The effects of simmelian ties on innovation of low-carbon technology: a study of top managers' environmental awareness and stakeholder pressure in China

Low-carbon technology innovation (LTI) engenders environmental protection and socioeconomic development. Hence, low-carbon innovation of enterprises becomes a crucial policy arena for national development and climate mitigation strategy. LTI is now associated with enhanced reputation and competitive edge of enterprises. We constructed a framework to empirically explore the impact of simmelian ties (ST) on LTI, testing the moderating effect of stakeholder pressure in this relationship. We used a sample of 385 employees from industrial enterprises in China through a structured questionnaire. The study results show that: first, when the enterprise is in a strong ST, the top managers' awareness of environmental benefits has a significant positive impact on LTI. Second, when the enterprise is in a weak ST, top managers' awareness of environmental risk has a significant positive impact on LTI. Third, pressure of key stakeholders and pressure of secondary stakeholders positively moderate the interaction between ST and top managers' environmental awareness (TMEA) on the impact of LTI. Fourth, the moderating effect of key stakeholders’ pressure was observed to be stronger than that of secondary stakeholders’ pressure. Theoretically, this paper contributes to literature by developing a framework to investigate interaction between ST, TMEA and LTI under different stakeholder pressures. Based on this framework, we provide a theoretical reference for enterprises to choose the appropriate and optimal TMEA for competitive edge.


Introduction
With the global crusade for emission limitation, enterprises now face a complex task of economic-environmental maximization. Hence, low-carbon technology innovation (LTI) plays a key role in the performance (economic and environmental) of industrial enterprises (Dou 2017). To this end, experts recommend more collaborative approaches toward technological innovation (Bagherzadeh et al. 2019). Strategic investments in low-carbon technologies by manufacturing firms help reduce greenhouse gas emissions. This may involve application of knowledge from several fields of discipline, technology in product design, manufacturing processes, sewage treatment and energy saving (Li et al. 2021). It is, however, challenging for an enterprise to achieve successful LTI by relying solely on its own technical experience and knowledge (Chen et al. 2021a(Chen et al. , 2021b. Therefore, looking beyond organizational boundaries for a wide range of heterogeneous knowledge through networking and alliances is more effective in achieving LTI (Chen et al. 2021a(Chen et al. , 2021b. This kind of collaborative efforts for mutual benefits has been termed as alliance innovation (Lin et al. 2012).
Alliance innovation network is an important network characteristic that shapes the technological innovation behavior and performance of the allied members. Good innovation alliance is beneficial for enterprises to obtain high-quality information and knowledge, thereby promoting LTI (Jiang et al. 2020a(Jiang et al. , 2020bLin et al. 2012). Zhou and Ren (2021) pointed out that cooperation between enterprises and non-competitive organizations such as suppliers and scientific research institutions is beneficial for LTI. Different innovation alliances impact LTI differently. The binary strong alliance relationship is likely to cause knowledge and information redundancy, while a multi-dimensional alliance with weak relationship will lead to the prevalence of opportunism in the process of cooperation. Both alliance relationships are not conducive to knowledge sharing and technological innovation (Wang et al. 2019).
Recently, the use of simmelian ties (ST) theory in social network research has gained popularity, and some scholars have introduced it into the field of management (Xu et al. 2020). Simmel (1950) suggested that relations embedded in a triad are stronger, more durable, and more able to produce agreement between actors than relations not so embedded. Based on Simmel's pioneering work, we refer to dyadic ties embedded in three-person and/or firms' cliques as ST in this study (Krackhardt and Kilduff 2002). Weak ST can bring new information to enterprises, but it also brings the challenge of how to transfer and integrate that new information. On the other hand, strong ST can bring relational capital such as trust to enterprises, but it also brings challenges such as information redundancy (Mors 2010). Sheng and Li (2012) pointed out that the triangular relationship structure of ST forms the cooperation and knowledge-sharing pattern of the highest trust among enterprises. It is therefore beneficial to harness heterogeneous knowledge and innovation strategies among enterprises. Cunningham et al. (2018) opined that ST addresses the problem of contradiction between the sharing and integration of external knowledge needed for the innovation process. Although existing studies have analyzed the impact of strong and weak STs on enterprise technological innovation, they failed to reach consistent conclusions. Moreover, available studies did not consider their impact on different types of technological innovation. Therefore, it is very important to study the influence of strong and weak ST on LTI.
At present, from the perspective of stakeholder pressure, there has been a lot of achievements in innovation research. Particularly, innovation studies from the perspective of stakeholder pressure keep expanding (Ahsa et al. 2019). However, few studies have discussed how the interaction between TMEA and LTI can be moderated by stakeholder pressure.
Herein, this paper develops a framework from the ST, alliance innovation network and stakeholder theories to investigate the interaction between ST, TMEA, LTI, and stakeholder pressure. Consequently, the study addresses the following questions.
1. How does ST affect LTI? 2. What is the relationship between TMEA and LTI? 3. What role does stakeholder pressure play in ST and LTI?
A key contribution of this study is the development of a conceptual model for evaluation of the impact of ST on LTI. This, in effect, opens the "black box" of ST and further contributes to the strand of research on the relationship between alliance innovation network and low-carbon innovation in theory. In addition, this study enhances understanding of low-carbon innovation from the perspective of top managers.
The remaining components of this paper are organized as follows: Section 2 provides a theoretical framework; Section 3 describes the research methodology; Section 4 focuses on the results. Finally, in Sections 5 and 6, we focus on the discussion, implications as well as the conclusion and limitations of the study.

