Environmental Regulations and Chinese Energy Sustainability: Mediating Role of Green Technology Innovations in Chinese Provinces

: The stable growth of an economy is based on the coordination between environmental protection and economic development. Environmental regulation may affect energy efﬁciency because of its function of correcting energy consumption externalities. This paper uses the SBM model and Tobit model to explore the impact on and pathways of environmental regulations of energy efﬁciency in 30 provincial-level administrative regions in China and explains temporal and regional heterogeneity. The ﬁndings suggested that the environmental regulation in all provinces is continuously strengthened and the energy efﬁciency in eastern China is relatively higher. There is a positive effect of environmental regulation on energy efﬁciency and there is a temporal and spatial heterogeneity. Environmental regulation affects energy efﬁciency through green technology innovation, industrial structure upgrading, energy structure transformation and other transmission paths, and its inﬂuence mechanism on energy efﬁciency also has regional heterogeneity. The policy suggestions are: further enhance the intensity of environmental regulation, reﬁne supporting safeguards and implement differentiated environmental regulation measures.


Introduction
As the world's largest producer and consumer of energy, coal is the main part of China's energy consumption because of the energy endowment of "more coal, less oil and poor gas". On the back of sustained economic growth, China's total energy consumption continues to grow, reaching 524 million tons of standard coal in 2021. From the 11th to 14th Five-Year Plan period, this country has continuously raised the target of energy consumption per unit of GDP to 13.5%. Based on the existing data, this energy consumption is 1.5 times that of the world average level. The common focus of policy-making departments, academia, the public and even the whole world is how to fundamentally transform the pattern of economic development, break the bottleneck that has long restricted the sustainable development of China's economic, social and ecological sustainable development, coordinate economy and environment, reduce carbon emissions and achieve carbon peak and carbon neutrality, which is a crucial proposition to promote high-quality development of economy and society [1,2].
In all ways, environmental regulation has an important tangible hand in improving energy efficiency and has a binding force on energy efficiency with a tangible system or intangible consciousness, which may improve energy efficiency. Scholars have various views on if environmental regulation can promote energy efficiency or not [3,4]; existing studies Sustainability 2023, 15, 8950 2 of 23 mostly analyze how environmental regulation acts on energy efficiency from the theoretical level, mainly focus on the role played by technological innovation and rarely conduct empirical analysis on other possible paths [5]. Environmental regulation indicators are mainly constructed based on pollution treatment cost, environmental tax, number of environmental protection personnel, pollution treatment volume, comprehensive treatment rate of waste, etc. [6,7]. In general, it is necessary to further confirm environmental regulation's effect on energy efficiency based on more comprehensive measurement, and the mechanism and path of action other than technological innovation need to be further clarified.
Compared to existing research, this paper attempts to answer three questions: first, whether environmental regulation acts on energy efficiency; if so, how is the temporal and regional heterogeneity reflected, at a time when environmental regulation plays a role in energy efficiency; third, through what pathways and mechanisms can environmental regulations affect energy efficiency. This paper's marginal contribution is mainly manifested in two aspects: in the measurement of the strength of environmental regulation and the index reflecting the strength of environmental regulation (REGU) is built based on government work reports (hereinafter referred to as reports); in detail, the frequency ratio of the words related to the environment in them. This is an exploration and practice of a text analysis method against the background of the big data era, which has enriched the application of this measurement method in similar studies. Secondly, total factor energy efficiency (TFEE) is used to measure energy efficiency, focusing on the fluctuation trend and mechanism of environmental regulation in the spatial-temporal dimension and energy efficiency, trying to systematically deconstruct the mechanisms and pathways of environmental regulation's influence on energy efficiency. Three theoretical hypotheses are proposed and verified by data. Based on this, the rest of this paper is arranged as follows: Section 2 is characteristics, facts and analysis of environmental regulation and energy efficiency; Section 3 is mechanism exploration and theoretical hypothesis; Section 4 is model, data and method; Section 5 is results analysis. Section 6 is conclusions and policy recommendations.

Measuring Method of Environmental Regulation
The paper makes use of one method and one index as the measuring methods. The text analysis method is adopted to study the government's environmental improvements and the environmental regulation intensity index (REGU) is constructed [6,8]. The construction method is as follows: first, collect reports from government departments' websites and provincial statistical yearbooks; the second step is to segment the collected reports' text, which is realized by using Python software (Version 3.2) with the help of the Chinese word segmentation database of Jieba; the third step is to use Python software to count terms' frequency and calculate the proportion of the frequency of environmental words to the total frequency of words. This proportion is utilized to measure the annual REGU of provinces. That is, the greater the frequency of environment-related words, the higher the REGU. The statistics of environment-related terms include: low carbon, sulfur dioxide, carbon dioxide, chemical oxygen demand, environmental protection, environmental protection, emission reduction, air, green, energy consumption, pollution, ecology, pollution, PM10 as well as PM2.5.

