Research on the influence of environmental regulation on the total factor energy efficiency of China’s construction industry

In order to reduce the global carbon emission pressure and improve the energy efficiency of the construction industry, this paper establishes the Un-Super-SBM model to measure the total factor energy efficiency of the construction industry in China, which based on the 2012–2019 Chinese provincial panel data with CO2 emissions as the non-desired output, and uses the panel data model to empirically analyze the impact of formal and informal environmental regulations on the energy efficiency of the construction industry. The results show that, from the national level, the impact of formal environmental regulation on energy efficiency of the construction industry shows an inverted U-shaped trend of promotion followed by inhibition, while the impact of informal environmental regulation on energy efficiency of the construction industry shows a U-shaped trend of inhibition followed by promotion. From the regional level, there are regional differences in the impact of formal and informal environmental regulations on the energy efficiency of the construction industry. Finally, the paper puts forward relevant policy suggestions to promote the improvement of energy utilization efficiency of China’s construction industry and achieve sustainable development.


Introduction
Along with the social and economic progress of China, energy utilization and ecological issues have been gradually exposed. The rough economic development has caused some degree of ecological pollution (Zhang and Cheng 2009), and the conflict between sustainable economic development and energy and environment has been growing prominence, and the world is facing challenges such as climate change and energy crisis (Y Zhao et al 2022b). Due to the scarcity of energy, the non-exclusivity of environmental products and the negative externalities of environmental pollution, market failure occurs from time to time (Yuan Hong et al 2020), and the 'invisible hand' of the mark et al one cannot entirely resolve the environmental pollution problem, which also constraints the sustainable development of society (Fan et al 2021). Therefore, there is a need for a guiding, regulatory system or guidelines from the government, thus compensating for market failures. The Paris Agreement has raised actions to respond to global climate change and objectives for 2015 (Bodansky 2016, Rogelj et al 2016. The agreement is binding on countries' carbon emissions behavior (Tollefson 2018). The report at the 19th National Congress of the Communist Party of China states that we ought to insist on the harmonious coexistence of man and nature and develop a green development and lifestyle (Jinping Xi 2017). In 2020, The Fourteenth Five-Year Plan puts forward new goals such as remarkable green transitions of production and lifestyle, substantial increase in energy utilization efficiency, and sustained decrease in pollutant emissions (Project synthesis report preparation team 2020). In the 'Fourteenth Five-Year 'National Cleaner Production Implementation Plan released in November 2021, it is also pointed out that the target is to save energy conservation and consumption reduction, reduce pollution and carbon, and improve quality and efficiency. It is thus clear that environmental regulations are being implemented with more stringent.
The construction industry is a typical resource-intensive enterprise with high energy consumption, which is a key field for energy conservation and carbon reduction. The issue of energy efficiency is a key constraint to sustainable development and is receiving increasing academic attention. For instance, Adedoyin et al (2020) argues that BRICS economies are achieving environmental sustainability by decoupling CO 2 from GDP. Borozan (2018) found that most EU regions are inefficient in terms of technology and energy efficiency. Jebali et al (2017) analyzed the energy efficiency of Mediterranean countries. Hou (2018) found that Chinese industry has significantly reduced pollution emissions by making a green transformation. Yang (2019) addresses concerns about urban energy efficiency and provides a comparison and analysis. In addition, some scholars have also put forward corresponding energy policy recommendations, arguing that the government should strengthen the regulation of energy efficiency (Lin and Zheng 2017), establish policies to support and develop technologies that reduce or recycle emissions Moon and Min (2017), or specify incentives and penalties (Trotta 2020). There is a certain relevance between energy efficiency and environmental regulation, and how to improve energy efficiency in the building sector under the influence of environmental regulation is something we need to look into and explore.
In this paper, under the background conditions of ecological civilization construction, the Un-Super-SBM model is established based on the theory of total factor energy efficiency and relevant data from 30 provinces across China. The energy efficiency of the construction industry including unexpected output is measured, and a panel data model is also developed to empirically analyse the implication of environmental regulations on energy efficiency in the construction industry. The results of the research can provide a basis for relevant departments to develop appropriate regulation policies and set reasonable emission reduction targets, which is of vital significance to accomplish the win-win situation of economic development and environmental protection as well as sustainable development. The figure of the technical route of the study is shown in figure 1.

