Environmental regulation, innovation capability, and green total factor productivity: New evidence from China

Given China’ rapid transformation, its economy is currently experiencing a change from a rugged development style to a sustainable development style with green development being critical to this transformation. Increasing green total factor productivity (GTFP) is now considered one of the significant signs of economic growth. With increasingly stricter environmental laws and regulations and a broad application of innovation capability (ICY) in modern life, this research investigates the impact mechanisms of both environmental regulations (ER) and ICY on GTFP, offering robust empirical results from panel data of 30 provinces in China covering the period 2006–2017. The results indicate that both ICY and ER effectively promote GTFP, but compared to ER, ICY has a heterogeneous effect on GTFP. Moreover, ICY plays a mediating role in ER and GTFP, while ER promotes GTFP through ICY. Accordingly, the paper puts forward some suggestions, such as to optimize and improve the ER policy, enact an innovation-driven development strategy, widely use ICY technology, and strengthen monitoring and supervision.


Introduction
With the continuous development of society and economy, economic and environmental contradictions are becoming more and more prominent, and the three global crises of resource shortages, environmental pollution, and ecological damage are increasingly turning serious. How to properly coordinate the relationship between economic development and environmental protection has thus become an emerging concern to government departments, enterprises, and scholars (Wang et al. 2022). On October 29, 2020, the Fifth Plenum of the 19 th Communist Party of China (CPC) called for promoting green development and harmonious co-existence between man and nature. China is further implementing a strategy of sustainable development, improving the overall coordination mechanism for ecological progress, building an ecological progress system, promoting the all-around green transformation of economic and social development, and building further its own modernization.
In the early period of China's development, many local governments did not realize that protecting the environment is as important as economic development, as "pollution and then governance" became the basic path of national economic development. In the pursuit of economic interests, many areas and regions lack bottom-line thinking and ignore the carrying limits of local ecosystems, thus overloading the ecological environment and causing huge and incalculable losses. The annual growth rate of China's total factor productivity (TFP hereafter) in 2016 was 2.3% when taking energy consumption, environmental impact, and emission factors into consideration, while the annual growth rate of green total factor productivity (GTFP hereafter) was only 1.15%. With the concept of "clear water and green mountains are gold and silver mountains" deeply rooted in the hearts of people, top-level design and institutional progress Responsible Editor: Ilhan Ozturk * Chien-Chiang Lee cclee6101@gmail.com 1 have accelerated, pollution control has been vigorously promoted, green development has been remarkable, and ecological and environmental quality has continued to improve. Environmental regulations (ER hereafter) are an effective way to promote the coordinated development of the economy, ecology, and society. Therefore, studying ER is of great significance to both green and high-quality development. Ever since the 18 th CPC National Congress, in order to cope with environment development changes at home and abroad, to grasp development autonomy, and to improve core competitiveness, China has adhered to the road of independent innovation with Chinese characteristics by implementing an innovation-driven development strategy and the concept of innovative development. However, due to problems such as unbalanced and inadequate innovation and development in some regions, the quality and efficiency of innovation are still low, and weak innovation capability (ICY hereafter) still exists. Some scholars believe the number of patent licenses is an important indicator of innovation capability (Zhu et al. 2021;Wen et al. 2022). With this as an example, by the end of 2017, Guangdong had 332,652 and ranked first in China, while Tibet Autonomous Region had 420, accounting for only 1 ‰ of the total patent licenses in Guangdong. At the same time, the proportion patents of eastern China accounted for 73% all the nation's total, or more than twice the sum of patent licenses in the central regions and western regions. The improvement of regional innovation levels sets the foundation for building an innovative country in an all-around way. Thus, this unbalanced and inadequate development of regional ICY has become a practical problem restricting China's implementation of an innovation-driven development strategy (Liu 2014;Liu and Lee 2021).
The 18 th and the 19 th National Congresses of CPC and the 14 th Five-Year Plan all clearly emphasized the need to give top priority to ecological development and green development and to promote high-quality economic development and high-level ecological and environmental protection in a coordinated manner. Measuring and evaluating green economic development and high-quality economic development are becoming hot issues in academia. The growth rate of TFP and its contribution to its output growth are regarded as the main bases for judging the mode of economic development and the improvement of economic quality (Wang et al. 2009). However, academia often adopts GTFP as a comprehensive indicator to measure and evaluate green economic growth, considering it as a green development index that combines economic growth with environmental protection and harmony between man and nature (Zhu and Wang 2019).
