applied to calculate the input and output of non-radial slacks for DMUs, eliminating the influence of external environmental factors and random interference, which measure the CEECI more accurately. In the first stage, the input-oriented DEA-BCC model was used to calculate the CEECI under the influence of external environment and random factors. In the second stage, the SFA model was constructed by taking the slacks of inputs obtained in the first stage as explained variables and environment variables as explanatory variables. This eliminates the influence of nonmanagement factors, including external environment and random factors, and obtains the input variables after adjustment of the construction industry in the regions. In the third stage, adjustments were made to the input variables used in the input-oriented DEA-BCC model. In this step, the CEECI was recalculated but did not include the environmental variables and the random factors, which made the efficiency values more real and accurate. Referring to Zhao et al. (2019), the analysis framework is shown in Fig. 1.

The first stage: the traditional DEA model
The BCC model proposed by Banker et al. (1984) is based on CCR model. It further decomposes the CEECI into the PCEE and SE under the hypothesis that variable returns to scale (VRS) change. In the meantime, compared with the CCR model, the BCC model eliminates the influence of scale factors and evaluates the management and decision levels of DMUs more accurately. In terms of the construction industry, it is much easier to control input than output. Therefore, this paper chooses the input-oriented DEA-BCC model, as shown in Model 1: Each province is regarded as a DMU when the CEECI is calculated. If there are n provinces, denoted as DMU j (j = 1, 2, 3……n), each DMU has m inputs and n outputs. The weight of input is expressed as v i (i = 1, 2, 3……m), and the weight of output is expressed as u r (r = 1, 2, 3…… s). The input vector and output vector of the DMUs are expressed as X j (x 1 j , x 2 j , x 3 j , ……x mj ) T and Y j (y 1 j , y 2j, y 3j, ……y sj ) T . θ denotes the efficiency value of DMU, and ε denotes the non-Archimedean, which is less than any positive number but greater than zero. In general, it is 10 −6 . S − and S + represent the slack variables of inputs and outputs, respectively.λ j represents the weight coefficient of inputs and outputs.

Inputs Outputs
The input -oriented DEA -BCC model  When the efficiency of decision-making units is evaluated, the traditional DEA model postulates that the greater the output, the higher the efficiency will be. However, when the CEECI is calculated, it contains not only the expected output but also the non-expected output such as carbon dioxide emissions. So, it is not appropriate to directly use the traditional DEA model. Therefore, it is necessary to transform undesired output into expected output. Refer to the method of linear data transfer function proposed by Seiford and Zhu (2002) to convert the variable of carbon emissions into the expected output. The specific method is as follows: where E ij represents the carbon emissions of the desired output after the adjustment; E ij indicates the carbon emissions of undesired output; and max(E i ) indicates the largest annual carbon emissions.

The second stage: the SFA model
In the second stage, the slack variables of the inputs are viewed as the explained variables from the first stage. Meanwhile, the environment variables are viewed as the explanatory variables. Then, the SFA model is constructed as follows to eliminate the non-management factors: Z j is the environmental variables; β i is the coefficient of the environment variables; V ij + μ ij is the mixed error; V ij represents the random interference; and μ ij represents the management inefficiency.
In order to have every DMU in the same environment, it is necessary to eliminate the influence of environmental factors and random interference on the CEECI. The adjusted formula is as follows: where X ij A is the input after adjustment, X ij is the input before adjustment, and max f Z j cates that all DMUs are put at the same environmental level.

The third stage: the adjusted DEA model
The adjusted input-output variable is used to calculate the efficiency value through the DEA-BCC model. At this time, the efficiency value does not include the environmental factors, random interference, and other non-managerial factors. Thus, it is more real and effective.

Input and output variables
(1) Input variables. The three variables of capital, labor, and energy are chosen (Zhao et al. 2019;Yao et al. 2015;Zhou et al. 2013). As for the index of capital input, there are differences in the measurements of capital stock in academic circles, and it is difficult to obtain the depreciation rate of fixed assets in the construction industry in China. Therefore, we choose the depreciation value of fixed assets in the construction industry directly as the index of capital input. As for the factors of labor input, the number of employees in the construction industry is selected as a measure of the input of labor in the construction industry.