Literature review
There are two main types of environmental regulation: formal environmental regulation(abbreviated as FER) and informal environmental regulation(abbreviated as IER). Among them, FER is government-led environmental protection strategies, mandatory interventions and constraints on enterprises' production activities, and measures taken to reduce pollution. Pargal and Wheeler (1996)] first introduced IER, argues that when government-imposed environmental regulation is weak, self-organized groups emerge to initiate actions to protect the ecological environment in order to defend their personal interests; common initiatives include non-government-led product boycotts and press disclosures of environmental pollution information. Based on different understandings of environmental regulation, the selected measures in the study of environmental regulation measurement are not uniform. The government can implement FER through policies such as collecting environmental taxes and setting emission standards as a way to reduce production inputs of enterprises and thus reduce pollution emissions (Chen andZhang 2012, M Greenstone et al 2012). IER can also be measured by input indicators such as pollution discharge fees, environmental protection related financial expenditure and environmental pollution control investment (Testa et al 2014, Naso et al 2017. Fredriksson and Millimet (2002) analyzed the strategic interaction and environmental policy formulation of each state in the United States, measured and formulated standards with formal environmental regulation cost input indicators. Ying Tian and Chao Feng (2022) divided environmental regulation into different types. The study found that there was an obvious non-linear relations between various environmental regulation and the internal factors of China's green total factor productivity.
The measurement of energy efficiency(abbreviated as EE) is well researched in academia. Charmes et al (1978) proposed the concept of data envelopment analysis (DEA). This model was originally used to assess the relative effectiveness of interdepartmental, and was also called DEA-CCR model, which can measure multiple input and output indicators. Patterson (1996) believes that the measurement indicators of EE can be classified into four main categories, namely, thermodynamic indicators, physical thermal indicators, economic thermal indicators and pure economic indicators. Farla and Blok (2001) used energy intensity as an indicator to calculate the changes in EE of steel industry in China, Brazil, France, Germany, Poland, the United States and Japan from 1980to 1991. Wasi Ul Hassan Shah et al (2022 used the DEA-SBM model to calculate the EE in each province and analysed the production technology gap in all parts of China.However, the article does not provide an indepth analysis of the factors affecting EE Paramati et al (2022) analyzed using data from 1990-2014 and the results of the study showed that environmental technologies contribute to the reduction of energy consumption and increase the overall EE of countries in OECD, but the metrics used in this study to measure EE are relatively limited. Huang et al (2011) used the Super-SBM model to measure the atmospheric EE of 17 cities in Shandong Province from 2008-2018,the results found that economic development, technological innovation and population density have positive effects on EE, while the effects of industrial structure and openness to the outside world are negative. Xie and Zhou (2020) used Super-SBM model to analyze the total factor green EE from the industrial structure and regional perspective, and found that the optimization and upgrading of the secondary industry can help improve green EE. Li et al (2013) used the Super-SBM model under non-expected output was used to measure China's regional EE and to explore the influencing factors of China's EE from 1991 to 2001. The results show that the overall average level of China's EE is low, with large differences among provinces and regions. However, the above studies focused on industrial triple waste or SO 2 , NO x and PM2.5 as an undesired output and did not provide a method to calculate CO 2 production or measure the amount of CO 2 produced by specific energy consumption.