Analysis of Spatio-Temporal Characteristics of Environmental Regulation
The results of some representative years can be seen in Figure 1. Figure 1 shows the change in REGU mean value in 30 provinces and provinces in the eastern, central and western regions of the country. The division of the three regions is on the basis of the "Seventh Five-Year Plan" in China, the same as below.  In the time dimension, the average value of REGU had a tendency to increase durin our study. By observing the mean value of REGU, it was found that the mean value from 1995 to 2005 was 0.0022 and the mean value from 2006 to 2018 was 0.0069. The averag annual growth rate of the environmental regulation index (REGU) was 7.79% from 199 to 2005  In terms of spatial differences, the average REGU in the eastern, central and wester regions is 0.0048, 0.0046 and 0.0049. According to the average level of per capita GDP an the three industries' value added in each region during the study period, REGU in the eas is a little high, with the average REGU of 0.0048 and GDP per capita of CNY 38,389.74, th highest level of economic development. The three industries accounted for 9.96%, 43.64% and 46.40%, among which the primary industry accounted for the lowest value and th tertiary industry accounted for the highest value. The lowest index was found in the cen tral region, with an average of 0.0046, GDP per capita is CNY 19,441.5, the proportion o three industries is 16.18%, 44.59% and 39.23% and the secondary industry has the highes proportion. REGU is the highest in the west, with an average REGU of 0.0049, average pe In the time dimension, the average value of REGU had a tendency to increase during our study. By observing the mean value of REGU, it was found that the mean value from 1995 to 2005 was 0.0022 and the mean value from 2006 to 2018 was 0.0069. The average annual growth rate of the environmental regulation index (REGU) was 7.79% from 1995 to 2005 and 9.36% from 2005 to 2018. The increase in environment-related terms' frequency in reports reflects the government's increasing emphasis on environmental governance. This may be the reason for different REGU values in different periods after 2005. Around 2005, the government's strategic guidance promoted all walks of life to conserve energy as well as reduce emissions. The Decision on Implementing the Scientific Outlook on Development and Strengthening Environmental Protection issued by the State Council in 2005 is a document of programmatic significance for environmental protection work, and environmental policies embodied the concept of sustainable development more. The "three changes" proposed by the Sixth National Environmental Protection Conference in 2006 are fundamental adjustments to China's economic and environmental relationship.
In terms of spatial differences, the average REGU in the eastern, central and western regions is 0.0048, 0.0046 and 0.0049. According to the average level of per capita GDP and the three industries' value added in each region during the study period, REGU in the east is a little high, with the average REGU of 0.0048 and GDP per capita of CNY 38,389.74, the highest level of economic development. The three industries accounted for 9.96%, 43.64% and 46.40%, among which the primary industry accounted for the lowest value and the tertiary industry accounted for the highest value. The lowest index was found in the central region, with an average of 0.0046, GDP per capita is CNY 19,441.5, the proportion of three industries is 16.18%, 44.59% and 39.23% and the secondary industry has the highest proportion. REGU is the highest in the west, with an average REGU of 0.0049, average per capita GDP of CNY 18,624.08, the proportion of the three industries of 16.49%, 40.90% and 42.61% and the second industry's proportion is relatively low.

Measuring Method of Energy Efficiency
This paper shows the TFEE of China's 30 provinces from 1995 to 2018 based on the most distant DEA model to the frontier, namely the SBM model. Some scholars have used a different approach [9][10][11][12]. DEA is a common method to calculate energy efficiency. Considering the ineffective decision-making units (DUM) gap between the current state and the strong efficient target, including equal proportion and relaxation improvement, while the measurement of inefficiency by the radial DEA model does not reflect the relaxation improvement. Tone (2001) proposed the SBM model, which measures inefficiency by the average proportion of each input or output that can be reduced or increased [13]. Consider n DUMs. Each DUM has N inputs, M expected outputs and I unexpected outputs. The vector form is x ∈ R N , y ∈ R M , b ∈ R I , respectively. The specific form of the SBM model including unexpected outputs is: where: x t kn , y t km , b t ki is the input-output volume of production units in the t period; s x n , s y m , s b i is input-output's slack vectors. According to the SBM model considering the undesired output, the energy target inputs and energy input slack can be measured and calculated. Hu and Wang (2006) first defined TFEE, which is the ratio of target energy input to actual energy input [14]. The calculation formula is: where: i and t denote the decision-making unit and time, TFEE represents the total factor energy efficiency, TEI represents the target energy input, AEI represents the actual energy input and LEI represents the energy input slack, which is the excessive energy input relative to the optimal production frontier. When 0 ≤ TFEE < 1, the energy efficiency is low and there is energy waste. When TFEE = 1, the energy use is effective. The selection and setting of the input-output index are involved in the calculation of TFEE in the SBM model. Descriptive statistics of the input and output index selected can been seen in Table 1. Capital investment is reflected by capital stock. The capital stock is calculated by the perpetual inventory method [15], and the equation is: where: K, I, δ are capital stock, investment in the current year and depreciation rate, i and t denote regions and years. We use the number of fixed assets formed, the fixed asset investment price index, to calculate current investment, and the investment price index, respectively. The depreciation rate is 9.6% [16]. Labor input: reflected by the number of employees in the whole society. Energy input: reflected by total energy consumption. Expected output: reflected in real GDP. Unexpected output: reflected by carbon dioxide emissions. The product of total energy consumption and carbon dioxide emission coefficient is used to estimate the value of total carbon emissions. We set 2.70 tons as the carbon dioxide emission coefficient per ton of standard coal [17,18].

Analysis of Spatio-Temporal Characteristics of Energy Efficiency
We mainly used MaxDEA8 software to measure the TFEE of China's 30 provinces. Figure 2 shows the change in the TFEE mean in 30 provinces and provinces in different regions. Capital investment is reflected by capital stock. The capital stock is calculated by the perpetual inventory method [15], and the equation is:

Input variables
where: , , are capital stock, investment in the current year and depreciation rate, i and t denote regions and years. We use the number of fixed assets formed, the fixed asset investment price index, to calculate current investment, and the investment price index, respectively. The depreciation rate is 9.6% [16].
Labor input: reflected by the number of employees in the whole society. Energy input: reflected by total energy consumption. Expected output: reflected in real GDP. Unexpected output: reflected by carbon dioxide emissions. The product of total energy consumption and carbon dioxide emission coefficient is used to estimate the value of total carbon emissions. We set 2.70 tons as the carbon dioxide emission coefficient per ton of standard coal [17,18].