Concerning the impact of ER on GTFP, academia has provided a large amount of literature research. Some use individual indicators for ER measurement, and some based on building an index system use the entropy method, principal component analysis, and adjustment index to obtain the comprehensive ER index and to then carry out empirical analysis and research on them. However, the results unveiling the effect of ER on GTFP are in disagreement and roughly divided into three categories. First, some studies have identified an inhibiting relationship between the two (Zárate-Marco and Vallés-Giménez 2015; Jorgenson and Wilcoxen 1990), especially in the longrun condition (Huang et al. 2018). Second, other studies have held the view that ER has a positive effect on GTFP (Wang et al. 2021) and can promote it (Ford et al. 2014). Third, under the influence of specific types of ER, GTFP shows a trend of differentiation-that is, command control type and incentive type of ER have a negative impact on GTFP, while public participation type of ER has a positive impact on GTFP. Several studies have revealed an inverted U-shape link between ER and economic growth (Zhang et al. 2018a, b), but inverted N-type and U-type are also presented (Gao et al. 2019;Shen et al. 2017).
There are also a large number of publishments describing the direct role of ICY on GTFP. Many foreign literature has focused on the observation and demonstration of enterprise R&D behavior and its influencing factors. Dorfman (1954) explained for the first time the decision mechanism of enterprise R&D expenditure from a theoretical model. Cohen and Levin (1989) empirically found that enterprise size and industry characteristics also have effects on enterprise R&D, which then impacts industry GTFP. The domestic literature has focused on the technological efficiency of industry and enterprise levels when researching ICY. Cheng et al. (2021) systematically analyzed with results showing although there are losses in GTFP caused by a deterioration in technological efficiency, these are offset by other increases in GTFP. Zhang (2006) believed that comprehensive ICY has a positive effect on TFP. Wang and Cao (2019) focused on the influence of Internet development on regional total factor energy efficiency and proved that such development plays a positive role in improving regional total factor energy efficiency. Wen et al. (2021) stated that industrial digitalization improves product innovation and GTFP, but has an insignificant effect on TFP.
None of the above studies have taken into account a combination of the economic impacts of ER and ICY. Is it possible for ER to affect GTFP through other factors such as ICY? How do environmental resources and ICY work under green economy development? What is the impact mechanism? What role do they play in green economic development and how can the three achieve high-quality economic development? Therefore, clarifying the relationships among ER, ICY, and GTFP and analyzing the influence mechanism between the three can help scientifically evaluate whether the economy has achieved high-quality green development under the premise of the full consideration of ecological and environmental constraints.
To sum up, in order to explore the relationships among ER, ICY, and GTFP more reasonably and comprehensively, it is of great significance to examine the following questions. What are the characteristics of GTFP development in China? Does ICY affect GTFP? As a restrictive means for the government to promote green economy innovation, does ICY play a mediating role between ER and GTFP?
Compared to existing studies, this paper offers the following contributions and differences. First, the research subjects are more comprehensive. This paper focuses on ER, ICY, and GTFP and explores their influence mechanism. Most existing studies just have looked at the relationship only between ICY and GTFP or between ER and GTFP.
Second, the empirical research herein is more robust. Existing research on ER of GTFP is mostly from the perspective of environmental regulation tools or the regional competition spillover effect. The mechanism of ER affecting GTFP is missing from a thorough research angle. Based on the verification of the non-existing spatial effect, we focus on moderating and mediating effect analyses of ICY between ER and GTFP and show that a shortage of the mediating effect exists.
Third, the calculation of GTFP is relatively scientific. Part of the literature only measures GTFP from the perspective of input and output and ignores the impact of unexpected output on GTFP. However, this study takes industrial wastewater utilization rate, SO2 utilization rate, and industrial solid waste utilization rate as unexpected outputs and measures GTFP by using the GML model.
Fourth, the selected research objective of regional ICY is more reasonable. Relevant ICY research at home and abroad has mainly focused on enterprises or industry levels (Zhang 2006). Due to China's current science and technology management system, enterprises have not become the main body of innovation activities, especially for small-and medium-sized enterprises (SMEs). Most of China's innovation activities are at scientific research institutions and universities, and the innovation activities of enterprises or industries are only a small part. Therefore, the enterprise or industry research level cannot cover all innovation activities in China. Porter and Linde (1995) believed that regional innovation closely relates to industry density, and regionalization helps to promote innovation and the diffusion of knowledge. Therefore, regional innovation can help realize the effect of industry agglomeration, but enterprise and industry innovation cannot. In this case, the regional level of research has many unique advantages over national and enterprise industry-level research, thus opening up a new perspective for our study.
Following the introduction, the rest of the paper is organized as follows. Section 2 presents a brief literature review of the existing studies on ER, ICY, and GTFP and then performs the impact mechanism of interaction between these three. Section 3 describes the variables, data sources, and methodology. Section 4 introduces the econometric models applied in this paper, the empirical results, and analyses. Section 5 further discusses the empirical results. Finally, the last section summarizes the conclusions and puts forward corresponding policy implications.