Different scholars hold different views on the influence of environmental regulation on EE, and there are three main views as follows: first, environmental regulation will have an inhibiting or promoting effect on EE; second, the relationship between the two is uncertain, not necessarily always promoting or inhibiting; third, the relationship between the two is related to external conditions, and its ultimate impact will vary due to different regional development, different industries, and different resource endowments. The National Research Council and EP Agency (1977) in their book 'Implications of Environmental Regulations for Energy Production and Consumption' state that the role played by environmental regulation is positive and that the economic benefits it brings are greater than the additional costs paid by companies for it. This was subsequently discussed and verified by many scholars. Kathuria (2007) took India as the research object, indicating that the IER with news reports as the main means had a controlling effect on urban sewage discharge. Lanoie et al (2011) and others analyzed the enterprise data provided by seven OECD member countries.The results of the study prove that reasonable environmental regulation can effectively promote the innovation development of enterprises and thus improve efficiency. Yarabik and Fairchild (2011) studies found that environmental pressure will have adverse effects on enterprise green innovation, and the government's increase in innovation subsidies can effectively increase innovation enthusiasm. Hancevic (2016) studied the impact of clean air amendments on EE and productivity and found that environmental regulations had a dampening effect on productivity, thus it indirectly has a negative impact on EE. The research of Naveedullah and Lefen (2021) focused on the forwardlooking environmental strategy of green innovation. The research has shown the positive moderating effect of environmental regulation in proactive environmental strategies and green innovation. Song and Han (2022) showed that the inhibitory effect of FER on EE is smaller than the promotional effect,and environmental regulations have a greater effect on boosting EE in high level areas. It can be seen that the existing literature is not uniform in its findings on the relationship between environmental regulation and EE.
A review of the above literature reveals the following limitations. Firstly, most of the existing studies analyze the energy efficiency of the whole country, and do not analyze the building industry, which consumes more energy, in detail. Secondly, the existing literature lacks studies on energy efficiency in the construction industry. Second, there is no uniform conclusion on the current research on energy efficiency by environmental regulation, which may be caused by the differences in the metrics of environmental regulation indicators. Thirdly, there is a lack of detailed calculation of the CO 2 generated by specific energy consumption. Finally, for the differentiation of EE in different regions, previous literature lacks the elaboration of specific improvement measures. Therefore,based on previous studies, this paper takes the Chinese construction industry, which consumes large amounts of energy, as the object of study, adds carbon dioxide emissions from energy consumption in the construction industry as a non-desired output to the total factor energy efficiency measurement framework, and adopts a more scientific approach to analyze the impact of formal and informal environmental regulations on energy efficiency in a comprehensive manner. It also explores the ways to improve energy efficiency in the construction industry and makes specific suggestions for the government to make environmental policy adjustments and for enterprises to achieve green and sustainable development, respectively.
3. Methods and data sources 3.1. Un-Super-SBM model The SBM (Slack Based Measurement) model is a non-radial,non-oriented DEA (Data Envelope Analysis) model proposed by Tone (2001), which can effectively address the slackness of inputs and outputs, making the results more accurate and reasonable. Later, Tone further improved on this basis and proposed the super efficiency SBM model (2003), which not only evaluates the efficiency of non-desired outputs, but also allows for further differentiation of efficient decision units.Therefore, this paper adopts the super efficiency SBM (called Un-Super-SBM for short) model containing unexpected output to measure energy efficiency. Suppose there are n decision units, each of which contains inputs, expected outputs, and unexpected outputs. Denote the input matrix is X = (x 1 , x 2 , K, x m ) ä R m×n , the expected output matrix is Y = (y 1 , y 2 , K, y p ) ä R p×n , the unexpected output matrix is Z = (z 1 , z 2 , K, z q ) ä R q×n . The model is constructed as follows.  where s x , s y and s z are the slack vectors of inputs, desired outputs, and non-desired outputs, respectively, and λ j is the weighting factor. The model calculates the efficiency value ρ 1. When ρ = 1, that is, when s x = 0, s y = 0, s z = 0, it implies that the decision unit is effective; when ρ < 1, it implies that the decision unit is non-effective and needs to be improved. The above formula meets the assumption that the return to scale is constant.