Analysis of Spatio-Temporal Characteristics of Energy Efficiency
We mainly used MaxDEA8 software to measure the TFEE of China's 30 provinces. Figure 2 shows the change in the TFEE mean in 30 provinces and provinces in different regions.   higher. The TFEE of each province is also quite different through the total study period. The TFEE value of Shanghai, Guangdong, Hainan and Qinghai provinces is 1, which indicates that the energy utilization of these four provinces is relatively sufficient. The TFEE value of 12 provinces including Beijing, Inner Mongolia, Jiangsu, Anhui, Fujian, Shandong, Hubei, Hunan, Guangxi, Chongqing, Gansu and Ningxia reached 1 in some years, with a certain potential to convert energy and reduce emissions. The TFEE of 14 provinces, including Tianjin, Hebei, Shanxi, Liaoning, Jilin, Heilongjiang, Zhejiang, Jiangxi, Henan, Sichuan, Guizhou, Yunnan, Shaanxi, and Xinjiang, did not reach 1 from 1995 to 2018, and the energy utilization is insufficient, which also has great potential to convert energy and reduce emissions. The trends of TFEE is shown in Figure 3.
qing, Shaanxi and other provinces fluctuated but remained basically stable. The TFEE values in Gansu, Hubei, Hunan, Inner Mongolia, Ningxia, Xinjiang, Zhejiang and other provinces fluctuated greatly. TFEE values in Fujian, Guangxi, Shandong and other provinces showed a downward trend as a whole.
In the spatial dimension, the average TFEE in the east reaches a high level (0.7983). The average TFEE values in the middle (0.5846) and western (0.5890) parts are relatively low. From 1995 to 2003, compared to the middle part, the average TFEE in the west was higher. From 2004 to 2018, compared to the western part, the average TFEE in the middle part was higher. The TFEE of each province is also quite different through the total study period. The TFEE value of Shanghai, Guangdong, Hainan and Qinghai provinces is 1, which indicates that the energy utilization of these four provinces is relatively sufficient. The TFEE value of 12 provinces including Beijing, Inner Mongolia, Jiangsu, Anhui, Fujian, Shandong, Hubei, Hunan, Guangxi, Chongqing, Gansu and Ningxia reached 1 in some years, with a certain potential to convert energy and reduce emissions. The TFEE of 14 provinces, including Tianjin, Hebei, Shanxi, Liaoning, Jilin, Heilongjiang, Zhejiang, Jiangxi, Henan, Sichuan, Guizhou, Yunnan, Shaanxi, and Xinjiang, did not reach 1 from 1995 to 2018, and the energy utilization is insufficient, which also has great potential to convert energy and reduce emissions. The trends of TFEE is shown in Figure 3.

Mechanism Discussion and Theoretical Hypothesis
According to relevant theories and existing research, environmental regulation can be used for energy efficiency through a variety of transmission mechanisms to coordinate China's economic and environmental relationship. This paper considers the transmission system of environmental regulations' impact on energy efficiency from three perspectives: green technology progress, industrial structure improvements (IH) and energy structure transformation.

Mechanism Discussion and Theoretical Hypothesis
According to relevant theories and existing research, environmental regulation can be used for energy efficiency through a variety of transmission mechanisms to coordinate China's economic and environmental relationship. This paper considers the transmission system of environmental regulations' impact on energy efficiency from three perspectives: green technology progress, industrial structure improvements (IH) and energy structure transformation.

Hypothesis 1 (H1): Environmental regulation affects energy efficiency through green technology innovation.
Green technology refers to the technical system with energy conservation and cleaner production effects [5]. There are two stages that reflect the environmental regulations' impact on energy efficiency through green technology innovation: The first stage is environmental regulations' impacts on green technology innovation. There are two aspects: "compliance cost" and "innovation compensation" [19,20]. According to the environmental protection theory of neoclassical economics, environmental regulations add the environmental governance cost of enterprises. There may exist the effect of "compliance cost" when it comes to green technology innovation. With limited funds, the increase in investment in environmental governance will make enterprises invest in green technology research and development less, generating the "crowding out effect". Environmental regulation may have "innovation compensation" for green technology innovation in accordance with the "Porter hypothesis" because increasing environmental governance costs are likely to make enterprises improve energy conservation, clean production and other technologies and invest more. The second stage is the impact of green technology innovation on energy efficiency. There are two aspects: first, enterprises reduce energy waste [21], overcome the marginal law of diminishing returns, make technology diffusion and structural improvements in their activities [22,23] and reduce energy costs by innovating energy utilization technology. Second, enterprises reduce pollution emissions by innovating cleaner production technologies [24].
To sum up, environmental regulation affects green technology innovation through the "compliance cost" effect or "innovation compensation" effect and then affects energy efficiency.