With regard to the indicators of energy input, the construction industry consumes from a great variety of energy sources; according to Cheng et al. (2018a), this paper selects eight kinds of energy consumption including raw coal, coke, gasoline, kerosene, diesel oil, fuel oil, liquefied petroleum gas, and natural gas.
(2) Desired output. Based on the discussion of Cheng et al. (2018b), this paper adopts gross construction output to measure the expected output. Based on the calculation method provided by the IPCC, the calculation method of carbon emissions in the construction industry is established as follows: I and J represent the year and region; E (ij)1 represents the direct carbon emissions; E (ij)2 represents the indirect carbon emissions; r represents the type of fossil fuel; E represents the consumption of fossil fuel; and NCV, CEF and COF represent the low calorific value, the carbon content, and the rate of carbon oxidation, respectively. The product of three variables represents the carbon emission coefficient. These are shown in Table 1. G represents the amount of building materials such as cement, steel, wood, aluminum and glass; ε r represents the coefficient of carbon emissions per unit of building materials, and α r represents the recovery coefficient of building materials, which refers to the research of.

The external environmental variables affected by non-management
The external environment should satisfy the hypothesis of separation. It means that they have an impact on the CEECI, but are not subject to the subjective control of the development of that industry (Simar and Wilson 2007). As to the features of CEECI, based the discussion of Zhao et al. (2019) and Zhou et al. (2020), this paper chose environmental variables affecting the CEECI from five aspects; these include the GDP, the level of industrialization, the degree of opening to the outside world, technological innovation, and energy structure. At the same time, the indicators are measured, respectively, by the ratio of the GNP, the added value of the tertiary industry to GDP, the total import and export volume, the number of patent applications, and the ratio of the electricity consumption to the total energy consumption.  Table 2.

Empirical analysis
The comprehensive CEECI of the traditional DEA model in the first stage  Lu et al. (2015). Secondly, the comprehensive CEECI is constantly increasing, which is increased from 0.792 in 2006 to 0.844 in 2017. Thirdly, during the period from 2006 to 2017, the comprehensive CEECI in six provinces was lower than 0.7, including Xinjiang, Shanxi, Shandong, Yunnan, Gansu, and Inner Mongolia. Taking Inner Mongolia as an example, it can be seen that the comprehensive average CEECI in Inner Mongolia is only 0.564, far below than the national average.
In order to further analyze the comprehensive CEECI in different regions of China, 30 provinces are divided into 7 regions according to the geographical location which was described in Fig. 2.
First of all, the average comprehensive CEECI in various regions is relatively high. And on the whole, it is in a rising trend of fluctuation. Secondly, the average comprehensive CEECI in South China and East China is higher than that in North China, Central China, Northeast China, Southwest China, and Northwest China. It is indicated that the comprehensive CEECI in developed provinces is generally higher than that in underdeveloped areas. Thirdly, the comprehensive CEECI in South China and East China showed a steady upward trend from 2006 to 2016. However, the comprehensive CEECI in North China, Northeast China, Central China, Northwest China, and Southwest China showed an obvious fluctuating upward trend after falling to the lowest value in 2011 or 2012. It is shown that the policy effect of improving energy efficiency is obvious, which is from the central and local governments of China.
In order to improve the authenticity and reliability of the results, it is necessary to further eliminate both the influence of different environmental factors and random interference and make further analysis on the CEECI.    H e i l o n g j i a n g 1 1 1 1 1 1 0 . 9 7 5 0 . 7 3 7 0 . 8 2 5 0 . 9 3 8 0 . 9 1 5 1 0 . 9 4 9 E a s tC h i n a S h a n g h a i 1 1 1 1 1 0 . 7 9 9 0 . 6 6 1 0 . 6 8 2 0 . 8 2 1 0 . 8 6 9 0 . 9 1 2 0 . 9 5 4 0 . 8 9 2 J i a n g s u 1 1 1 1 1 1 1 1 1 1 1 1 1 Z h e j i a n g The SFA regression analysis at the second stage In the second stage, the slacks of the three inputs of construction industry were taken as the explained variables; these were calculated by the traditional DEA model in the first stage. At the same time, five environmental variables were selected as the explanatory variables. The SFA model was constructed to eliminate the influence of external environmental factors and random interference on input relaxation variables. The original inputs were adjusted. According to the estimated SFA results in Table 4, the γ of the three SFA models all passed the significance test at the 1% level, indicating that the selection of environmental variables is reasonable. At the same time, the one-tail error of LR passed the significance test of 1% in the three SFA models, which demonstrates that it is appropriate and necessary to eliminate the influence of environmental variables with non-management factors when the CEECI is investigated. When the impact of environmental factors on inputs is analyzed, the positive coefficient of environmental factors indicates that increasing the value of environmental factors will lead to an increase in input slacks. This situation means that when the degree of utilization of the construction industry inputs is reduced, it will not be conducive to improvements in CEECI.