Analysis of the impact mechanism of ER and GTFP
When referring to ER and environmental governance, people often think of administrative means relating to environmental protection. In recent years, China has issued the Law on the Prevention and Control of Environmental Pollution, the Environmental Protection Law of the People's Republic of China, the Environmental Impact Assessment Law, the Clean Production Promotion Law, and other laws and regulations, but domestic environmental governance depends not only on administrative means, but also on adjustments to market-oriented economic resources. Economic tools like environmental tax policies, environmental credit policies, environmental poverty alleviation policies, environmental protection industry policies, etc., as well as resource industry agreements, environmental certifications, environmental leader systems of pollutant discharge enterprises can all be used as important methods and channels for environmental governance.
Appropriate ER can spur enterprise technological innovation in certain environments-namely, the weak Potter hypothesis, while appropriate ER can promote the competitiveness of enterprises in a certain environment-namely, the strong Potter hypothesis (Porter and Linde 1995). No matter strong or weak, ER has always been effective at solving the externality of environmental pollution. Nameroff et al. (2004) believed that the government should develop environmental regulatory policies to support and encourage enterprises to produce green products and services, thus significantly reducing the external additional costs of innovation competition. Song and Wang (2016) showed that if an enterprise's technological innovation considers environmental protection, then this will help to improve environmental governance and subsequently promote the coordinated development of the economy and the environment (Song and Wang 2016).
Many local governments in China in fact have strengthened ER on enterprise production and operation activities through a combined series of administrative and economic perspectives, such as formulating strict environmental protection regulations, resource industry agreements, and Environmental Science and Pollution Research (2022) 29:39384-39399 39386 environmental certification programs. They all encourage enterprises to take the following measures to deal with ER. The first one is to improve the production process and technology, reduce pollution emission intensity, improve production efficiency, and reduce or cut down environmental costs in order to gain an environmental innovation effect. Second, inspired by the encouraging policies of government ER, such as green subsidies and capital preferences, enterprises can take the initiative to carry out technological innovation to obtain such monetary incentives and form an innovation compensation effect. Third, for projects with high investment, high energy consumption, and high pollution, enterprises consider the strict environmental protection policies and prefer to be in green innovation projects and high energy consumption and high pollution projects to form an investment screening effect. Hence, this study proposes the following hypothesis.
H1: ER pushes the improvement of GTFP through the coordinated development of the economy and the environment.

Analysis of the impact mechanism of ICY and GTFP
Innovation is different from other factors of production, as it can help improve resource utilization efficiency, production efficiency, and reduce environmental pollution to directly improve GTFP (Su and Zhou 2021). There is very rich research on ICY and how it promotes economic development and improves TFP. One strand of literature focuses on the impact of ICY on regional economic growth from the perspectives of technological innovation, factor agglomeration, knowledge spillover (Yamashita 2021). It is generally believed that the improvement of ICY contributes to the optimization of labor structure, industrial structure upgrading, and innovative technology application, which are conducive to better TFP and thus promote regional economic growth. Another kind of literature has directly studied the impact of ICY and technological progress on TFP from the perspectives of regional development differences, Internet development, and industrial structure optimization, as well as the influence of ICY on GTFP, whereby the former plays a significant role in promoting the latter (Ana, 2007).
Economic development between regions is becoming more and more integrated. The end result is that the cost of innovation activity exchanges and cooperation are being reduced rapidly and that innovation subjects are finding it easier to obtain innovation information and innovation technology and easier to learn and imitate innovation technology. All these factors help improve ICY in these regions and further optimize the labor structure, promote industrial structure upgrading, and push economic growth. At the same time, the implementation of a national innovation-driven development strategy is deepening and taking innovation research, innovation investment, and innovation achievements as new performance indicators. Local governments are gradually increasing innovation resources, which improve the level of innovation output, due to the regional closing effect and the competition effect. Overall, this forms a spatial spillover effect of ICY and creates positive effects on the economy .
Due to the influence of regional policy differences, local governments formulate and implement their own innovation incentive mechanism according to the actual situation, resulting in differences in ICY between various regions, and so the impact of regional differences on GTFP is not the same. At the same time, along with development of the Internet, applications of new technologies related to resource utilization, environmental protection, the generation of new materials, new energy, and other new industries, as well as new modes of the digital economy, all are directly affecting technological progress and technological efficiency. All these factors influence the change of GTFP (Wang and Cao 2019;He et al. 2021). Hence, this study proposes the next hypothesis.