Hypothesis 2 (H2):
Environmental regulation affects energy efficiency through industrial structure upgrading.
Industrial structure upgrading is the upgrading process from a lower form to a higher form. The internal mechanism is the efficient allocation of factors [25]. Environmental regulations' impact on energy efficiency through industrial structure improvement is mirrored in two stages.
The first stage is environmental regulations' impact on industrial structure upgrading. There are three aspects: first, industrial transfer. High-polluting enterprises will tend to put production activities in areas with weak environmental regulation intensity in effect because of environmental regulation, forming industrial transfer and affecting regional industrial structure improvement. Second, the scale and number of regional enterprises changed. For one thing, regional environmental regulation makes more barriers [26]. For another thing, the exit barriers of high-pollution and high-energy-consumption industries have been lowered [27], affecting the scale and quantity of enterprises in the region, leading to the adjustment of factor allocation and affecting the industrial structure improvement. The third is the change in enterprise production behavior. Green technology innovation promotes productivity with less energy use, which is helpful for enterprises [28] and increases regional productivity growth with great environmental performance [29]. For consumers, environmental regulation can arouse consumers' awareness of energy conservation, promote changes in consumer demand and affect enterprise production [27,30]. For investors, environmental regulation will affect the demand of investors, update the process of the enterprise production by appropriate investment opportunity to match with the investment and then affect the production behavior of enterprises [31][32][33]. The change in an enterprise's production behavior will bring about changes in the input-output ratio of production factors and finally realize industrial structure upgrading.
The second stage is industrial structure upgrading's effects on energy efficiency. The energy consumption and pollution emissions of industries are the main reasons why industrial structure upgrading affects energy efficiency. Petty-Clark law reveals industrial structure change law: with the economic development, the ratio of the primary industry gradually drops, and the secondary industry occupies the leading position as time passes; with the further development of the economy, the ratio of the secondary industry has dropped while the ratio of the tertiary industry has risen as time passes. Generally, the primary and tertiary industries' energy consumption and pollution emissions are relatively low, and the secondary industry pollution emissions and energy consumption, especially in heavy industry, are relatively high, so the energy efficiency will also change in the industrial structure upgrading process [30].
To sum up, environmental regulation has led to industrial transfer, changes in the size and quantity of regional enterprises, changes in the production behavior of enterprises and ultimately affects industrial structure upgrading, which also affects energy efficiency on account of the variations in energy consumption and pollution emissions among industries. The energy structure's transformation is the change in human energy utilization from firewood to coal, to oil and gas and then to new energy [34]. Reducing the ratio of nonrenewable energy consumption contributes to promoting the transformation of energy structure under the pressure of resource depletion and environmental degradation [35]. Environmental regulations' effects on energy efficiency through the energy structure's transformation are reflected in the following two stages.
The first stage is the translation of environmental regulation to the energy structure. There are two effects. First, environmental regulation will directly promote the substitution of energy elements and promote the energy structure's transformation. Second, environmental regulation will make enterprises choose energy factor substitution in production, thus promoting the transformation of energy structure.
The second stage is the energy structure transformation's impact on energy efficiency. A large amount of sulfur, nitrogen oxide, dust and carbon dioxide is produced during coal utilization. Relatively speaking, clean energy utilization is more environmentally friendly. Therefore, energy structure transformation will promote energy efficiency [36].
To sum up, the restriction environmental regulation imposes on energy consumption and the biased choice of energy consumption caused by environmental regulation promote the substitution of energy elements and thus affect the transformation of energy structure. Due to the different pollution emissions caused by different energy consumption, the transformation of energy structure promotes energy efficiency improvements.

Model Settings
Since TFEE calculated by the SBM model is between 0 and 1, which is a restricted dependent variable, and the use of OLS will lead to inconsistent estimates, the Tobit model [37] is a way to analyze environmental regulations' effects on TFEE to solve the problem of the limited data of the explained variable. The specific estimation equation of the benchmark regression model is: where TFEE is total factor energy efficiency; REGU is environmental regulation intensity; X refers to other control variables; ε is a random disturbance term; β is the core estimation parameter, representing the net effect of environmental regulation on energy efficiency; i and t represent regions and years, respectively.

Explained Variable
Energy efficiency (TFEE). Due to the definition by [14], TFEE calculated based on the SBM model is used as the explained variable.

Core Explanatory Variables
Environmental regulation intensity (REGU). The text analysis method is used to measure government environmental governance, and the environmental regulation intensity (REGU) index [6,8] is constructed as the core explanatory variable.

Control Variables
According to the existing research results, the control variables include: The level of economic development (PGDP) is expressed by the logarithm of GDP per capita [38]. The degree of opening to the outside world (OPEN) is characterized with the proportion of actual FDI in GDP [3,39,40]. Transport infrastructure level (INFRA) is characterized by the per capita road area [41]. The energy price (PRICE) is calculated by the industrial producer purchase price index [42]. DENSITY, the ratio of permanent population to administrative area, is utilized to represent the population density.

Conductive Variables
Green technology innovation (TECH), technological progress closely related to environmental protection, is directly reflected in green technology innovation. Green technology innovation is characterized with the logarithm of green patent applications [43], to illustrate that energy consumption entities refine energy efficiency through green technology innovation under environmental regulation.
Industrial structure upgrading (IH), which refers to the industrial structure upgrading process from a lower form to a higher form can be measured by the advanced degree of industrial structure. The IH index is constructed to represent industrial structure upgrading [44]. When the IH is larger, the upgrading level of industrial structure is higher. The specific construction method is as follows: Step 1: record the ratio of the added value of the three industries in GDP as a member of a space vector and form a set of three-dimensional vectors X 0 = (x 1,0 , x 2,0 , x 3,0 ).
Step 2: calculate the angle between vector X 0 and vectors X 1 (1, 0, 0), X 2 (0, 1, 0), X 3 (0, 0, 1), respectively. The included angle formula of vectors is: Step 3: calculate the IH index, where θ 1 represents the effect of the transfer of the first industry to the second and third industries. It indicates the effect of the transfer from the second industry to the third industry.
The higher the value of the IH index, the higher the level of industrial structure upgrading. Energy structure transformation (ES). Energy structure transformation is the human energy utilization transformation from firewood to coal, to oil and gas and to new energy. Reducing the proportion of non-renewable energy consumption is a crucial direction to improve energy structure transformation. This paper uses coal consumption proportion to characterize the energy structure transformation [45]. With reference to the China Energy Statistical Yearbook, the coal consumption data are changed to "kilogram standard coal" by the conversion coefficient of standard coal (0.7143 kg standard coal/kg). The specific count equation is:

Descriptive Statistics of Variables
The relevant variables and descriptive statistics involved when empirically analyzing environmental regulations' effects on energy efficiency with Formula (1) are shown in Table 2. Table 3 reports the results of the multicollinearity test. The maximum value of the variance inflation factor (VIF) is 8.56 and the mean value of VIF is 3.04, which suggests that there is no serious multicollinearity among the variables selected for this paper.