Low-carbon technology innovation
According to the traditional innovation theory, innovation can be divided into incremental innovation and breakthrough (radical) innovation. Incremental innovation refers to a gradual improvement of the existing technology. Radical innovation on the other hand brings about a significant technological progress. It is, therefore, difficult for old technology to compete with new technology brought about by radical innovation (Wu et al. 2019). Radical (otherwise refers to breakthrough) innovation, by nature, makes old technology obsolete and leads to a change or an overhaul of the whole industry (Mascitelli 2000). More specifically, radical innovation often forms industrial core technology or even technical standards, which constitute a huge technical barrier for budding enterprises to catch up. LTI is a technological paradigm of unlocking hi-tech and economic opportunities (Lai et al. 2017). Four common LTI strategies include: (1) development and application of carbon-free energy technology and smart grid technology; (2) development and application of carbon reduction technology; (3) decarbonization technology; (4) introduction, digestion, absorption, and promotion of advanced low-carbon technologies (Martin 2015).
In this paper, we operationalized LTI as follows. First, it must meet the technological paradigm of reducing carbon dioxide and other greenhouse gas emissions. Second, LTI must improve technological efficiency of existing technology. It is, thus, worth emphasizing that the innovation subjects of this paper are industrial enterprises, and hence, the focus of this paper transcends basic theoretical findings. We focus more on practical application of technologies, improvement of major technologies and the production of innovative technologies (Jiang et al. 2020a(Jiang et al. , 2020b.

Simmelian ties
Simmelian ties theory originated from Simmel's research on group interaction. ST research mainly analyzes the relationship structure between three individuals. He posited that two individuals cannot form a unit of social analysis, and thus, a group should contain at least three individuals (Simmel,1950). Moreover, there is no difference between the influence of three individuals and more than three individuals on an individual's behavior (Reiss 1950). The triangular structure of ST makes the trust between enterprises reach the highest and optimal levels. This kind of trust is beneficial to cooperation and knowledge sharing. It is also beneficial to the transmission of heterogeneous knowledge, the diffusion of innovation information among enterprises, and promotion of technological innovation of enterprises (Sheng and Li 2012). ST can provide composite knowledge for industrial transformation.
Simmel raised the ties between individuals to the level of society, which became his greatest contribution to innovation theory (Dekker 2006). Tambayong (2011) contended that when distinct individuals or groups are connected to the same third party, such association or ties can lead to ST. The main difference between ST and the connection between two individuals is that the tripartite relationship tends to inhibit individual interests, weaken individual power, and, thus, buffer conflicts.
The advantages of ST lie in three aspects. First, two individuals are more independent than three. This is because there will be no "minority to majority" situation in dual partnerships. However, in a group with three or more individuals, an individual's actions may be checked by majority decision. This means that an individual's interests may be suppressed by collective interests (Xu et al. 2020). Second, ST weakens the bargaining power of single individuals, and hence, any negotiations that can threaten cooperation cannot be advanced. Third, conflict is inevitable in cooperation, but it is easier to resolve disagreements among groups of three or more members than between two individuals. In a bilateral agreement, the conflict between individuals was easily intensified. Conversely, in multi-membership groups, the presence of third parties can mediate disputes between two parties seamlessly (Reiss 1950).

Simmelian ties and low-carbon technology innovation
With the rise of low-carbon development, several scholars have introduced the social network theory into research on low-carbon innovation. Extant dataset shows that interorganizational network plays an important role in the process of low-carbon innovation. For instance, enterprises can get access to diversified knowledge and information about lowcarbon production process. Also, energy conservation, emission reduction, and low-carbon marketing strategies could be shared among firms to accelerate the low-carbon innovation process (Jiang et al. 2020a(Jiang et al. , 2020b. In the tripartite alliance formed through ST, one party's negative cooperation or self-interest behavior will not only be strictly restrained by the other parties, but also seriously affect the success rate of LTI. In addition, ST inherently suppresses self-seeking behavior of individuals through the triangular relationship of mutual restraint (Reiss 1950) and potentially promote LTI. Nevertheless, there is yet any empirical research on whether the relationship between ST and LTI is similar to that of inter-organizational network on general innovation.
In this paper, we mainly discuss the relationship between inter-organizational network and LTI, i.e., we explore the impact of both strong and weak ST on LTI. In addition, we introduce the TMEA variable as a specific performance of top managers' cognitive behavior on environmental practices. Based on top managers' cognition of environmental practice, TMEA has been divided into top managers' awareness of environmental risks (TMAER) and top managers' awareness of environmental benefits (TMAEB) (Gadenne and Mckeiver 2009).
TMAEB refers to the assertion that top managers take green innovation as an important means to reduce costs and increase profits (Gadenne and Mckeiver 2009). TMAER, on the other hand, refers to the belief that top managers promote green innovation of enterprises as part of their social corporate responsibilities and moral constraints, ostensibly to reduce the negative impact of corporate behavior on the environment (Zhang et al. 2015). Although there is a lack of text on the relationship between ST and LTI, a study on the relationship between ST and general innovation will enable us through the extension of knowledge on the theory of ST from general innovation to the field of LTI.