Analysis of the impact mechanism on ER, ICY, and GTFP
International academia has widely discussed the common research topic of green ICY driven by ER in both developed and developing countries. Chen et al. (2014) conducted an empirical analysis with results showing that ER is conducive to environmental management and green ICY and has a positive impact on GTFP. Zhang et al. (2018a, b) noted that the main driving force for an enterprise to adopt green innovation is ER pressure. In other words, the stricter ER is, the more pressure an enterprise feels to promote green innovation and keep itself ahead under fierce market competition. Previous studies have also shown that ER can promote enterprise development and diffuse green technology, because of the compensation effect of innovation. In this sense, ER has an incentive effect on enterprise green innovation technology and green innovation performance (Hamamoto 2006;Tian and Lin 2017).
There are also empirical studies in China by Wang and Zhang (2018) and Zhang and Lv (2018) that confirm the same effect above. Taking a sample of 285 Chinese cities as examples, Chen et al. (2019) found that technological innovation under strict ER helps to reduce environmental pollution. Its internal mechanism includes three channels: energy-saving effect, industrial upgrading effect, and population agglomeration effect. Qian and Li (2018) used industrial industry data to verify that technological progress is an important factor in promoting China's industrial energy savings and reducing consumption and CO2 emissions, among which the energy-saving and consumption reduction performances of technological innovation are the highest.
Although existing studies have made some beneficial explorations on the driving and interactive impacts of ER and ICY on GTFP and many valuable conclusions have been drawn, there are still two following deficiencies. First, most studies have analyzed the driving effect of ER on GTFP, but have paid less attention to the green development effect of ICY. GTFP, unlike the more traditional TFP, places more emphasis on the impact of green economic growth on the environment. Second, although the existing literature has carried out significant research on the role of ICY in promoting GTFP, it ignores the joint role of ER. It closely relates to innovation on economic growth, industrial upgrading, and green development effect, as well as the restriction of environmental regulation on the green development effect of innovation. To further verify the relationships among ICY, ER, and GTFP, the following hypothesis is put forward.

H3: ER promotes the development of ICY to further affect GTFP.
On the basis of learning from existing research results and using panel data of 30 provinces and cities in China for the period 2006-2017, we focus on the relationship between ER, ICY, and GTFP in combination with analyses of the moderating effect and the mediating effect. The research framework is shown in Fig. 1, whereby the mechanism is studied in order to give certain implications and suggestions for the improvement of environmental policies, innovation policies, and the transformation of local economic growth mode in China. The aim is to fill the existing research gap.

Independent variables
This research mainly examines the influence mechanism and action path of ER and ICY on GTFP. Therefore, GTFP is particularly important as the explained variable. This study chooses variables of input elements, expected output, and unexpected output and then uses the GML model to calculate GTFP. Detailed data are as follows.
Since there are no official statistics on capital stock in China's provinces, the academia mainly uses the methods of Zhang et al. (2004) and Shan (2008)  according to the carbon emission coefficient published by IPCC (Zeng and Ye, 2021), and total energy consumption represents the energy input of each province (Sun and Yang, 2020). The total amount of fixed capital formation, fixed asset price index, and the number of employees are from the China Statistical Yearbook, and the total energy consumption data are from the China Energy Statistical Yearbook. discharge, total wastewater discharge, and industrial solid waste production amount (Zhang and Qiao 2021). Based on data availability, this study use industrial wastewater utilization rate, SO 2 utilization rate, and industrial solid waste utilization rate (Wu et al. 2020). The data come from the China Environmental Statistics Yearbook and China Environment Yearbook. (4) To ensure the robustness of the results, this research utilize an alternative explained variable to recalculate GTFP2 using the SFA model. Please see Table 1 for the specific values.