Data Source
The data based on individual indicators were updated until 2018. Due to the availability of data, we adopt China's provincial panel data from 1995 to 2018 for empirical analysis. The text of the reports used to calculate the environmental regulation indicators comes from the provincial government websites and yearbooks. The data of per capita GDP, GDP, added value of the three industries, actual FDI, the permanent population and the area of administrative divisions are derived from the Wind database, where GDP and added value of the three industries are reduced according to the relevant indexes, and the base period is 1995. The purchasing price index of industrial producers stems from the China Price Statistical Yearbook. The total energy consumption and coal consumption are from the China Energy Statistical Yearbook. The per capita road area is derived from the National Bureau of Statistics. The fixed asset investment price index and total fixed capital formation stem from the National Bureau of Statistics and the Historical Data of China's GDP Accounting: 1952-2004, The number of green patent applications comes from the CNRDS database. For the individual missing data in the analysis process, the linear method is used to complete, including Chongqing's partial missing data (1995)(1996), and the corresponding data of Chongqing from 1995 to 1996 are excluded from the data of Sichuan Province.

Benchmark Regression Results
Since TFEE calculated on the grounds of the SBM model is a restricted dependent variable, the use of OLS will lead to inconsistent estimates, so the Tobit model is used for regression according to Formula (1), and the results can be seen in Table 3. Table 3 uses REGU as the core explanatory variable to characterize the impact of REGU on TFEE. The RHO values are all above 0.8, and individual effect changes mainly explain TFEE changes in China's provinces. A likelihood ratio test (LR) tells us that the first hypothesis "H 0 : σ µ = 0" needs to be rejected and there is individual effect, so the mixed Tobit model needs to be rejected and we should use the panel random effect Tobit model. Wald test results and log-likelihood value show that the overall fit of the model is good.
The regression results in Table 4 illustrate the core explanatory variable environmental regulation and other control variables' effects on TFEE. Column (6) in Table 3 is taken as an example to explain the regression results.   Environmental regulation. After adding a series of control variables, the consequences of benchmark regression show that the influence coefficient of REGU on TFEE is positive and significant, and increasing environmental regulation intensity will improve energy efficiency. Moderate environmental regulation can encourage enterprises to conduct green technology innovation and conserve energy and reduce emission and also enable enterprises to reduce consumption of fossil energy such as coal, increase clean energy consumption and achieve energy efficiency improvement. Environmental regulation affects the entry and exit mechanism of regional industries, changes the size and number of regional enterprises and also makes some enterprises move to regions where the environmental regulation is weak, affecting energy efficiency through regional industrial structure. In addition, environmental regulation urge enterprises to produce products that meet environmental protection requirements and the needs of consumers and investors. Changes in enterprise production behavior affect the adjustment of factors, promote industrial structure upgrading and affect energy efficiency.
Economic development level. The PGDP has a noticeably favorable effect coefficient for TFEE. With the improvement of economic development level, residents frequently have higher standards for the condition of the environment. Advanced industrial structure and technology levels are more effective in dealing with pollution and other problems brought about by energy consumption, thus promoting energy efficiency.
Open to the outside world. The influence coefficient of OPEN for TFEE is significantly positive. The improvement of openness will facilitate companies to introduce cutting-edge production technology and cutting-edge management principles and play a positive role in improving regional energy efficiency.
Transportation infrastructure. The impact coefficient of INFRA for TFEE is significantly negative, which indicates that transportation infrastructure may have an adverse impact on energy efficiency. More reasonable design and planning are needed for the construction and utilization of transportation infrastructure to lessen pollution production and energy use in the construction and use of transportation infrastructure, which has a beneficial impact on energy efficiency.
Energy price. The impact coefficient of PRICE for TFEE is significantly negative, demonstrating that decreased energy efficiency is a result of rising energy prices. The reason may be that the relative price of China's energy, under the influence of government regulation and other factors, is not a good reflection of the market supply and demand and cannot demonstrate the full social cost of energy and the energy price is low. As a relatively cheap input, coal and other energy resources are over-consumed in the production process of enterprises, which leads to low regional energy efficiency.
Population density. DENSITY has a significant positive impact coefficient for TFEE, which means that the relationship between the two is positive. The formation of industrial agglomerations is based on higher population densities, and the scale economy impact of industrial agglomerations contributes to regional energy efficiency increase. The high population density facilitates the construction and intensive use of public facilities and also means that residents of the area have high levels of enterprise management and a great understanding of energy conservation, which are helpful for increasing the region's energy efficiency.

Robustness Test
To check robustness, the results of benchmark regression were retested by changing the measurement method of the environmental regulation variable and the measurement method of the energy efficiency and changing the regression method.
First, the measurement method of environmental regulation is changed. From the perspective of pollutant discharge, three indicators, namely, industrial solid waste output, the amount of industrial sulfur dioxide and the amount of chemical oxygen demand in industrial wastewater, are selected to build the indicator REGUW to measure the intensity of environmental regulation [19]. Secondly, the measurement method of energy efficiency of the explained variable is changed. Two other indicators reflecting energy efficiency are adopted: one is the global Malmquist-Luenberger index which includes the unexpected output, expressed in FGML. The second is the Global Malmquist-Luenberger index which does not include the unexpected output and is expressed in QGML [46]. Finally, since the data from 1995 to 2018 are used in this paper, and the time span is large, the feasible generalized least squares (FGLS) estimation deals with the possible heteroscedasticity and autocorrelation of the disturbance term, and the influence of the regression method on the robustness of the benchmark regression results is explained. Table 5 represents the results of the robustness test. Columns (1) and (2) report the results after changing indicators for core explanatory variables. In the benchmark regression, REGU is reflected by the percentage of words referring to the environment in reports. In the robustness test, the environmental regulation intensity index REGUW is constructed by linear standardization and weighted average treatment of the pollutant emission intensity of wastewater, exhaust gas and solid waste. The REGUW impact coefficient is positive and significant. The results of empirical analysis using different environmental regulation intensity indicators show that the main conclusions still stand after changing the measuring method of REGU. Columns (3)-(6) report the results of changing the indicators of explanatory variables. The explained variable of columns (3) and (4) is FGML, the explained variable of columns (5) and (6) is QGML and the impact coefficient of REGU is positive, which manifests that changing the measurement method of energy efficiency will not affect our basic core conclusion. The estimation methods used in columns (1) to (6) are the same as the benchmark regression. Column (7) reports the results of using FGLS estimation. It also shows that the baseline regression has a certain degree of robustness. In general, although the results in Table 5 are somewhat different from those in Table 4, the benchmark study's findings are largely consistent with the significance and symbolic direction of the core variables, so it can be said that the positive impact of environmental regulation on energy efficiency has strong robustness and reliability and can be promoted by increasing REGU.