Strong simmelian ties, TMAEB and LTI
Different strength of ST will have different influence mechanisms on enterprise technological innovation (Tortoriello and Krackhardt 2010). In strong ST, the frequent and close social interaction between enterprises may promote the formation of strong relationship between enterprises and partners. At this point, the low-carbon innovation knowledge obtained by the enterprise from other partners is often homogeneous with that of the enterprise (Sheng and Li 2012). However, the absorption and integration of complex knowledge require a lot of energy and time, which by extension requires top managers to have a strong sense of profit-making ambitions (Gadenne and Mckeiver 2009). Therefore, TMAEB can enable enterprises to use a lot of resources to deal with these complex knowledge structures, lead enterprises to digest and integrate it, and help enterprises to achieve breakthroughs in low-carbon technology (Zhang et al., 2015). Furthermore, TMAEB also helps enterprises to carry out deep knowledge search, which helps enterprises to better understand the knowledge structure of low-carbon technology. This allows enterprises to efficiently absorb low-carbon knowledge and integrate with their existing knowledge to achieve low-carbon innovation. In addition, a strong ST can also connote close connections between organizations. This kind of connection can increase the frequency of communication between organizations, thus facilitating knowledge and information flow within the network. The close relationship within the network may be relatively closed and lead to information overload (Wei and Hao 2012). This hinders enterprises from absorbing and integrating valuable knowledge and reduces the efficiency of enterprise innovation (Xu et al. 2020). However, TMAEB enables enterprises to screen all kinds of knowledge and take effective environmental protection measures in order to effectively reduce the interference of redundant knowledge (Zhang et al. 2015). Since top managers deem energy conservation and environmental protection as a means of pursuing interests, enterprises must lean toward environmental protection schemes. Currently, it is difficult for TMAER to achieve the effect of TMAEB (Xu and Chen 2017).
Additionally, in strong ST, network members interact with a limited number of other enterprises for a long time. As a result, enterprises in the network accumulate more knowledge and information resources for low-carbon technology innovation than their counterparts (Sheng and Li 2012). TMAER will make managers think that undertaking LTI is a helpless social responsibility of enterprises, thereby creating risk aversion toward innovation. In this case, senior managers' awareness of low-carbon innovation is not strong. However, top managers are surrounded by a lot of redundant and repetitive knowledge. Information overload makes it difficult for business leaders to discover new knowledge that is important for LTI. On the other hand, TMAER makes managers pay more attention to simple and familiar knowledge, while ignoring complex and heterogeneous knowledge (Gadenne and Mckeiver 2009). To sum up, in the context of strong ST, TMAEB is more conducive to LTI than TMAER. Therefore, we propose the following hypothesis: H 1 : In strong ST, TMAEB is more conducive to LTI than TMAER.

Weak simmelian ties, TMAER and LTI
If the cooperation experience between enterprises is short and the interaction background is different, a social interaction mode of weak relationship connection will be formed, which can make enterprises form a weak ST (Sheng and Li 2012). There are relatively weaker connections among organizations with weak ST, resulting in many structural holes in the network (Xu and Chen 2017). In weak ST cases, enterprises can only obtain a small amount of knowledge from each organization through TMAEB. However, since the knowledge and information transmitted by such connections are basically at a low level, enterprises can access and obtain a large amount of non-redundant, heterogeneous, and diversified knowledge from these weak connection relationships (Sheng and Li 2012). Therefore, it is difficult for enterprises to obtain useful knowledge from heterogeneous and diverse knowledge through TMAEB, so as to promote LTI. In addition, the formation of weak ST increases the risk of opportunism; however, TMAER enables enterprises to expand the sources of knowledge acquisition and effectively disperse the opportunity risk generated by certain knowledge sources, which partly improves the success rate of LTI (Jiang et al. 2020a(Jiang et al. , 2020b. In weak ST, TMAER enables managers to take the concept of energy conservation and environmental protection as the creed of enterprise operation while taking the initiative to assume environmental responsibility. This helps enterprises to establish weak connections or relationships with other organizations (Sheng and Li 2012). The TMAER cannot only effectively reduce the invalid connections among organizations, but also give enterprises an obvious advantage in accessing and acquiring the latest information and knowledge requisite for low-carbon innovation (Xu et al. 2020).
Extant literature has proposed that there are a lot of weak connections among members in low-density networks (Sheng and Li 2012). Although it is beneficial in terms of the transfer of heterogeneous knowledge, it is, however, not beneficial with regard to the transfer of complex technical knowledge. Moreover, it is also difficult to exchange and transfer many modular and systematic knowledge (Jansen et al. 2006). Therefore, if corporate executives believe that environmental protection measures will reduce costs and improve production efficiency, such weak connections make it difficult to obtain the required complex and deep knowledge needed to meet LTI (Sheng and Li 2012). Meanwhile, top managers focus on reducing carbon emissions to make profits, which reduces the opportunities for enterprises to acquire heterogeneous knowledge in different fields (Jiang et al. 2022). To sum up, in the weak ST, TMAER is more beneficial to LTI, and thus, we hypothesize that H 2 : In weak ST, TMAER is more conducive to LTI than TMAEB.