It can be seen from Table 4 that when the level of economic development is improved, the input slacks of energy  Notes: ***, **, * denote the level of significance at 1%, 5%, and 10%, t-value is in parentheses consumption in the construction industry and the fixed asset depreciation will be significantly increased. This indicates that improvements in the level of economic development will increase the degree of relaxation of energy consumption and capital input. It means that the effective utilization of inputs will be reduced, which is not conducive to improvements in the CEECI. The level of industrialization has a significant negative effect on the slacks of energy consumption and capital but has a significant positive effect on the slack of labor. This indicates that with improvements to industrialization levels, the slacks of energy consumption and capital in the construction industry decrease, which is conducive to the improvements of CEECI. However, when the level of industrialization is improved, the slacks of labor input will increase, and resources will not be fully utilized, which is not conducive to the improvement of the CEECI.
There is a significant negative correlation between the input slacks of technical level and labor, which indicates that with the improvements in technical level, the input slack of labor will decrease and the degree of resource utilization will increase. At the same time, the increase of technical level is conducive to increasing the total output value of the construction industry, reducing the emission of air pollutants, and improving the production efficiency of the construction industry. Therefore, it has a positive impact in improving the regional technical level for the CEECI.
The degree of opening to the outside world has a significant negative correlation with the input slack of energy consumption in the construction industry. However, the input slacks of labor and capital fail to pass the correlation test. This indicates that as the degree of the opening to the outside world is increased, there is a decrease in the slack of energy consumption in the construction industry, which is conducive to improvements in CEECI.
There is a significant negative correlation between the input slacks of energy consumption structure and energy consumption and capital in construction industry. It indicates that, with the optimization of the energy consumption structure, the input slacks of energy consumption and capital in the construction industry gradually decrease, which is beneficial to the improvement of CEECI. The improvement of energy structure is conducive to reducing the emission of air pollutants. In addition, the capital investment for controlling the emission of pollutants will be correspondingly reduced. Therefore, it will have a beneficial impact on improving the CEECI.
From the above analysis, it can be seen that environmental factors have different influences on input relaxation, which makes the construction industry in different regions of China in different environments. Therefore, it is necessary to eliminate the influence of non-management factors and adjust the input variables to face the same environment.
The empirical results of the DEA model with the adjusted inputs at the third stage Table 5 lists the real CEECI in 30 provinces of China after excluding the influence of environmental factors and random interference. Firstly, the real CEECI in Jiangsu, Zhejiang, and Hainan is higher than that in other provinces. And their efficiency value is 1. However, the real CEECI in Sichuan Province is far lower than that in other provinces, which is 0.752. This shows that although the interference of external environmental factors has been eliminated, there are still regional differences in CEECI. It is due to uneven regional development. Secondly, the real CEECI in Chinese provinces with higher economic development level is higher than that in underdeveloped areas. There are obvious regional differences between them. The reason may be is that different regions in China are in different stages of economic development, so the energy, capital, and labor inputs consumed by the construction industry are quite different. Although the economies of South China and East China are relatively developed, which need to consume more energy, they are relatively higher in technology and have less unexpected output such as air pollutants. Therefore, the comprehensive CEECI is higher.