Time Heterogeneity
The results of previous studies have stated that the average value of REGU increased significantly from 1995 to 2018, but the average value and annual growth rate of REGU in the two periods from 1995 to 2005 and 2006 to 2018 were quite different. Through the analysis of China's environmental policies, it can be discovered that the government has further strengthened environmental regulation since 2005. For example, the Decision on Implementing the Scientific Outlook on Development and Strengthening Environmental Protection issued in December 2005 requires "achieving sustainable scientific development", and this decision has had a key position in China's journey to protect the environment. Therefore, the sample was further divided into two sub-samples, one for 1995 to 2005 and the other for 2006 to 2018, to identify the difference in the role of REGU in TFEE in the two periods. Table 6 reports the Tobit regression in both periods. The impact effects were not significant from 1995 to 2005. Between 2006 and 2018, REGU promoted TFEE. Possible reasons for this are that REGU from 1995 to 2005 was weak and did not impose great pressure on enterprises. When REGU is weak, it cannot make the cost of environmental governance of enterprises rise significantly and cannot make the production behavior of enterprises change significantly, and the impact on TFEE is not significant. From 2006 to 2018, the government increased focus on environmental protection, the concept of environmental policy was further changed and the REGU was further strengthened, which made the cost of environmental governance of enterprises rise and forced enterprises to reduce energy costs and pollution emissions through TECH, use of clean energy in production, changes in production behavior and location selection, ultimately improving TFEE.  Table 4 show that REGU promotes TFEE from the overall sample of 30 provinces across the country. However, considering regional differences, we divide the data into three sub-samples, east, middle and west, to further study the regional heterogeneity. Table 7 denotes regional heterogeneity results. In the eastern and western regions, there is a positive impact coefficient of REGU on TFEE, where environmental regulation makes enterprises face greater environmental governance pressure, which can stimulate firms to bring forth new ideas in green technologies, force enterprises to adjust energy consumption structure, change production behavior and location selection and promote TFEE. There is no positive impact coefficient of REGU for TFEE in the middle part, where the REGU during the period in question is lower than in the eastern and western regions. Polluting industries tend to move to the central region where REGU is low. In addition, the REGU in the middle part may not constitute a major environmental governance pressure for enterprises, and the compensation income for TECH is less than the cost of environmental governance. Companies will spend more to fight pollution but lack sufficient impetus for TECH. Considering the average value of REGU in different regions (the average value in the eastern, central and western regions is 0.0048, 0.0046 and 0.0049, respectively), the test results of regional heterogeneity also preliminarily indicate that the low REGU may have limited effect on improving TFEE.

Mechanism Test
As mentioned in the previous mechanism discussion, REGU may affect TFEE by influencing TECH, IH and ES, which will be tested in the next step.
The following model is developed to explain whether explain whether the transmission mechanism of REGU on TECH, IH and ES [47][48][49] is established: where: D i, t is the transmission variable, which is green technology innovation (TECH), industrial structure upgrading (IH) and energy structure transformation (ES). The logarithm of patent applications is used to reflect the green technology innovation TECH, the proportion of coal in the total energy consumption is used to reflect ES and the IH index is constructed to reflect the industrial structure upgrading. In the estimation Formula (8), TECH, IH and ES are not restricted dependent variables, so it is not necessary to adopt the Tobit model which is consistent with the benchmark regression and is applicable to the interpreted variable as a restricted dependent variable for regression, but the panel fixed effect model is used for estimation.

Test on the Transmission Mechanism of Green Technology Innovation of Environmental Regulation for Energy Efficiency
REGU increases the cost of environmental governance of enterprises and affects TECH through the "compliance cost" effect and "innovation compensation" effect, thus affecting regional TFEE. Existing research manifests that when the green progress index increases, TFEE also increases [50], and TECH is the main pathway for energy use right trading systems to affect energy efficiency [51].
When testing the transmission mechanism of TECH of REGU for TFEE, the explained variable D in Formula (8) is TECH. The panel fixed effect model is built using Formula (8), and Table 8 displays the results. Utilizing the regression result from column (2) as an illustration, the impact coefficient of REGU is positive and significant, indicating that it primarily "compensates" for innovation and that it can encourage energy consumption entities to implement green technology innovation and promote energy efficiency. REGU increases the cost of corporate environmental governance, resulting in the inability of enterprises to achieve expected profits under the existing technical conditions, thus stimulating the power of enterprises to innovate green technology, ultimately improving TFEE and also enabling enterprises to improve competitiveness while meeting environmental requirements. Regression of the primary explanatory variable with a one-period lag can reflect the lag of REGU on TFEE through TECH, and can explain the robustness of the research finding [52,53]. The results of (3) and (4) in Table 7 demonstrate that the transmission mechanism of TECH of REGU for TFEE is reasonably significant and has some robustness, and the effect is also present in the long term.
The regions are separated further for the grouping regression to uncover regional differences in the transmission mechanism of TECH of REGU for TFEE. See Table 9 for results. The eastern region's environmental control coefficient is notably positive, while the central and western regions' coefficients are both positive and negative but not significant. This transmission mechanism thus varies significantly between regions. Table 9. Test of the transmission mechanism-green innovation technology (by region).