The effect of stakeholder pressure on TMEA and LTI
The consumers, shareholders, labor unions and government departments that enterprises interact with have immense impact on the latter's development strategies. These individuals or groups are called stakeholders (Freeman 1994). The survival and development of enterprises depend greatly on the acquisition of resources from the external environment, and stakeholders are the main source of resources to enterprises (Jiang et al. 2018). Stakeholders exert influence (or power) on the enterprise while providing resources to it. However, this influence increases with increasing degree of firm dependence (Pfeffer and Salancik 1978). Stakeholder pressure can be regarded as the main driver for enterprises to take measures to reduce carbon emissions. This is reflected by the corresponding environmental regulations, environmental laws, administrative orders and reward and punishment measures. Clarkson (1995) argued that stakeholders stress can be divided into pressure from key stakeholders and pressure from secondary stakeholders.
In detail, pressure of key stakeholders refers to the organizations or individuals that play a decisive role in the survival and development of enterprises, such as employees, consumers, shareholders, among others. Pressure of key stakeholders is regarded as a key force to promote LTI (Vliet et al. 2020). To obtain legitimacy, enterprises usually actively carry out low-carbon innovation to comply with and meet the requirements of major stakeholders. Furthermore, obtaining all kinds of heterogeneous knowledge from outside the organization is an effective choice for most enterprises to carry out LTI. Therefore, in order to meet the technical standards and environmental protection requirements under the pressure of major stakeholders, several enterprises will actively search for knowledge and technology related to low-carbon technology from outside the organization (Jiang et al. 2019). Therefore, under the ST, in order to meet the low-carbon requirements of major stakeholders, enterprises will be amenable to all kinds of knowledge to promote lowcarbon technology innovation under the role of executives' environmental awareness (Jiang et al. 2018). Pressure of secondary stakeholders, on the other hand, refers to individuals or organizations that can interact with enterprises but do not directly participate in decision making, such as the government and the media. The impact of secondary stakeholders' pressure on enterprises is not as strong as the impact of key stakeholders' pressure. However, environmental pressure from relevant enterprises, the government, media, non-governmental organizations (NGOs), the public, investors, among others, can drive enterprises to widely absorb knowledge from outside under the environmental awareness of top managers and eventually promote their low-carbon innovation (Jiang et al. 2020a(Jiang et al. , 2020b.
In conclusion, it is not difficult to infer that under the pressure of key and secondary stakeholders, the willingness and behavior of enterprises in the network to acquire lowcarbon knowledge will increase significantly. This makes it easier to obtain relevant knowledge from outside the organization, regardless of the closeness of the relationship between enterprises, and regardless of the environmental awareness of executives to accelerate low-carbon innovation (Jiang et al. 2020a(Jiang et al. , 2020b. Research has shown that pressure from key and secondary stakeholder pressure impact enterprises differently. The pressure of key stakeholders has strong binding force, making choices of organizations very limited (Henriques and Sadorsky 1999). However, the pressure of secondary stakeholders is relatively less effective (Testa et al. 2018). Therefore, under the condition of ST, we believe that compared with the pressure of secondary stakeholders, the relationship between enterprise low-carbon technology innovation is more likely to be positively adjusted by the pressure of primary stakeholders (Odziemkowska and Henisz 2021). Therefore, under the condition of ST, we believe that compared with the pressure of secondary stakeholders, the relationship between the interaction of ST, TMEA and enterprise LTI is more likely to be positively moderated by the pressure of key stakeholders. Based on the above analysis, the following hypotheses (H 3 , H 4 and H 5 below) were proposed. The theoretical model of this paper is also shown in Fig. 1. H 3 : Pressure of key stakeholders positively moderates the interaction between ST and TMEA on the impact of LTI; H 4 : Pressure of secondary stakeholders positively moderates the interaction between ST and TMEA on the impact of LTI; H 5 : Compared with the pressure of secondary stakeholders, the relationship between ST and TMEA on LTI is more likely to be positively moderated by pressure of key stakeholders.

Questionnaire
First, we reviewed the relevant literature and developed a preliminary questionnaire. Second, we consulted experts and revised the questionnaire. Subsequently, we selected 8 enterprises in Chengdu and Chongqing for in-depth interviews to further improve the data collection process. Finally, according to the interviews of the sampled enterprises, the measured scale was improved. Specifically, the study scale consisted of 24 questions. We used a five-point Likert scale ranging from 1 (highly disagree) to 5 (highly agree).