Panel data model
To explore the relationship between FER and IER and EE in the construction industry, this paper establishes a panel data model for regression analysis, with logarithmic treatment of the variables, with the aim of eliminating heteroscedasticity (Xu and Xu 2022). Model 1 as shown in equation (1) is established.
In addition, in order to verify whether the effect of environmental regulation on EE is linear, the quadratic term of the intensity of environmental regulation is introduced in Model 1. If the coefficients of the primary and secondary terms are opposite, the relationship between the two is shown to be non-linear, and vice versa is linear.When the coefficients of the primary and secondary terms are positive and negative respectively, the relationship between the two is an inverted 'U' shaped relationship of first promoting and then inhibiting, and vice versa. Model 2 as shown in equation (2) is established.
where β is the variable coefficient, EE it indicates the annual EE of the construction industry by province, FER it and IER it indicate the intensity of formal and informal environmental regulation in each province per year respectively, X is control variables collection, λ is the coefficient, and ε it is the error term.

Indicators for measuring energy efficiency
(1) Input indicators Based on the selection and research of energy efficiency evaluation indicators by scholars such as X. Li (2020), Zhou and Li (2021), Sueyoshi and Goto (2011), and combined with the actual situation of the construction industry and its own characteristics,this paper takes energy, capital, labour and mechanical equipment as input indicators.
(2) Output indicators Most scholars at home and abroad generally divide them into two categories: one is to consider only economic outputs without considering non-desired outputs; the other is to consider both desired and nondesired outputs. In this paper, the latter is used as a reference to select the energy evaluation indicators of the construction industry, and the specific indicator variables explanation are shown in table 1.
Among them, CO 2 emissions from the construction industry are divided into direct and indirect emissions, in which the energy consumed by direct emissions mainly includes 10 kinds of primary energy and two kinds of secondary energy, namely, raw coal, coal, coke, crude oil, gasoline, kerosene, diesel, fuel oil, liquefied petroleum gas and natural gas, and electricity and heat; indirect emissions are CO 2 emissions generated by other industries induced by the construction industry in the production process. The calculation of total energy inputs and CO 2 emissions in this paper only involves the above 10 primary energy sources and two secondary energy sources, and the following CO 2 emission measurement model is established based on the IPCC's CO 2 emission accounting method.
Where E is CO 2 emissions, C m is the energy consumption, α m is average low-level energy heat generation, f m is the default CO 2 emission factor of energy, C h and C e are the heat and power energy consumption, f h is the effective CO 2 emission factor for heat and f e is the effective CO 2 emission factor for electricity in different regionsare the effective CO 2 emission factors of heat and power. According to the established CO 2 measurement model, 30 provinces in China were selected as the research objects to calculate the CO 2 emissions from the construction industry in each region of China between 2012 and 2019, and the calculation results are shown in table 2 below.

Indicators of the panel data model
(1) Explained variables In this paper, energy efficiency is used as the explanatory variable and is denoted by EE.
(2) Explanatory variables In this paper, the intensity of FER can be reflected by the amount of government investment in pollution control. Therefore, this paper draws on the approach of Yantuan Yu and Zhang (2022) and Fabio Iraldo et al (2009) to correct the pollution control cost per unit of output value by the share of industrial output in the province's GNP, and measure the intensity of FER by the corrected value,which is measured by the following formula. Sit, Pit, and Yit are the cost of pollution treatment per unit of industrial output value, the amount of industrial pollution control investment completed, and the industrial output value of each province for each year, respectively. As public awareness of environmental protection is influenced by a variety of factors, a single indicator cannot accurately measure the intensity of IER.Therefore, this paper refers to the indicators and measures used by Pargal Wheeler (1996) and D Zhao et al (2022a) and takes education level, income level of the working population, age structure and population density as indicators, and uses the entropy weighting method to give corresponding weights to these series of indicators for comprehensive measurement. This method can judge the discrete degree of evaluation objects more scientifically and make the evaluation results more objective and reasonable.

(3) Control variables
Combining the studies of previous scholars and the availability of data, the index selection and metrics of scholars such as Guo and Yuan (2020), Ying Wang et al (2022) and Y Zhang et al (2020) were used as references, and the level of science and technology, development level, capitalization level, energy consumption structure, and openness level of the construction industry were used as control variables. The variables are defined as shown in table 3 below.