The Gaussian kernel is used to estimate the time evolution of CEECI, as shown in Fig. 3. Firstly, from the position of variable distribution, the CEECI takes 2010 and 2013 as the boundary, showing a trend of first moving to the left and then moving to the right. This situation demonstrates that the overall level of CEECI decreased and then increased, showing a fluctuating upward trend. There is no obvious change in the right skewed distribution pattern of each efficiency, which indicates that the CEECI is still mostly in high efficiency areas. Secondly, the number of peaks consists of one main peak and one side peak, which gradually evolves into one main peak, showing that the CEECI gap is gradually decreasing. Thirdly, the number of peaks was one side peak to the left of a main peak and evolved into a main peak gradually. It shows that the phenomenon of multi-polarization of CEECI is reduced.

Comparison of comprehensive and real CEECI
A comparison of Tables 3 and 5 indicates three points. Firstly, compared with the first stage, the CEECI has obviously improved from 0.809 to 0.936, which has increased by 16%. It shows that the external environment of Chinese construction industry has significant potential for improvement. Secondly, the average CEECI in North China, Northeast China, East China, Central China, South China, Southwest China, andNorthwest China increased by 18.49%, 18%, 8.18%, 15.15%, 6.78%, 21.75%, and27.1%, respectively, from 2006 to 2017. This shows that environmental factors and random interference underestimate the CEECI. At the same time, it is confirmed again that an analysis of the SFA model is necessary and meaningful in the second stage. Figure 4 compares the comprehensive and real CEECI in 30 provinces. According to Fig. 3c, it can be found that after removing the influence of environmental factors and random interference, the rankings of 10 provinces have risen significantly. Among them, Ningxia, Xinjiang, Gansu, Inner Mongolia, Guizhou, and Shaanxi have increased their rankings by more than five. Most of these areas are located in Northwest and Southwest China. Because these provinces have relatively weak economic development, technological innovation and energy structure and other external environment, their CEECI is relatively low. Take Inner Mongolia as an example, according to the China Construction Industry Statistical Yearbook, the average annual energy consumption of the construction industry in Inner Mongolia was 161.71 ten thousand tons of standard coal between 2006 and 2017, which is much higher than the national average of 106.43 ten thousand tons of standard coal in the construction industry. There is a large energy input in the construction industry of these areas. And the long-term coalled energy structure has hindered the construction industry from transforming into a green, energy-saving intelligent building industry. At the same time, the economic development in Northwest and Southwest China is relatively backward. It is less attractive to high-quality talents in the construction industry, which leads to the low quality and weak technology of the frontline operators in the construction industry. N o r t hC h i n a B e i j i n g 0 . 8 8 4 0 . 9 5 6 0 . 8 9 6 0 . 9 4 5 0 . 9 7 6 1 1 1 1 1 1 0 . 9 9 8 0 . 9 7 1 T i a n j i n 1 1 1 1 1 0 . 9 0 4 0 . 9 0 7 0 . 8 1 9 0 . 9 0 9 0 . 9 8 1 0 . 9 9 5 0 . 9 3 5 0 . 899 H e i l o n g j i a n g 1 1 1 1 1 1 1 0 . 9 8 2 0 . 9 9 3 0 . 9 9 9 1 1 0 . 9 9 8 E a s tC h i n a S h a n g h a i 1 1 1 1 1 0 . 9 2 1 0 . 8 3 9 0 . 8 3 0 0 . 9 4 1 0 . 9 2 3 1 1 0 . 9 5 5 J i a n g s u 1 1 1 1 1 1 1 1 1 1 1 1 1 Z h e j i a n g G u a n g x i 0 . 9 9 6 0 . 9 9 6 1 1 1 1 1 1 1 1 1 1 0 . 9 9 9 H a i n a n Therefore, it is difficult to improve CEECI from environmental factors such as economic development, energy structure, and technological innovation. On the contrary, after excluding the environmental factors, the CEECI in Fujian Province dropped by 13 ranks. It is the province with the largest decline. This shows that Fujian has created an external environment conducive to the green development of the construction industry. This shows that Fujian has created an external environment, which is conducive to the green development of the construction industry. Fujian Province has successively promulgated a number of policies and regulations such as the Green Building Development Regulations in Fujian Province. And the Fujian Province continues to optimize the industrial structure and takes smart construction as a new direction for the development of the construction industry. During the "13th Five-Year" Plan (2016-2020) period, Fujian Province has completed a total output value of 5.6 trillion yuan in construction industry, an average annual growth rate of 12%, which is among the highest in the country. As a result, the CEECI in Fujian decreased from 11 in the first stage to 24 in the third stage. It is indicated that the external environment has a significant effect on improving the CEECI in Fujian.