Variable source
The measurement of ST was operationalized from Simmel (1950), Xu et al., (2020), Krackhardt and Kilduff (2002). We designed four items to measure this construct, as described below.
TMEA is a moderating variable. In this paper, we followed the method of Gadenne and Mckeiver (2009) to measure the constructs, TMAER and TMAEB. Four items on both TMAER and TMAEB were accordingly deduced.
The items on stakeholder pressure were adapted from Garces-Ayerbe et al. (2012). It, however, included two dimensions, namely pressure of key stakeholders and pressure of secondary stakeholders. In all, stakeholder pressure had seven items. Corporate environmental behavior is the response of enterprises to the environmental protection pressure from employees, customers, competitors, shareholders, community, government, and media.
LTI is the dependent variable. This variable was mainly operationalized from the study of Jiang et al. (2019) and Chen et al. (2021aChen et al. ( , 2021b. This variable includes corporate low-carbon levels at the leading levels in the same industry, and the proportion of low-carbon innovative products in the total sales of enterprises According to the objectives of this study, we chose years established, enterprise size, enterprise type, and industry type as control variables. The enterprises were divided into three types according to the date of establishment, i.e., less than 3 years, 3-5 years, and more than 5 years. Enterprise size was divided into five types based on the number of employees, i.e., less than 100, 101-200, 201-500, 501-800 and more than 800. We divided enterprises into four types: state-owned enterprises, foreign-funded enterprise, joint venture enterprise and private enterprises. We took the chemical industry as the benchmark industry and then set the industry dummy variables. All research variables are shown in Table 1.

Sample and data collection
In this paper, Beijing, Wuhan, Chengdu, Chongqing, Xi'an and Nanjing were selected for our case study. The settings cover both economically developed and less developed areas in China, demonstrating strong representativeness. The scope of this study is the chemical, textile, paper and machinery manufacturing industries, which have a great impact on lowcarbon development. We mainly focused on field and interview research and used online survey for distant enterprises. According to the catalog provided by local government departments, enterprises were randomly selected. We screened out the top managers of these enterprises and investigated them. The research participants mainly include chairpersons, general managers, deputy general managers, general manager assistants, low-carbon department managers and low-carbon project leaders. These top executives are believed to play an important role in the low-carbon development of enterprises.
Between June and September 2021, we distributed questionnaires in two separate batches, with a total of 564 questionnaires administered. A different analysis was performed on the returned questionnaires, and no significant difference was found. Therefore, we combined the questionnaires returned from both batches and eliminated invalid and incomplete filled questionnaires. A total of 385 valid questionnaires were recovered. The effective recovery rate was 68.26%, as shown in Table 2.   Top managers' awareness of environmental benefits (TMAEB) TMAEB1: Top managers believe that environmental initiatives will bring benefits to enterprises.
TMAEB2: The top management of the enterprise thinks that the production of environmental protection products will increase the sales revenue.
TMAEB3: The top managers think that environmental protection measures will reduce costs.
TMAEB4: The top managers think that environmental protection measures will improve the production efficiency.
Pressure of key stakeholders (PKS) PKS1: Employees think it is necessary for employees to take measures to reduce emissions.
Garcés-Ayerbe et al. (2012) PKS2: Consumers think it is necessary for employees to take measures to reduce emissions.
PKS3: Shareholders think that it is necessary for enterprises to reduce emissions.
Pressure of secondary stakeholders (PSS) PSS1: The media think that it is necessary for enterprises to reduce emissions.
PSS2: The community believe that it is necessary for enterprises to reduce emissions.
PSS3: Local and national governments believe that it is necessary for enterprises to reduce emissions.
PSS4: Competitors think it is necessary to take emission reduction. LTI2: The proportion of the sales of low-carbon products in the total sales of enterprises has been increasing.

Low-carbon technology innovation (LTI) LTI1: The low-carbon level of enterprises is in the leading
LTI3: Enterprises have set up a good social image due to low-carbon technology innovation.
LTI4: Enterprises continue to develop low-carbon technology and products.
LTI5: Enterprises continue to improve their manufacturing processes to meet higher standards of low-carbon production.

Reliability and validity
Before testing the hypotheses, it was necessary to test the reliability and validity of the study constructs. The results are shown in Table 3. From the results, the Cronbach's α coefficient values of the six latent variables and their respective dimensions were all above 0.7, indicating that the scale is very reliable. In addition, the lowest CR was 0.785, which indicates that the aggregate validity of the scale was good. The variables used in this paper are from the mature scale. After the questionnaires were completed, some experts were further invited and their opinions sought, after which some modifications were made to the questions. Therefore, the scale had a good content validity.

Confirmatory factor analysis and homologous deviation test
Before testing the research hypothesis, confirmatory factor analysis was first carried out on LTI, ST, pressure of key stakeholders and pressure of secondary stakeholders. We designed three other measurement models as competitive models. As shown in Table 4, the fitting index of the 4-factor model was the best, indicating that this model can best show the factor structure of the measurement model. In this paper, the potential error variable factor was added to the 4-factor model to construct a 5-factor model for testing. We got five index values,χ 2 /df=1.702, CFI=0.924, NFI=0.928, IFI=0.924, RMSEA=0.048, which were improved to a certain extent compared with the 4-factor model, indicating that the four variables constructed in this paper have no significant homologous deviation.