Results and discussion
4.1. Results of total factor energy efficiency measurement in the construction industry Based on the Un-Super-SBM model constructed above and related data, MATLAB was used to measure the EE of the construction industry in 30 provinces in China from 2012 to 2019, and the detailed results are shown in  From the provincial level, the EE level of the construction industry in most provinces is generally fluctuating upward trend. Among them, there are obvious distinctions in EE among provinces, with Jiangsu Province having the highest energy efficiency, followed by Beijing, and Zhejiang, Guangxi, and Shanghai, whose energy efficiency mean values are all greater than 1. This indicates that the construction also energy use levels in these provinces are optimal during the study period, and their construction industry energy use levels reach the production frontier surface. While Inner Mongolia has the lowest energy efficiency, its efficiency mean value is only 0.3066, Qinghai, Gansu, Shanxi, Guizhou, Ningxia, Yunnan and other provinces also have low energy efficiency, its energy efficiency mean value are below 0.5, indicating that relative to the effective frontier surface, half of the energy inputs in these provinces are not effectively used, in a state of relative technical ineffectiveness. For further analysis and comparison between regions, dividing China's 30 provinces into three regions: East, Central and West, according to the degree of regional development and geographical location, and the energy efficiency levels of different regions are further analyzed. The specific results are shown in figure 3 and table 5.
From the above measurement results to make the national as well as the East, Central and West 2012-2019 energy efficiency level change trend chart, as shown in figure 4. At the national level, the EE level of China's construction industry has shown a floating trend in recent years, rising steadily from 2012 to 2014, reaching a maximum in 2014 and then declining, with little overall change in its energy efficiency values from 2015 to 2019. From the regional level, the EE of China's construction industry shows an obvious situation of high in eastern China and low in western China. The EE in the eastern region is higher than other regions and the national average, and the efficiency value as a whole fluctuates upward; the central region has a similar trend to the national energy efficiency change and has been floating in last several years; the EE level in western has been rising since 2012 to 2014, and then declining year by year after 2014. From this it is clear that there are different degrees of differences in EE of the construction industry in each region of China.

4.2.
Pre-processing results of panel data 4.2.1. Descriptive statistics of the data Before proceeding with the empirical analysis, it is necessary to understand the structure and distribution characteristics of the data firstly, and to make a macro grasp of the distribution of the values about the relevant variables for subsequent generalization and organization of the data. Here descriptive statistical analysis of the variables of interest was carried out using SPSS, and the results are presented in table 6.

Correlation and covariance test of data
Since the problem of co-linearity among the variables in the panel data will most likely lead to pseudo-regression results of the model, this paper uses stata16.0 software to verify the correlation of the variables, and the results are presented in table 7. From table 7, we can obtain that although the correlations among different variables are small, there may be slight multicollinearity among individual variables, and in practice, there will be interactions among variables in most cases, which may result in high correlation coefficients. Therefore, the variance inflation factor(VIF) test was used to further test each variable, and if VIF > 10 and Mean VIF > 2, the model has a multicollinearity problem. The results are presented in table 8: Among them, the maximum VIF is 1.63 and the Mean VIF is 1.43. Consequently, there is no serious multicollinearity.

Unit root and co-integration test of data
For the purpose of examining the smoothness of the variables in the panel data and exclude the pseudoregression problem in the model, this paper uses the LLC and IPS tests to perform unit root tests with the help of stata16.0 software, and the results are presented in table 9. Note: * , ** , *** denote significance levels of 10%, 5%, and 1%, respectively. According to the above table, both tests yielded P < 0.05, so the variables are stationary on the first-order difference and meet the requirements of the cointegration test. In this paper, the Pedroni test (Westerlund 2007) was used to conduct the cointegration test, and the results are presented in table 10.
The analysis of the test results in table 10 shows that all of the above statistics reject the original hypothesis, indicating that the cointegration relationship among the variables holds. Therefore, there is no spurious regression in the model, and the data can be used for panel regression analysis.

Regression results based on panel model
To empirically analyze the implications of FER and IER on EE in the construction industry, using panel data from 30 provinces across the country from 2012-2019 for regression analysis. There are three main types of mixed estimates, fixed effects and random effects models,and the type of panel data model require to be judged before conducting the regression analysis.Here the judgments were made by F-test and Hausman test (Liping Wang et al 2022), and results are presented in table 11 below.
According to the above results, it is clear that both the F-test statistic and the Hausman test statistic reject the original hypothesis at the 1% level, so both Model 1 and Model 2 should be used as fixed-effects models, as presented in table 12 below.
In the above table, Model 1 shows the baseline effect of environmental regulations on EE in construction business, while Model 2 shows a non-linear and more significant relationship between FER and IER and EE in construction business.