Dependent variables and control variables
The core dependent variables of this paper are ER and ICY. The control variables are industrial added value, technological progress, industrial structure, and urbanization level.
(1) ER. Currently, there is no final defined method for measuring ER, but there are three common methods to measure variables. The first one is taking a certain policy implementation as a cutoff (for example, the Action Plan for Air Pollution Prevention and Control), measured by dummy variables (0-1) (Wang et al. 2021). The second one is to measure the comprehensive ER index by the industrial sulfur dioxide removal rate (%), industrial smoke (powder) dust removal index (%), industrial solid waste comprehensive utilization rate (%), industrial wastewater treatment rate (%), household waste harmless treatment rate (%), and adjustment coefficient . The entropy method and adjustment coefficient method are used to measure ER intensity . The third one is to measure ER by the proportion of total investment in environmental pollution control in GDP or the number of environmental events disclosed (Mulatu 2017;Yang et al. 2021a, b). Since some environmental indicators have been calculated as undesirable output indicators and to avoid endogenous model problems, this paper takes the number of environmental event disclosures as a measure of ER indicators and takes the proportion of total environmental pollution control investment in GDP as the alternative variable of ER. The data are derived from China Environmental Statistics Yearbook and China Environmental Yearbook.
(2) ICY. ICY has a significant impact on GTFP (Zhang and Qiao 2021), but it is more convincing to use the number of patents to reflect the level of ICY (Crosby 2000). The higher the number is of regional patent application authorization, the stronger is the region's ICY, the more it can promote the use and progress of energy-saving technology and then help improve GTFP (Wang and Cao 2019  industrial added value is expressed by the GDP of secondary industry; technological progress is expressed by per capita science and technology expenditure; the industrial structure is expressed by the ratio of the tertiary industry to secondary industry output value; and urbanization level is expressed by the proportion of the urban population at the end of the year. The data are from the China Statistical Yearbook and the China Science and Technology Statistics Yearbook.

Descriptive statistics
The data used in this paper are mainly from  Chung et al. (1997) presented the Luenberger productivity index, which considers both reduced input and increased output simultaneously without considering the measurement angle. Therefore, it is much more common than the Malmquist productivity index. Referring to Oh (2010), we use the global ML index (GML) to measure GTFP (Cheng et al. 2020) and decompose it into technical efficiency change (EC) and technological progress (TC).

GML Model
Among them, → D G 0 (•) is the Malmquist function, with the directional vector set to (g x , g y , g z ) = (−x, y, −b) , so as to minimize the input and non-expected output while maximizing the desired output. The input and expected output are strongly or freely disposable, while the unexpected output is weakly disposable.

Panel data model
Based on the past research (Wang and Zhang 2020;Wu et al. 2020;Wang and Zhang 2018), this paper takes GTFP as the independent variable and ER and ICY as the core dependent variables and constructs the benchmark measurement model as follows: Among them, i and t represent provinces and years, respectively; i and t represent unobservable individual and time fixed effects, respectively; it represents the random error terms; GTFP indicates the GTFP of the independent variables; ER explains the ER of dependent variables; ICY indicates the ICY of dependent variables; and sec , te , is , and urban indicate the industrial added value, technological progress, industrial structure, and urbanization level of the control variables, respectively. Referring to Wang and Zhang (2020) and Chen et al. (2019), the urbanization level has an impact on green total factor energy efficiency.
In this paper, the proportion of total environmental pollution control investment in GDP has been taken as the alternative variable of ER2.
(b) The explained variable has been replaced by GTFP2, which is re-calculated by the SFA model.