Correlation analysis
The mean value, standard deviation and correlation analysis of each variable are shown in Table 5. It is evident that there was a significant correlation between ST, TMEA, pressure of key stakeholders, pressure of secondary stakeholders and LTI. The correlation coefficients were 0.745 (P<0.01), 0.714 (P<0.01), 0.674 (P<0.001) and 0.152 (P<0.001), respectively. Therefore, there is a strong correlation between both independent and dependent variables. This, therefore, provided support for further regression analysis. Furthermore, the control variables were also significantly correlated with the independent and dependent variables, indicating that it was necessary for us to control these variables.

Regression analysis
The results of regression analysis and collinearity test are shown in Table 6. The variance inflation factor (VIF) values were all less than 5.216, and the tolerance degree (TOL) was greater than 0.462, which could rule out the problem of collinearity among variables. Model 1 is a benchmark model with only control variables. Based on the benchmark model, ST and TMEA were brought to model 2. Model 3 is a main effect model with control variables, independent variables, and moderating variables. It can be observed from Table 6 that all the models were significant at a confidence level of 0.1%. Moreover, the ΔR 2 value of the other models was significantly improved compared to the benchmark model. This indicates that the fitting degree of the model was enhanced, and the independent variables selected in this paper indeed improved the interpretation of the equation. According to model 2, the direct effect of ST and TMEA on LTI was significantly positive, indicating that both variables can affect LTI of enterprises. In model 4, the interaction term between ST and TMEA was added, and this indicated a significant positive impact on LTI (β=0.476，p<0.01). The results indicate that the interaction between ST and TMEA can significantly promote LTI, and thus, it is an important factor affecting LTI. To judge the differential impact of different levels of ST and TMEA on LTI, we analyzed the binary combination of strong ST, weak ST, TMAER and TMAEB. In addition, we substituted positive and negative 1.5 times standard deviation of ST and TMEA mean value into the regression model, so that the interaction between ST and TMEA could be measured, as shown in Fig. 2. As demonstrated in Fig. 2, in the case of weak ST, TMAER is more able to promote LTI than TMAEB. However, in the case of strong ST, the use of TMAEB was more conducive to promote LTI than TMAER. Therefore, TMAEB under strong ST and TMAER under weak ST represented the optimal combinations of ST and TMEA. This could maximize the promotion of LTI, and thus, H 1 and H 2 were verified. When top managers hold TMAEB constants, ST becomes positively correlated with LTI. However, whenever top managers hold TMAER constant, ST becomes negatively correlated with LTI, as shown in Fig. 2. Due to the limitation of ST and TMEA, it is difficult for enterprises to pursue both improvements simultaneously. Therefore, the complementary advantage of ST and TMEA is an effective way to realize LTI. To improve the effect of LTI, when strong ST is embedded in an enterprise, the top managers should rather opt for TMAEB. With this strategy, such enterprises can conduct in-depth knowledge search and acquire expertise in a few complex areas of low-carbon technology. When weak ST is embedded in enterprises, they need TMAER to obtain diverse and heterogeneous knowledge of LTI.
According to Models 5 and 6, the three interactions of secondary stakeholders' pressure, ST and TMEA, as well as the three interactions of key stakeholders' pressure, ST and TMEA have a significant positive impact on LTI. Both pressure of key stakeholders and pressure of secondary stakeholders positively moderate the impact of ST and TMEA on LTI. As a result, H 3 and H 4 were verified. By comparing Model 4 with Model 5, we found out that the addition of the interaction terms of secondary stakeholders' pressure, ST and TMEA can explain 4.6% of the total variance of LTI (ΔR 2 =0.051, p<0.05). By comparing Models 4 and 6, the interaction of key stakeholders' pressure, ST and TMEA can explain 8.9% of the total variance of LTI (ΔR 2 =0.089, p<0.05). Therefore, compared with the interaction items of secondary stakeholders' pressure, ST and TMEA, the interaction items of key stakeholders' pressure, ST and TMEA can explain a lot of the variation in LTI. Hence, compared with pressure of secondary stakeholders, the relationship between ST, TMEA and LTI is more likely to be positively moderated by pressure of key stakeholders. H 5 is, therefore, verified.