Discussion of nationwide regression results
Based on the panel data regression results, a non-linear relationship between environmental regulation and EE is observed, and this finding is generally consistent with most of the existing literature. Specifically, the quadratic  coefficients of FER and IER are one negative and one positive, and significant at 1% and 5% levels, respectively. This indicates that the implication of nationwide FER on EE in the construction industry exhibits an inverted 'U'-shaped trend of first promoting and then inhibiting, while the impact of informal environmental regulations exhibits a 'U'-shaped trend of first inhibiting and then promoting. This suggests that within a certain intensity range, relatively low-intensity FER can promote EE in the construction industry, but if they exceed the intensity that construction firms can afford, they can negatively affect the growth of energy efficiency. Conversely, when the intensity of IER is weak, it may be detrimental to energy efficiency, and if it reaches a certain intensity, informal environmental regulation will promote the growth of EE in the construction industry. This shows that both FER and IER have a two-way influence on EE. For other control variables, the level of foreign openness does not pass the significance test, denoting that its implication on EE is not significant. This is mainly because the gradual rise in the level of our economy and technology, the increasingly intelligent and standardized management, and the diminishing influence of foreign investment on all aspects of construction business. The implication of the technology level, the gross value of construction output, and the level of capitalization in construction business on EE is positive, which is similar to the findings of Chen (2020). The negative impact of the energy consumption structure in construction business on EE denotes that the use of disposable energy not only produces a large amount of polluting gases and makes the undesired output increase, but also is very detrimental to the growth of EE, which is consistent with the findings of Li and Shi (2014). Therefore, China needs to optimize the energy consumption structure.

Discussion of region-wide regression results
Compared to previous studies, there are significant differences between the findings of the three regions and other literature during the sample period examined in this study, which may be due to changes in the level of development of the construction industry, energy consumption, and the level of environmental regulation over time. Specifically, the quadratic coefficients of FER and IER are negative in the East, negative FBR number and positive IER number in the central region, and both positive in the West, indicating that an inverted 'U' shaped relationship exists between FER and IER and EE in the East, an inverted 'U'-shaped relationship between FER and IER and EE in the central region, and a 'U'shaped relationship between FER and IER and EE in the West.
FER has had different impacts on EE in different regions, the main reason is that the the central and eastern regions are relatively more economically developed, after the local government implements FER policies, most of the larger construction enterprises can afford the environmental costs and will comply with the relevant government regulations and systems,timely update their equipment and improve their production technology Note: Values in parentheses are t-statistic values; * , ** , and *** denote 10%, 5%, and 1% significance levels, respectively.
for green and innovative production to reduce pollution, thus EE is improved. Although the environmental pollution problem in the central and eastern regions has been mitigated, the situation is still serious due to the rapid development of its industries. For the sake of achieving the objectives of environmental regulation, the government will still increase the intensity of regulation, construction companies are paying increasing costs while passively improving environmental technology. If the intensity of FER continues increasing, the benefits of innovation for construction companies will not be sufficient to cover the increased environmental costs, which will inhibit the growth of EE. The economic and industrial development in the West is somewhat slower than that of the central and eastern regions, and the mechanism of FER also differs from that of the central and eastern regions. When it is on the left side of the 'U' curve, the intensity of FER is low and construction enterprises lack the incentive to innovate. Most of them will choose to pay environmental taxes or increase the expenditure on pollution control, which undoubtedly increases the cost of enterprises. However, as environmental regulations continue tightening, construction companies will begin to invest in green innovations to further improve EE when they are on the right side of the 'U' curve due to high environmental taxes and pollution fees. IER also has had different impacts on EE in different regions, the reasons for this are that the eastern region is more developed, with higher per capita income and education levels, more focused on the pursuit of quality of life and the environment, and more environmentally conscious. The general public and environmental organizations are more effective and efficient in enforcing informal environmental regulations, and can be important promoters for building companies to take measures to reduce pollution and improve energy efficiency. However, in many cases corporate emissions and other green behaviors have met national standards, but have failed to meet public requirements. In the face of continues pressure from the public and environmental organizations, the production costs of construction companies continue to rise, and some smallscale, less innovative companies are unable to withstand that pressure and face operational difficulties or even bankruptcy, and the innovative development of construction companies as a whole is affected, which is ultimately detrimental to energy efficiency. For the central and western regions, which is more focused on economic improvement and industrial development, the public and environmental organizations exert less pressure on enterprises in the early stages of implementing IER, and most enterprises can solve their pollution problems by paying less taxes on emissions or paying for pollution treatment, and energy efficiency becomes less and less efficient. However, as the level of informal environmental regulation increases, companies are paying higher and higher taxes on emissions and pollution control costs, and in order to reduce costs, construction companies choose to use innovation subsidies for green innovation, thus promoting energy efficiency.
For other control variables, the level of technology positively moderates the EE in the central and eastern regions, while it negatively moderates it in the west. Probably because of the lower level of development in the western region, the current investment in advanced equipment and technology is insufficient, and the rough development approach is not easy to change in the short term and cannot have an immediate effect. The development level and capitalization level in all regions of China have a significant positive moderating implication on EE, and the coefficient of the development level on EE is larger. The construction energy consumption structure of each region has a negative implication on EE, and the implication is more significant in the central and western regions that pursue economic progress and industrial development. Benefit from excellent geographical conditions and economic development, the eastern region has a higher level of external openness, and environmental regulations indirectly contribute to the improvement of EE in the eastern region by influencing foreign investment. The relatively low level of external openness in the central and western regions may lead to foreign investment that does not have the full effect of improving energy efficiency through technology spillovers.