Benchmark regression analysis
According to the Hausman test and Eq. (4), we estimate the impacts of ER and ICY on TFP by the fixed-effect model. Benchmark regression results are in Table 2. Columns (1), (2), and (3) in Table 2 represent control region effect, control time effect, control region and time effects, respectively. The results show that the coefficient of ER is significantly positive at the 1% level, indicating that ER promotes GTFP. Thus, we verify H1: ER pushes the improvement of GTFP through the coordinated development (7) lnGTFP it = 0 + 1 * lnER2 it + 2 * lnICY it + 1 * lnsec it + 2 * lnte it of the economy and the environment. On the one hand, the enhancement of ER drives industrial structure upgrading. It not only transfers capital and labor from low-productivity and high-pollution industries to high-productivity and clean environmental technology industries, but also reallocates resources to improve environmental quality, which can increase economic productivity and improve GTFP. On the other hand, strengthening environmental supervision also helps to develop high-tech intensive and environmentfriendly industries with high technical spillover effects.
Columns (1), (2), and (3) in Table 3 represent the control region effect, control time effect, control area and time effect, respectively. The results show that the coefficient of ICY is significantly positive at the 1% level, indicating that a 1% unit increase in ICY increases GTFP by 0.003 unitsthat is, ICY positively promotes GTFP. Thus, we verify H2: ICY contributes to the improvement of GTFP through the coordinated development of the economy and innovation.
Most enterprises in general are supervised by ER. If the profit margin shrinks due to increasing costs in order to meet the requirements of ER, then enterprises are likely to be abandoned by the market. Enterprises will hence actively solve the problem of environmental pollution and implement the installation of related pollutant equipment. A strong ICY can promote enterprises to better allocate resources and greatly improve GTFP.
Column (1) in Table 4 is listed as a least square method. The results show that the ER coefficient is positive but  nonsignificant, and ICY is significant at the 1% level, indicating that ER and ICY promote GTFP. Column (2) of Table 4 is the control region effect, column (3) is the control time effect, and column (4) is the control region and time effect. The results of columns (2)-(4) of Table 4 show that the ER coefficient is significantly positive at the 1% level and ICY is also significantly positive, indicating that ER and ICY promote GTFP. The government or industry departments have adopted a series of compulsory ER measures such as formulating environmental protection policies, restricting production pollution, and initiating strict environmental certification, forcing enterprises to improve the production process and technology, reduce pollution emissions, and thus improve GTFP. At the same time, affected by environmental subsidies, green technology incentives, and other incentive ER, enterprises have taken the initiative to invest in the research and development of green technology innovation and actively participate in green policy subsidy incentives in order to improve production efficiency and finally raise GTFP. Innovation capability has a positive role in promoting GTFP. The improvement of ICY makes for a broad application of innovative technology, produces technological progress, improves technological efficiency, and has a positive impact on GTFP. The benchmark regression results support hypotheses H1 and H2.
For the control variable, the industrial added value coefficients in the columns (1)-(4) in Table 4 are significantly negative, showing industrial added value has a significant inhibitory effect on GTFP. It means that as the industrial added value increases, the existing technology of various provinces cannot inhibit the negative impact of industrial production, resulting in the environment bearing the negative impact caused by the industrial added value and thus inhibiting the improvement of GTFP. The coefficients of technological progress in columns (2)-(4) are significantly positive. Technical progress promotes GTFP, denoting that as technology advances, green production technology, pollution control technology, and resource-saving technology are developed and promoted, applied to actual production, and greatly enhanced production environment technology efficiency. The coefficient of the industrial structure in columns (2)-(4) is significantly positive. Industrial structure promotes the improvement of GTFP, meaning that, along with the adjustment of the industrial structure, the output value of the tertiary industry is increasing and the secondary output value continues to decline. Thus, the proportion of industry has declined, the proportion of the service industry continues to rise, environmental pollution caused by the secondary industry is greatly reduced, and then GTFP improves. The columns (2)-(4) for urbanization level are significantly positive. Hence, the improvement of the urbanization level means more urban infrastructure construction and urban public services and pushes technical talents to high urbanization areas. This strengthens a region's human capital, which is conducive to the generation of technological innovation and thus improves GTFP. At the same time, the improvement in the urbanization rate is often accompanied by more investment in environmental governance and environmental protection, which also promote GTFP and thus improve it.

The robustness test
In order to further test the robustness of regression estimates, according to Eq. (6)-Eq. (8), respectively, this paper further conducts robustness analysis through time processing, regional processing, variable replacement, and a transformation of model robustness. The test results are shown in the table below.
(2) Regional processing. The columns (3)-(5) in Table 5 exclude the eastern, central, and western regions. They form new samples containing only the central, eastern, and central provinces and then analyze them with fixed-effect models. Although the regression results are slightly different than the benchmark regression, the directions of dependent variables are completely consistent with the benchmark regression. (3) Variable replacement. The columns (6)-(7) in Table 5 represent the robustness test using ER replacement variables and lagging ER variables, respectively. Although the regression results vary slightly from the benchmark regression, the dependent and control variables are completely consistent with the benchmark regression. (4) Modeling transformation. Column (8) of Table 5 performs the regression analysis using least square dummy variables fixed model (LSDV). The regression results show the same significance as the benchmark regression coefficients and the direction of explanatory variables are the same, too.

Endogeneity analysis
After the benchmark regression and robustness test regression control the appropriate variables, the empirical results demonstrate significant effects on ER, ICY, and GTFP. However, the measurement errors of variables, omissions of potential variables, and two-way causal relationships between variables all have implications for the empirical results. Since there may be obvious differences in the intensity of ER and ICY in each province, the provinces will also differ in formulating ER and ICY. At the same time, because this study adopts provincial panel data, there are some missing observations or some variables that cannot be collected, and related variables may be left out. It is possible for a two-way causal relationship between ER and ICY and green technology development to exist, which is endogenous (Wen et al. 2019). To solve the endogenous problem, this study verifies the causal relationship between ER, ICY, and GTFP by using the lag variable as a tool variable and the dynamic panel model (differential GMM) method (Yamashita 2021). At the same time, the mechanism between the three factors will be analyzed later. The results of the endogenous tests are shown in the table below.   Columns (1)-(4) of Table 6 select ER lag variable as an instrumental variable, ICY lag variable as an instrumental variable, ER lag variable, and ICY lag variable as the endogenous test. Column (4) chooses the dynamic panel model (differential GMM). Because of fewer sample data, a onestep estimation is used to test. The results of columns (1)-(4) unveil that ER has a significantly positive effect, and ICY also has a significantly positive effect. Therefore, it can be concluded that the relationship between ER, ICY, and GTFP remains unchanged, and the regression results of the benchmark regression and robustness tests are confirmed.