Decomposition of the real CEECI
In order to further analyze the reasons for the change of the actual CEECI, it is decomposed into pure technical efficiency and scale efficiency. The PCEE removes the impact of economies of scale and reflects how to use production technology to maximize the expected output of the construction industry, and it reduces the emission of air pollutants. The scale efficiency (SE) indicates the effective degree of economies of scale. Figure 5 shows the real CEECI, PCEE, and SE trends of the construction industry in 30 provinces and seven regions of China. It can be found that the change trend of SE is most similar to the real CEECI. This shows that the CEECI is mainly determined by SE. Taking Northeast China as an example, SE in Northeast China dropped to the lowest value in 2012. Although PCEE increased slightly, the real CEECI was closest to SE, and the lowest value during the study period occurred in 2012. Similarly, the SE in the Southwest is similar to the real CEECI, showing obvious fluctuation and rising trend. Compared with PCEE, SE in Chinese seven major regions are relatively small, which is in the increasing returns to scale stage. It is necessary to accelerate the development of green and energy-saving intelligent construction industry, reduce the emission of building pollutants, improve the efficiency of carbon emission in construction industry, and develop economies of scale. After 2013, PCEE showed an obvious upward trend. Among them, the PCEE in South China remained at 1 from 2011 to 2017. It is worth noting that in May 2011, the Chinese government promulgated the Outline of Construction Industry Informatization Development from 2011 to 2015, which may continue to promote the transformation of Chinese construction industry to informatization and intelligence. This has had a powerful impact on PCEE in the construction industry.
In order to further study the inter-provincial differences in CEECI, the average PTE of 0.966 and the average SE of 0.968 were taken as the critical points of efficiency. Meanwhile, the PTE was classified into four categories: "High-High," "Low-High," "High-Low," and "Low-Low," as shown in Fig. 6. The first category is the type of "High-High." It mainly includes 11 regions in Beijing, Zhejiang, Jiangsu, Hainan, Jiangxi, Heilongjiang, Chongqing, Shaanxi, Guangxi, Ningxia, and Guizhou. The PCEE and SE of the construction industry in these areas are relatively high, reaching more than 0.96. It indicates that the scale of resource allocation for construction industry carbon emissions is reasonable in these regions, and the level of management and decision-making for inputs is high, which makes the comprehensive CEECI higher. However, the PCEE of Chongqing and Shaanxi is relatively low, which is located at the bottom of area "High-High." Compared with Jiangsu and Hainan, there is still room for improvement.
The second category is "Low-High." The PCEE is high, but the SE is lower than the national average of 7 provinces, including Shanghai, Tianjin, Guangdong, Hebei, Fujian, Jilin, and Qinghai. These provinces should focus on improving the scale economy of construction industry. Especially in Hebei, Jilin, and Fujian provinces, the SE is far lower than the national average level of 0.968. In addition, the SE in Tianjin is 0.966, which needs to be increased by 2.1% to enter the "high and high" region. Therefore, it is necessary to focus on improving the SE of the construction industry, raising the level of resource allocation and making it achieve economies of scale. Only in this way can these provinces improve the green development level of the construction industry.
The third category is the "High-Low," which includes Shandong, Liaoning, Anhui, Hunan, Hubei, Xinjiang, Yunnan, and Gansu. The value of SE is high in these areas, and there is a big gap between the value of PCEE and the national average. The value of PCEE in Shandong province is 0.892, which is the lowest in China. Therefore, these provinces need to intensify innovation. At the same time, the lever of information technology in the construction industry should be improved to develop green and energy-saving intelligent buildings. Furthermore, provinces in these regions need to further improve the level of management relating to the inputs and decision-making effectiveness of the construction industry. These measures can improve the CEECI.