Limitations
There are some limitations in the study of this paper. First, only direct emissions are involved in the calculation of CO 2 emissions. Indirect emissions are not taken into account because indirect emissions involve other industries, which are more complicated, and the relevant data are difficult to obtain, which may cause the actual CO 2 emissions from the construction industry to be small. Second, due to the availability of data, this paper is based on data from 30 provinces and cities in China to carry out the study, and the research unit cannot be subdivided into city level, and the size of spatial scale may affect the error of the research problem. In addition, in the panel data regression analysis, this paper only analyzes from a static perspective and does not introduce the lagged term of environmental regulation to study the dynamic changes of the impact on EE. The above points will be the focus of the authors' future in-depth research.

Research conclusions
First, To address the issue of the relationship between FER and IER and the total factor EE of China's construction industry, using the Un-Super-SBM model to measure the EE of China's construction industry in each province over the years, and establishes a panel data model with reference to panel data for 30 provinces (except Tibet) in China from 2012 to 2019, with the national and central-east-west regions as the research objects, and empirically analyzes the implication of FER and IER on the total factor EE of China's construction industry and its regional heterogeneity, and obtains the following conclusions.
By measuring the EE of the construction industry in all provinces of China, it is found that there are remarkable differences in EE between different provinces and regions. From a national perspective, the overall total factor EE all demonstrated a floating trend, rising year by year from 2012 to 2014, then declining, and more stable overall from 2015 to 2019; from a regional perspective, China's inter-provincial EE demonstrated a trend of high in the east and low in the west, and EE in the eastern region higher than other regions and the national average.
Second, Regarding the implication of FER on the total factor EE of the construction industry, from the overall national level, it is clear that the relationship between the two is an inverted 'U'-shaped relationship of promoting and then inhibiting, which shows that when the government adopts a reasonable environmental regulation policy, it can drive the improvement of EE . However, once the intensity of formal environmental regulations exceeds a certain range, enterprises have to increase their capital investment to meet the government's requirements, and their environmental pollution treatment costs and innovation investment are too expensive, which reduces the profits of construction enterprises and their motivation to continue green innovation. At the regional level, the impact of FER on EE is regionally heterogeneous. The implication of FER on energy efficiency in the construction industry is inverted 'U'-shaped in the eastern and central parts of China, and 'U'-shaped in the western part. Therefore, the government ought to grasp the strength of FER and make gradual progress.
Third, Regarding the implication of IER on total factor EE in the construction industry, at the national level as a whole, it is clear that the relationship between the two is a 'U'-shaped relationship of inhibiting and then promoting, which suggests that lower intensity informal environmental regulations will inhibit the growth of EE, and when EE declines to a certain threshold, as the informal environmental regulations gradually increase in intensity as the general public and environmental organizations continue to exert pressure, construction companies pay higher and higher taxes and treatment fees, and companies start to choose green innovation, and energy efficiency starts to gradually increase again. From a regional perspective, there is also regional heterogeneity in the impact of IER on EE. In the eastern part of China, the implication of IER on EE in the construction industry is in an inverted 'U'-shape, while the other regions are in a 'U'-shape. Therefore, the government can actively guide the public according to the situation in different regions and raise the attention of other members of the society to the construction industry enterprises, so as to jointly promote EE.