Heterogeneity analysis
The previous section uses the fixed-effect model, panel variation factor model, and dynamic panel model to find the relationship between ER, ICY, and GTFP, while this part focuses on the impact of heterogeneity among the three. The robustness test uses regional processing, distinguishes the east, central, and western processing into different sample data, and achieves consistent regression results with the benchmark regression. This part also conducts heterogeneity tests of ER strength (strong and weak), ICY level (high and low), and GTFP level (high and low). The relevant test results are shown in the table below.
The columns (1)-(6) of Table 7 represent the regression results of high-intensity ER (greater than ER mean), lowintensity ER (less than ER mean), high ICY level (greater than the ICY mean), low ICY level (less than equal to ICY mean), high GTFP level (greater than GTFP mean), and low GTFP level (less than equal to GTFP mean). The results show that whether the sample data are at a highintensity ER level or are at a low-intensity ER level, all have a positive effect in promoting GTFP. When the sample data are at a high ICY level, there is an obvious positive promotion effect on GTFP, but when the sample data are at a low ICY level, there is a negative relationship to GTFP, but this is not significant, indicating that the influence of ICY level on GTFP shows strong heterogeneity. When the sample data are at a high GTFP level, ER and ICY are not significant at 10% level. When the sample data are at a low GTFP level, ER and ICY have an obvious positive effect on GTFP, but ICY is not significant, thus presenting a strong difference.

Further Analysis
The previous part analyzes in detail the impacts of ER and ICY on GTFP, but does not answer how ER and ICY affect GTFP. This part analyzes the relationship between ER, ICY, and GTFP from three dimensions: spatial effect, moderating effect, and mediating effect, respectively.

Spatial correlations test
To verify the applicability of the fixed-effect model, spatial correlation is tested. A further spatial measurement model is needed to analyze whether GTFP presents a spatial correlation or not. If spatial correlation does not exist, then the fixed-effect model is applicable. The existence of spatial correlation is usually determined by the Moran index with the formula below: GTFP of province i ; n represents the total number of regions; and W ij is the adjacency space weight matrix. The results of the spatial correlation test are in Table 8.
The test results show that Moran's I of 2006-2017 is not significant, except for the absence of partial data in the years 2006, 2015, and 2016. This indicates that the GTFP space is irrelevant. To ensure robust conclusions of spatial noncorrelation, this paper uses the economic weight matrix for further validation (Table 9). Moran's I index is not significant except for the year 2006 and years 2015-2017.

Moderating effect analysis
In order to further test the mechanisms of ER and ICY on GTFP, this paper refers to the verification method of Wen et al. (2005) and further verifies whether ER can affect GTFP through the interaction with ICY (Lee et al. 2021a, b). The specific model is shown as follows: Among them, 3 is the interaction coefficient of lnER it and lnICY it . If the coefficients α 1 , α 2 , and α 3 are all significant, then the moderating effect exists. If the coefficient 3 > 0 is significant, then it shows that ER can have a positive impact on GTFP through the interaction with (10) lnGTFP it = 0 + 1 * lnER it + 2 * lnICY it + 3 * lner it * lnict it + 4 * lnsec it + 5 * lnte it + 6 * lnis it + 7 * lnurban it Results tested by the moderating effect show that the coefficient 3 is positive but not significant at the 10% level (Table 10). It means that ER cannot have an impact on GTFP through its interaction with ICY. Thus, the two cannot jointly affect GTFP, indicating that the moderating effect does not exist.

Mediating effect analysis
In order to further test whether there is an indirect effect between ER, ICY, and GTFP, this paper follows Wen et al. (2005) to build a mediating effect model, so as to verify whether ER can affect GTFP through ICY. The specific model is shown as follows: If the coefficients β 1 , t 1 , θ 2 are significant, then the mediating effect exists. According to the regression results in columns (1)-(3) of Table 11, ER has a significant promotion influence on GTFP, ER has a significantly positive effect on ICY, ICY has a significant promotion effect on (11) lnGTFP it = 0 + θ 1 * lnER it + θ 2 * lnICY it + 1 * lnsec it + 2 * lnte it + 3 * lnis it + 3 * lnurban it + i + t + it GTFP when examining the influences of ER and ICY on GTFP, and the regression coefficients of ER and ICY are significantly positive. It can be judged that ICY has a significant mediating effect in the model. Its mediating effect is 0.018*0.002/0.001 = 3.6%. Therefore, combined with the moderating effect and the mediating effect results, we believe that ER affects the change of GTFP through ICY. The moderating and mediating effect results support hypothesis H3. It indicates ER has an influence on tGTFP through ICY (Zhu and Wang 2019).
Using the Sobel test, the mediating effect is 0.001 at the 1% significance level, and the mediating effect is 19.03% of the total effect. In other words, ICY shows a positive effect between ER and GTFP. The same conclusions mentioned above are obtained using the Bootstrap method.