Discussion and implications
The present study has developed an integrated model for simmelian ties (ST, strong simmelian ties and weak simmelian ties) and top managers' environmental awareness (TMAER and TMAEB) on low-carbon technology innovation. Based on the analysis of 385 questionnaires, the study cogently has established the impact of the interaction between ST and TMEA on LTI. Furthermore, the regulatory role of the stakeholders was also explored. This study, therefore, contributes knowledge on the Table 6 Regression analysis Means were measured based on average factor scores; SD means standard deviation; *** shows significance at the level of 0.001; ** shows significance at the level of 0.01; * shows significance at the level of 0.05. Independent variables 1 2 3 4 5 6 7 Years established 0.125 ** 0.107 ** 0.112 ** 0.108 ** 0.107 ** 0.098 ** 0.078 ** Enterprise size 0.248 ** 0.145 ** 0.123 ** 0.124 ** 0.123 ** 0.107 ** 0.078 ** Simmelian ties 0.475 * 0.458 * 0.475 * 0.436 * 0.475 * 0.452 * 0.425 * TMEA 0.065 * 0.054 * 0.076 * 0.071 * 0.049 * 0.053 * Pressure of secondary stakeholders 0.642 *** 0.646 *** 0.632 *** 0.645 *** 0.638 *** Pressure of key stakeholders 0.572 *** 0.547 *** 0.512 *** 0.551 *** 0.547 *** Simmelian ties×TMEA 0.476 *** 0.467 *** 0.463 *** 0.469 *** Simmelian ties×TMEA×PSS 0.046 ** 0.227 ** Simmelian ties×TMEA×PKS 0.265 *** 0.325 * relationship between ST and LTI in enterprises while expanding the understanding on the factors and drivers that impact the relationship. First, we included the interaction term of ST with TMEA to Model 4 and observed that it had a significant positive impact on LTI (β= 0.476, p <0.001). This shows that the interaction of ST and TMEA can significantly promote LTI. The study established that TMEA is an important embodiment of the search and application of low-carbon innovation knowledge (Sheng and Li 2012). Combined with the interaction diagram of the ST and executive environmental awareness (Fig. 2), it can be seen that H1 and H2 are verified. Enterprises in ST have a high knowledge integration ability, and the transformation of innovative knowledge into low-carbon technology is relatively efficient. Furthermore, in the different intensity of the ST, different TMEA can obtain the ideal effect of lowcarbon technology innovation. In the case of weak ST, we established that TMAER can better promote low-carbon innovation than TMAEB (Fig. 2). However, in the case of strong ST, enterprises adopt TMAEB, rather than TMAER, to promote low-carbon technology innovation. This conclusion aligns with the observation of Xu et al. (2020), who believes that external relations of different strengths need to match different TMEA in order to contribute to the green innovation of enterprises.
Second, it is obvious in model 5 that the interaction of secondary stakeholders' pressure, ST and TMEA has a significant positive impact on LTI (β= 0.046，p<0. 01). Therefore, H4 is verified. Model 6, on the other hand, shows that the interaction among pressure of key stakeholders' ST and TMEA has a significant positive impact on LTI (β= 0.265，p<0. 001). Similarly, H3 was verified. Therefore, both pressure of key stakeholders and pressure of secondary stakeholders positively moderated the impact of ST and TMEA on LTI. This conclusion is inconsistent with the findings of Peng and Wei (2015) that TMEA positively moderated stakeholder pressure and firm ecological innovation. The possible reason is that with the continuous improvement of China's carbon trading market and the implementation of environmental policies, enterprises face great pressure due to carbon emissions. Both p key and secondary stakeholders' pressure have an important impact on corporate emission reduction. Moreover, it can be found by model 5 that pressure of secondary stakeholders, ST, and TMEA explain 5. 1% of the total variance in LTI (ΔR 2 = 0. 051, p <0. 05). According to model 6, the addition of the interaction terms of key stakeholders' pressure, ST and TMEA explains 8.9% of the total variance in LTI (ΔR 2 =0.089, p<0.05). Therefore, H5 is verified. In this study, we found a significant difference in the moderating effect of key and secondary stakeholders' pressure. The impact of key stakeholders' pressure is, however, stronger than pressure of secondary stakeholders. The conclusion shows that the moderating role of key stakeholders is more obvious.
The theoretical contributions of the study are as follows: (1) This paper reveals the impact mechanism of the interactive combination of ST and TMEA on low-carbon innovation from two levels inside and outside the organization. On the one hand, it helps us better understand the mechanism of low-carbon innovation from the perspective of executives and enriches the relevant research in the field of low-carbon innovation. At present, few studies have discussed the role of executive commitment, values, leadership, etc., on enterprise low-carbon innovation (Jiang et al. 2019). This study reveals the important role of executives in the process of enterprise low-carbon innovation and reignite discussion on the lack of attention to the cognitive factors of enterprise executives in the current green innovation research pointed out by Lewis et al. (2014). Again, this study provides a new research idea for the academic debate on the relationship between ST and innovation.
(2) By constructing a theoretical framework, this study introduces social network theory and executive environmental awareness into the research of enterprise low-carbon innovation, which provides a theoretical basis for cracking the black box in the process of enterprise green innovation. (3) This study also has the potential to set the basis for proliferation of mature theoretical achievements such as social network theory and executive environmental awareness from general innovation to green innovation research.
The findings of this research also provide some valuable insights to encourage enterprises to carry out low-carbon innovation. First, in the process of enterprises carrying out low-carbon technology innovation via cooperation mode, enterprise managers should evaluate the inter-organizational network embedded in the enterprise and then choose the appropriate environmental protection awareness scheme for optimal benefits (Xu et al. 2020). Strong ST leads to stronger homogeneity in knowledge shared among enterprises. Therefore, the novelty of knowledge acquired by enterprises through strong ST is poor. When enterprises carry out low-carbon technology innovation activities in strong ST, TMAEB should focus on several key partners and strengthen their relationship with these specific organizations. Enterprises can obtain knowledge on specific links in a low-carbon field to break through the key technologies in low-carbon innovation (Tortoriello and Krackhardt,2010). Moreover, when enterprises carry out low-carbon technology innovation activities in a weak ST, TMAER is widely dispersed to various partners. Under this condition, enterprises should establish cooperative relations with as many organizations as possible and carry out low-carbon technology innovation by obtaining a variety of low-carbon knowledge. Weak ST does not only allow companies to gain diversified knowledge, but also it has the stability of ST. Therefore, TMAER is more conducive to low-carbon technology innovation of enterprises. In addition, during the implementation of lowcarbon technology innovation, enterprises should pay attention to the construction of alliances and relationships, as well as the choice of partners. ST demonstrates a small affiliate innovation network where stakeholders have a high alliance cognition and play important roles in promoting knowledge sharing and technology exchange.
Second, under the supervision and pressure of stakeholders, enterprises can consciously carry out low-carbon technology innovation. Stakeholders put forward environmental requirements for enterprises, by aiming at the promotion of the external impact of ST on LTI. In terms of key stakeholders' pressure, enterprises should develop and improve various energy-saving and emission reduction rules and regulations. This can be done by actively participating in the certification of low-carbon products, reduction of fossil energy consumption, improvement in the utilization rate of resources, and other measures to encourage enterprises to carry out low-carbon technology innovation (Pan et al. 2021). On the other hand, within the framework of secondary stakeholders' pressure, enterprises are encouraged to build good relationships with the government, promote extensive and in-depth cooperation with competitors in the field of low-carbon innovation, and actively participate in low-carbon trading. The greater the pressure of stakeholders, the more valuable knowledge can be obtained from the tripartite alliance. This can encourage enterprises to develop low-carbon technology innovation. Therefore, enterprises should make good use of ST in the innovation alliance to restrain individual self-profit behavior, prevent the risk of alliance termination, and realize low-carbon technology innovation.
Third, the environmental awareness of top managers in the ST relationship may be different; thus, a win-win vision should be established among organizations. Organizational win-win vision is a kind of management ability at the strategic level, which can help enterprises to systematically evaluate and select partners that ensure that knowledge can be shared in the implementation process of low-carbon technology innovation (Jiang et al. 2019). From the foregoing, enterprises should strengthen the cultivation of environmental awareness of top managers and improve the supporting incentive mechanism to improve the creativity and innovation of senior enterprise managers (Huang et al. 2020). This, in effect, emboldens senior managers to have a sense of belongingness to organizations that are connected by ST. In addition, enterprises also need to enhance the willingness of senior managers to share knowledge, form a virtuous circle, and then promote lowcarbon technology innovation activities.