Government level
First, the government needs to reasonably adjust the intensity of environmental regulations, clarify the characteristics of provincial construction industry development, and implement differentiated regulation policies. Local governments should integrate with the overall national regulatory policy, and take local conditions into account. The intensity of FER in the central and eastern regions should not exceed the extreme value of the inverted 'U' curve, while the intensity of FER in the relatively backward western region should be appropriately increased. In addition, the government should increase tax incentives and innovation subsidies for enterprises whose investment in innovation is greater than their income, and provide technical support for enterprises to research and develop green production technologies to stimulate them to innovate. For enterprises with insufficient motivation for environmental management and weak innovation incentives, government departments can implement a dynamic and differentiated ladder system of fines for businesses that do not meet standards to force them to actively innovate green technologies.
Second, strengthen the linkage of provincial and regional environmental controls and encourage collaboration among multiple entities to jointly promote EE. The government encourages the circulation of resources such as technology and talents between different provinces and regions, further develops low-carbon and green production methods, and strengthens exchanges and cooperation between provinces and regions to achieve synergistic development. In addition, basic theoretical knowledge and related applied research can be combined with scientific and technological achievements to promote cooperation between enterprises and universities and research organizations, to help construction enterprises improve their green technology and further narrow the provincial and regional energy efficiency gap.
Third, a comprehensive supervision system should be established in the whole society, the environmental information disclosure system should be refined, and the power of IER should be fully utilized and valued. From the current situation, the social approach to environmental governance is mostly of the direct government control type, which means environmental quality monitoring and environmental product provision mostly done by the government and less public participation. The government needs to develop appropriate policies to provide favorable conditions for the development of environmental organizations, so that the intensity of IER can be enhanced. In addition, the government oughts to establish and gradually refine the environmental monitoring system for public participation and the environmental information publication system to guarantee the transparency of environmental information of relevant enterprises. The public needs a perfect monitoring system as a strong support for the exposure of emission violations and related enterprises.

Corporate level
First, construction companies need to improve their business systems and green production systems and actively provide feedback to society in light of their own conditions. Construction companies should build a green production system that is suitable for their own development and meets environmental regulation standards, use green as one of the criteria to measure design and production, and communicate their green innovation ideas to the public and society to reduce information asymmetry in order to obtain government innovation subsidies and outside investment.
Second, construction enterprises should increase investment in technological innovation, pursue progress from within themselves and their enterprises, and actively carry out green production innovation to improve energy use efficiency. Construction companies should make full use of the spillover effect brought by technological innovation, so as to reduce innovation cost investment and enhance market competitiveness. This can be achieved by organizing regular training and learning and innovation exchange sessions, integrating innovation into corporate culture, and properly planning and allocating limited R&D funds and increasing welfare subsidies for technical staff to achieve technological innovation, thereby improving the energy use efficiency of their own enterprises.
Third, construction companies need to strengthen communication with the outside world, draw on the technology and experience of advanced enterprises, and actively seek cooperation with scientific research institutions and exemplary enterprises. By strengthening the connection and communication between enterprises and scientific research institutions in different regions, we can improve the conversion between various production factors and related technology, and realize the synchronization of energy conservation and consumption reduction in different regions. Construction enterprises can discuss and learn by conducting exchange meetings and scientific and technological lectures, or reach cooperation with scientific research institutions to achieve green innovation with the technical support of scientific and technological research institutions, thereby promoting EE in the local construction industry.