Conclusion and Implications
This paper selects panel data from 30 administrative provinces and cities in China (except Hong Kong, Macao, Taiwan, and Tibet) in the period 2006-2017. First, we select the input elements, including expected output and non-expected output indicators. The GTFP index of 30 provinces and cities is calculated through the GML index model, and then the calculated GTFP is set as the explained variable. ER and ICY are the explanatory variables to analyze the relationship between the three. Utilizing robustness test, endogenous test, and heterogeneity test, this study believes that ICY can promote GTFP and that ER can also help improve GTFP. Moreover, compared to ER, ICY shows obvious heterogeneity to GTFP-that is, the stronger ICY is, the stronger is  its effect in promoting GTFP. Based on the spatial correlation test, the results show there is no spatial correlation of GTFP. Using the moderating effect and mediating effect test, we further verify the interaction of ER and ICY to GTFP. Results show that ER can affect the change of GTFP through ICY. Based on the above conclusions, this paper offers the following suggestions listed below.
First, the China government should insist on implementing policies related to ER. The empirical results show that ER not only help improve GTFP, but also positively help improve ICY. At the same time, the research results of different scholars have shown that the relationship between different ER types and GTFP presents different trends. Therefore, it is suggested that local governments continue to implement relevant policies on ER, choose appropriate ER types according to the local current situation, and strive to maximize resource benefits while protecting environmental protection. In addition, local governments should further strengthen the ER mechanism and clarify the governance scope, such as improving the reward and punishment system, offering precise subsidies for innovative enterprises, and shutting down seriously polluting enterprises.
Second, an innovation-driven development strategy should be firmly implemented. For China, its rapid growth of productivity is one of the important signs of implementing innovation-driven development transformation. Restricted by various factors, China's economic growth has not shifted to the track of relying on innovation. In order to effectively promote an innovation-driven development strategy, the government should reform and improve the innovation management system, adhere to the dual-wheel drive of scientific and technological innovation and institutional innovation, carry out comprehensive innovation and reform, enhance the technical foundation of economic and social development, release the potential of ICY, and enhance its role in promoting GTFP.
Third, every local government should focus on an innovation-driven development strategy, further refine policies and measures, adjust the existing innovation incentive policy mechanism, and effectively reduce the innovation cost of enterprises, such as introducing preferential innovation incentive policies and increasing research and development subsidies for technological innovation. In addition, the government and enterprises should keep an eye on the innovation of systems and mechanisms, strengthen the promotion of environmental protection concepts, actively guide or support the industry to carry out the application and introduction of green innovation technologies, implement green transformation, strengthen environmental protection technology innovation and the guidance of green production, and realize the coordinated promotion of environmental and industrial upgrading.
Fourth, the empirical results show that ICY not only facilitates the improvement of GTFP, but also promotes it as a mediating variable of ER. Thus, both need to have strengthened monitoring and supervision with the help of ICY. The China government should enhance innovation and support more related applications of information technologies (such as artificial intelligence, blockchain, cloud computing, and big data), increase the monitoring of environmental governance, establish a big data supervision platform to collect local environmental pollution observations, ensure the effectiveness of central decision-making and supervision, and reduce the possibility of local governments from cooperating with polluting enterprises. In addition, relevant authorities should further optimize the implementation supervision mechanism of ER, give full play to the positive role of the Internet, and ensure smooth channels for all of society to participate in environmental governance (Yang et al. 2021a, b).
Abbreviations GTFP : Green total factor productivity; TFP : Total factor productivity; ICY: Innovation capability; ER: Environmental regulation Authors' Contributions Three authors provided critical feedback and helped shape the research, analysis, and manuscript. Chien-Chiang Lee is responsible for conceptualization and writing of the original draft; Mingli Zeng is responsible for the paper's visualization, investigation, and writing of the original draft; and Changsong Wang is responsible for the overall investigation and formal analysis and writing of the original draft.
Funding Chien-Chiang Lee is grateful to the Social Science Foundation of Jiangxi Province of China for financial support through Grant No: 21JL02.
Availability of data and materials Data are available from the authors upon request.

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The authors declare that they have no competing interests.