East
Central West The eastern region's TECH transfer mechanism is established. When compared to the central and western regions, the eastern region's considerably greater geographic advantages draw in talent and a higher level of human capital, it is more technology intensive and it has more space for enterprise technological innovation. It can effectively innovate green technologies and improve energy efficiency under environmental regulation. In the central and western regions, the impact coefficient of environmental regulation is not significant, indicating that the effect of energy saving and reduction of emissions through encouraging TECH may not be ideal. The reason may be that although these two regions have implemented REGU, their innovation capacity is insufficient due to the lack of human capital, and the usefulness of the method is difficult to demonstrate.

Test of Transmission Mechanism of Environmental Regulation for Industrial Structure Upgrading of Energy Efficiency
There are three primary ways in which REGU influences IH. First, due to regional variations in the severity of environmental regulation, several energy-intensive and highpolluting businesses have relocated to regions with lax environmental regulation, changing the regional industrial structure. Second, REGU has raised barriers to entry and lowered barriers to exit, affecting the scale and number of energy-intensive and high-polluting enterprises in the region and affecting the upgrading of regional industrial structure. Third, REGU can affect consumer demand and investor demand and force enterprises to change production behavior, adjust factor input and promote the upgrading of industrial structure. The energy consumption and pollution of the three industries are different, so the TFEE will change as the industrial structure shifts to primary, secondary and tertiary industries at once. Wang et al. (2022) believe that the IH is the key factor affecting TFEE [54] and the two are positively related. In other studies, the scholars' conclusions on this are inconsistent, with some arguments supporting the idea that industrial upgrading promotes energy efficiency [30] and others concluding that there is a blocking effect [55].
In order to test this transmission path, a panel fixed model is constructed according to Equation (8) for regression. At this time, the explained variable D in Equation (8) is industrial structure upgrading IH (Table 10). Taking results in column (2) as an example, the coefficient of REGU is negative and significant, implying that it can affect TFEE by inhibiting the upgrading of industrial structure. This is probably because environmental regulations will change the regional industry entry and exit mechanisms, affect the size and number of regional enterprises and restrict the development of regional high-energyconsumption and high-polluting industries, thus acting on energy efficiency by inhibiting the upgrading of regional industrial structures. The core explanatory variable lags behind the first period of the robustness test. The results of using the environmental regulation indicator lag behind the first period as the explanatory variable ( (3) and (4) of Table 10), which means that the transmission mechanism of REGU for the IH of TFEE is significant and also exists in the lagging period, with certain robustness. Note: Clustering robust standard error is shown in parentheses, and ** p < 0.05, *** p < 0.01.
Next, we discuss whether the transmission mechanism of IH holds across regions ( Table 11). The coefficient of REGU shows that existing regional differences in the transmission mechanism of IH of REGU for TFEE. It is positive but not significant in the eastern region and it is significantly negative in the central and western regions.
In the eastern region, the increase in the intensity of REGU may make the industrial structure develop towards a higher level, but this effect is not significant. After years of development, the three industrial structures in this region have reached a relatively stable and balanced state, so it is difficult to realize the positive role of REGU in TFEE through IH.
In the central and western regions, REGU inhibits the IH. REGU raised the entry barriers and lowered the exit barriers of energy-consuming and high-polluting industries, and even forced the closure and elimination of enterprises with substandard emissions, inhibiting the upgrading of industrial structure and thus affecting energy efficiency.

Test on the Transmission Mechanism of Energy Structure Transformation of Environmental Regulation for Energy Efficiency
China's main source of energy is coal, and clean energy is more environmentally friendly than coal, because it does not produce a lot of pollutants. Environmental regulation will restrict energy supply, and the biased choice of energy consumption caused by it will promote the substitution of energy elements, facilitating energy restructuring, and promote the improvement of energy efficiency. Existing empirical evidence shows that an increase of 1 unit in the proportion of raw coal consumption will reduce energy efficiency by 0.5844 units [46], and an increase of 1% in the proportion of power consumption will increase the energy efficiency by 0.5-0.7% [56]. Increased coal consumption is detrimental to energy efficiency growth, while the opposite is true for oil, electricity and gas consumption [36]. Reducing the proportion of coal consumption and promoting the transformation of energy consumption structure will have an important and positive significance for energy efficiency. Taking ES as the explained variable, a panel fixed effect model is constructed according to Formula (5) for regression (in Table 12). Taking (2) in Table 12 as an example, this result indicates that REGU can significantly reduce the proportion of coal in energy consumption, that is, REGU promotes the transformation of energy structure and further promotes the improvement of TFEE. As there are different types of energy and different types of pollution, there are also differences in the cost of governance. Therefore, enterprises will prefer to consume clean energy, thus promoting the transformation of energy structure and improving energy efficiency. The core explanatory variables are lagged for a period to carry out the robustness test, which can reflect the lag of the transmission mechanism of energy structure transformation in the impact of REGU on TFEE, and to some extent explain the robustness of the research conclusions (columns (3) and (4)). Columns (3) and (4) report the results of lagging the environmental regulation index for one period as an explanatory variable, and the results indicate that the impact mechanism of environmental regulation on energy efficiency through the transformation of energy structure is relatively significant and has a certain robustness, so there is a lagged impact effect.
Transmission mechanisms for ES in each region are identified further. See Table 13 for relevant results. The environmental regulation factors are not consistent between the east, central and west regions. The transmission mechanism of ES has obvious regional differences. In the eastern and central regions, REGU may promote the ES and improve TFEE, but this effect is not significant. China has visibly improved the clean energy industry in recent years, but there are problems such as high investment costs and high energy consumption in the process of investment. Compared with traditional energy, clean energy has disadvantages in application. Coal is still the most consumed energy source by businesses, so the ES has not yet achieved obvious results.
The promotion and use of new energy are limited by natural conditions. The western region has a good endowment of new energy resources and has the advantage of developing new energy. Therefore, REGU in this region can effectively drive the transformation of ES and promote energy efficiency.