The fourth category is the type of "Low-Low," which mainly includes Henan, Shanxi, Sichuan, and Inner Mongolia. The overall level of CEECI in these parts is low, and both PCEE and SE have some space for improvement in varying degrees. This may be caused by the characteristics of Fig. 6 The decomposition of real CEECI in different regions resource endowment. According to the data of China Energy Statistics Yearbook, the energy consumption input of construction industry in Henan, Shanxi,Sichuan,and Inner Mongolia is 127.23,108.89,154.18,and 161.71 ten thousand tons of standard coal, respectively. This data is much higher than the national average of 106.43 ten thousand tons of standard coal. It is necessary to optimize the energy structure of construction industry and increase the use of clean energy, which is consistent with the research conclusion of Zhang et al. (2017). In addition, these provinces are located in the Central, Southwest, and North China, which have a low level of economic development and technology. They contribute less to the CEECI. Therefore, both SE and PCEE need to be further improved, which can promote the improvement of CEECI.

Analysis of the internal influencing factors of the CEECI
In order to further analyze the internal factors affecting the CEECI, this paper excludes the influence of external environmental factors and random interference, taking the real CEECI, PCEE, and SE of the third stage as dependent variables and selecting the level of development (Ind), the energy structure (Energy), the amount of labor (Labor), the total power of construction machinery and equipment (P), and the construction intensity of construction industry (Cci) as influencing factors. Taking the added value of construction industry, the ratio of coal consumption to total energy consumption in the construction industry, the number of laborers in the construction industry at the end of the year, the total power of selfowned construction machinery and equipment at the end of the year, and the ratio of construction area to added value in construction industry as specific indicators, the stochastic Tobit model is constructed as follows: where i and t represent the index value of enterprise i in the first year; β 0 is the constant; β 1 − 5 is the coefficient that is estimated for each influencing factor; and ε it is the random interference. See Table 6 for the estimated results.
By observing Table 6, it can be found that the development level of the construction industry has a significant positive effect on the CEECI, PCEE, and SE of its carbon emissions.
It indicates that the higher the development level of the construction industry, the higher its CEECI will be. One possible reason is that the higher the development level of the construction industry, the higher the technical level of carbon emissions. The reason is that increasing the development level of the construction industry will improve the technical level of carbon emissions to a certain extent, which is conducive to the economic development in an efficient and low-carbon way. However, the energy structure, the number of workers, the total power of construction machinery and equipment, and the construction intensity of construction industry can inhibit the CEECI, PCEE, and SE of carbon emissions in construction industry. A possible reason is that when the construction industry needs more and more labor, its labor-intensive characteristics are more obvious. The degree of science and technology is correspondingly lower, which may inhibit the improvement of CEECI. When the total power of construction machinery and construction intensity in the construction industry is greater, the demand for energy is greater. This situation means that the more greenhouse gases, such as carbon dioxide, are produced, the lower the CEECI will be when the technical level of carbon emissions is limited.

Enlightenment
(1) Firstly, government decision-makers should refer to the real CEECI after excluding the external environment and random interference items, so as to make more effective policies and regulations. Due to the different external environments such as the economic development, technological innovation, and energy structure of various provinces in China, the traditional DEA model cannot eliminate the differences in the external environment of the construction industry. As a result, the CEECI in each province does not match the actual situation. Therefore, government departments should base their decisions on the actual CEECI. At the same time, taking into account the differences in the external environment of various provinces, the government scientifically formulates relevant policies to improve the CEECI and promote the green development of the construction industry.
(2) The external environment must be ameliorated to improve the CEECI. First, enterprises should both optimize the energy consumption structure of the construction industry and increase the technological development of the construction industry, so as to both improve the production technology of building materials and the transformation mechanism of low-carbon science and technology. In addition, green building materials and clean energy sources such as nuclear power and wind energy will be developed. By developing high technology, the energy consumption structure can be optimized and upgraded and the CEECI improved. Second, the provinces should exchange and learn more about the concept of lowcarbon and efficient production and management in the construction industry. The central and western regions of China should take the initiative to learn the carbon emission technology and advanced management systems and concepts of the construction industry in the Eastern region. It can reduce the differences and imbalances in regional development. Third, we should strengthen the degree of opening to the outside world and introduce foreign advanced carbon emission technologies. It can promote the spillover effect of knowledge and technology and improve the overall level of CEECI, so as to better cope with international emission reduction targets.