Conclusions and limitations
This paper reveals the influence mechanism of the interaction between ST and TMEA on LTI. This helps us to better understand the mechanism of enterprise low-carbon technology innovation from the perspective of TMEA. In effect, the study helps to enrich the relevant research on the field of low-carbon innovation. Currently, only a few studies have been conducted on the role of executive values, leadership, and environmental awareness on low-carbon technology innovation (Bi and Wang 2015). The present study further reveals the important role that top managers play in the concept of low-carbon technological innovation. This makes up for the lack of attention to top managers in the ecological innovation research pointed out by Peng and Wei (2015). In addition, this study provides a new research idea for academics to debate on the relationship between ST and innovation.
This paper analyzes the impact of different intensities of ST and TMEA on LTI under the moderation effects of key and secondary stakeholders' pressure. Specifically, we explore the response mechanism of enterprise low-carbon technology innovation under the pressure of different stakeholders. We further explain the realization mechanism of enterprise low-carbon technology innovation. The paper provides a comprehensive analysis framework on ST, TMEA, stakeholder pressure and LTI, and provides a theoretical basis for the 'black box' in the process of LTI. Furthermore, the paper deepens the theory of ST and stakeholder theory and promotes the extension of research results from general innovation to low-carbon innovation.
Although this study contributes significantly to the narrative on low-carbon innovation, we note certain limitations. First, only frontline employees of processing and manufacturing enterprises in Beijing, Wuhan, Chengdu, Chongqing, Xi 'an and Nanjing were selected for the study. In future studies, data can be collected on a wider range to enhance the generalization of the research results. Second, the data used in this study were obtained strictly through cross-sectional means. Future research can be conducted on longitudinal studies. Moreover, future studies can combine the subjective evaluation index with the objective evaluation index to analyze the structural relationship between the variables to better explain the model. Finally, some variables such as regulatory pressure and imitation pressure may also play a role in moderating the relationship between ST, TMEA and LTI. A follow-up study can therefore be conducted on these variables.

Declarations
Ethical Approval In the research process of this paper, there is no ethical issues, no moral disputes, after the review of the academic department of Sichuan Normal University.

Consent to Participate
The research has been carried out in accordance with the China Enterprise Association. All investigator provided written informed consent prior to their inclusion within the study.

Consent to Publish
The author agrees to publication in the Journal of Environmental Science and Pollution Research. The author confirms that the work described has not been published before (except in the form of an abstract or as part of a published lecture, review, or thesis); that it is not under consideration for publication elsewhere; that its publication has been approved by all co-authors, if any; that its publication has been approved (tacitly or explicitly) by the responsible authorities at the institution where the work is carried out.

Competing Interests
We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled, "The Effects of Simmelian Ties on Innovation of Low-carbon Technology: A study of top managers' environmental awareness and stakeholder pressure in China".