Conclusions and Policy Recommendations
This research examines the effect of REGU on TFEE using panel data from 30 Chinese provinces. Initially, we described the potential effects of environmental regulation on energy efficiency. Secondly, we used the SBM model to measure total factor energy efficiency taking into account the carbon emission constraint and the ratio of phases connected to the environment in government reports was used to determine the level of environmental control. On this basis, the spatio-temporal evolution characteristics of the two were analyzed. Then, a Tobit model was constructed to study the impact effects, the time and regional heterogeneity of REGU on TFEE. Finally, we examined the transmission mechanism of REGU on TFEE through TECH and identified regional differences. This paper puts forward conclusions, policy recommendations, shortcomings and research prospects.

Conclusions
Firstly, there are obvious regional differences in China's REGU and TFEE. During the study period, China's TFEE shows an overall "N" curve change, with obvious regional differences. The intensity of environmental regulation tended to increase from 1995 to 2018 and, especially after 2005, the annual average growth rate of REGU was faster, reflecting the government's emphasis on environmental protection. The highest mean REGU is found in the western region, followed by the eastern region and finally the central region. The average level of TFEE in each province shows an increasing trend from 1995 to 2000, but declines from 2001 to 2007 and fluctuates again from 2008 to 2018, showing an overall "N" type fluctuation. TFEE is higher in the east and relatively lower in the midwest. There are large differences in different provinces.
Secondly, the impact of REGU on TFEE is positive, and there are time differences and regional differences. From a national perspective, REGU has promoted the improvement of TFEE, which also passed the stability test. In the eastern and western regions, the REGU is beneficial to the improvement of TFEE, but it is not significant in the central region.
Thirdly, REGU can act on TFEE through TECH, IH and ES. REGU can act on TFEE by stimulating TECH, inhibiting IH and promoting ES. In the eastern region, the TECH transmission mechanism of environmental regulation for energy efficiency is significant, but not in the central and western regions. The transmission mechanism of IH is significant in the central and western regions, but not in the eastern regions. The transmission mechanism of ES is significant in the western region, but not in the eastern and central regions.

Policy Recommendations
The following recommendations are made in this study based on the examination of the research conclusions and the aforementioned analysis results: First, the level of REGU by utilizing a range of tools should be increased. We should intensify environmental regulation even more, develop scientific and stringent environmental regulation policies, strengthen the legal framework for energy development and use and environmental protection, flexibly combine different environmental regulation tools such as environmental tax and emission right trading, fully exploit the complementary and synergistic functions of various types of environmental regulation tools and promote energy development and utilization. Additionally, it is understood that environmental regulations have a good impact on energy efficiency. In order to make the idea of energy conservation and environmental protection thoroughly ingrained in people's minds, we should increase public awareness of environmental protection, clarify corporate environmental responsibilities and encourage the establishment of environmental protection organizations. The environmental information disclosure system should be improved and a smooth information feedback mechanism should be established, so that the public and social organizations participate in environmental supervision.
Second, while encouraging TECH, guiding industrial structure upgrading and promoting energy structure transformation, we should refine supporting safeguard measures while implementing environmental regulation. We should cooperate with each department to form "synergy" for innovation, strengthen in-depth cooperation and stimulate innovation vitality with talents. Enterprises should increase the investment in technology research and development, actively introduce and innovate technology, improve the innovation ability of enterprises and maintain the competitiveness of enterprises under environmental regulation through advanced green technology. Scientific research institutions and universities should cultivate innovative talents in industry-university cooperation, carry out technological breakthroughs in energy conservation and clean production, transform green scientific and technological achievements into real productive forces and empower green development. Ecologically fragile areas should be guided to shift from the primary industry to tourism and other services to drive regional economic growth, so as to achieve both ecological livability and economic development. Enterprises are urged to improve their production behavior, produce environmentally friendly products and promote the rational allocation of energy and other factors.
Finally, local advantages should be used to adopt diverse environmental regulating measures. Despite the fact that environmental regulation has a favorable impact on energy efficiency, regional disparities in economic structure and environmental conditions have a major impact on the impact and transmission mechanism of environmental regulation for energy efficiency. Avoiding "one-size-fits-all", adjusting the emphasis of the implementation of environmental regulation measures relating to the regional advantages, enhancing the effectiveness of environmental regulation's implementation and promoting the improvement of energy efficiency are all things that different regions should do.

Shortcomings and Research Prospects
First, due to the lack of relevant data of enterprises and prefecture-level cities at present, we conducted empirical analysis based on provincial panel data. In the future, on the basis of further collection and collation of relevant data, the research can be expanded to the micro level. Second, existing studies have shown that the path of environmental regulation's impact on energy efficiency may not be limited to green technology innovation, industrial structure upgrading, energy structure transformation, etc., which were tested in this paper. Therefore, in-depth analysis and examination of other possible influencing mechanisms should be considered in further studies. Finally, due to various reasons, no in-depth research has been conducted on whether a threshold effect exists in the positive impact of environmental regulation intensity on energy efficiency. This is one of the directions that needs further study in the future.