(3) The differences in CEECI should be considered fully and relevant policies in a targeted manner formulated. Firstly, the PTE and SE are the type of "Low-Low" areas represented by Henan, Shanxi, and Sichuan. These areas should strengthen innovation in management concepts and reform management systems. At the same time, the scale benefits of the construction industry should be noted, so as to promote the development from disorder to standardization and from dispersion to intensive. Secondly, the type of the "Low-High" areas represented by Shanghai, Tianjin, Guangdong, and so on has lower CEECI caused by lower SE. For the areas, attention should be paid to large-scale development, but the more urgent task in the type of "High-Low" is to strengthen innovation of management systems and methods which can promote the efficient development of carbon emissions in the construction industry. Thirdly, Beijing, Zhejiang, Jiangsu, and other "High-High" areas are ideal in terms of PTE and SE. However, it is still necessary to continue to strengthen the management innovation of carbon emissions input resources in the construction industry on the existing basis. At the same time, there should be a strengthening of the industrialization and intensive development of the construction industry in order to improve economies of scale.

Conclusion
The traditional DEA model ignores the influence of environmental variables and random interference terms, which may lead to deviations in CEECI. Therefore, this paper adopts a three-stage DEA model to eliminate those environmental variables and random interference affected by non-management factors. It more accurately measures the CEECI in 30 regions of China from 2006 to 2017. The influencing factors of CEECI are analyzed using the Tobit model and the conclusions are summarized as follows: (1) The CEECI will indeed be affected by external environmental variables. After excluding environmental variables and random interference, the average CEECI increased by 16%. This verifies the existence of environmental factors and random interference. The CEECI was underestimated in the traditional DEA model. (2) There are regional differences in CEECI. The CEECI in South China, East China, and Northwest China is higher than that in North China, Northeast China, Central China, and Southwest China. However, with the development of time, both the multi-polarization phenomenon of CEECI and the regional development gap are reduced.
(3) The real CEECI is decomposed into PCEE and SE. It is found that the CEECI is mainly determined by SE. At the same time, according to the national average level of PCEE and SE, 30 Chinese provinces are divided into four categories, and each group has specific methods to improve the CEECI. (4) Considering the influence of external environmental variables on input slacks, the estimation results show that the level of economic development, the technological innovation, the degree of opening-up, and energy structure have a significant positive impact on the CEECI. In addition, with improvements in industrialization, the slack of energy and capital in the construction industry decreases. This promotes improvements in CEECI, although it may lead to increasing slack in labor investment, which, in turn, has an inhibitory effect on the CEECI. (5) According to the internal influencing factors of CEECI, the energy structure, the number of workers, the total power of construction machinery, and the construction intensity of the construction industry can inhibit the CEECI, PCEE, and SE of carbon emissions in the construction industry with the development level of the construction industry having a significant positive effect on it.
According to the analysis results, relevant policy suggestions are put forward: Government decision-makers should (1) take the real carbon emission efficiency of Chinese construction industry CEECI as the main decision-making basis; (2) optimize the external environment and improve the CEECI; and (3) fully consider the differences in CEECI and formulate relevant policies to improve the CEECI.
The research conclusion of this paper is consistent with that of most scholars. It is believed that the efficiency is surely affected by the external environment. After the three-stage DEA model is used to eliminate the influence of external environment, the CEE will increase or decrease (Zhang et al. 2017;Li and Lin 2016;Chen et al. 2016). And there are obvious spatial differences, which show that the CEE in the eastern region is higher than that in the central and western regions (Ding et al. 2019). In addition, most scholars believe that CEE is mainly dominated by technological progress (Cheng et al. 2018b;Yan et al. 2017b). However, this paper thinks that the CEECI is mainly determined by scale efficiency, which may be related to the characteristics of construction industry itself. Generally speaking, there are still some shortcomings in this paper. As far as the research object is concerned, limited by the availability of data, this paper selects the provincial data of China and does not use the more microscopic data of prefecture-level cities. In the future, we can try to study the CEECI at a more microscopic level. In addition, in terms of research methods, although the three-stage DEA model is used in this paper to avoid measurement errors to the greatest extent, there are no further revision and innovation when dealing with unexpected output. And the linear function transformation method is used to transform the unexpected output into expected output. Future research may consider adopting directional distance function and other methods for further innovation.