Effect of R&D Subsidies on External Collaborative Networks and the Sustainable Innovation Performance of Strategic Emerging Enterprises: Evidence from China

Building external collaboration networks is key to the sustainable innovation performance of strategic emerging industries (SEIs) in the context of open innovation. R&D subsidy policies in China are typically designed to support R&D investment, though the question remains whether this policy tool can stimulate sustainable innovation performance by building external collaborative networks for enterprises. At present, few studies discuss the behavioral additionality of subsidies in the context of emerging economies, and relevant studies are mainly conducted from the single perspective of input additionality. This paper integrates the input, output, and behavioral additionality of R&D subsidies into the same framework and investigates the relationships among R&D subsidies, external collaborative networks, R&D investment, and the sustainable innovation performance of strategic emerging enterprises (SEEs) among Chinese SEIs listed enterprises in 2010–2019, mainly using the panel fixed effects regression model. The results show that R&D subsidies in China promote sustainable innovation performance and that this effect is mediated by external collaborative networks and R&D investment. Additionally, R&D subsidies negatively moderate the indirect effect of external collaborative networks on sustainable innovation performance, and the moderating effects of R&D subsidies under heterogeneous samples differ in sign, statistical significance, and impact magnitude. Based on the conclusions, policy-makers must comprehensively consider the multiple effects of R&D subsidies, develop more sophisticated policy tools for network coordination, and implement differentiated subsidy policies to align with open innovation in the future.


Introduction
Strategic emerging industries (SEIs) are essential to the economy and are crucial to creating sustainable economic growth [1,2]. In recent years, both developed and developing countries have attached great importance to the development of SEIs, especially China, and phrases such as "vigorously developing SEIs" and "cultivating and expanding SEIs" frequently appear in government work reports. In this context, promoting high-quality SEI development is an important issue for the government. As the core driving force of high-quality development, innovation can bring more efficient technology [3,4], which will be the main direction for the government in planning SEIs development. To stimulate enterprise innovation activities, Chinese governments have committed substantial resources to R&D subsidies, especially for SEIs. For example, China has set up the National Special Fund Program for SEIs to encourage strategic emerging enterprises (SEEs) to invest in R&D in the form of subsidies and similar initiatives since 2012. This paper is interested in exploring the practical significance of whether R&D subsidies in China designed to support R&D investment successfully stimulate innovation and improve SEEs' sustainable innovation abilities. Moreover, SEEs' innovation activities are complex, have significant knowledge spillover, and have tight resource constraints [5,6]. Therefore, determining how to build external collaborative networks effectively in a complex innovation environment is important for enterprises to achieve sustainable innovation [2,7,8]. To realize this purpose, this paper also tries to address whether R&D subsidies improve sustainable innovation performance through external collaborative networks, as well as what role R&D subsidies play in the relationship between external collaboration networks and SEEs' sustainable innovation performance. In the current context of high-quality development, it is particularly important to discuss these issues.
The literature pays less attention to the sustainable innovation performance of SEEs, mainly focusing on the hotly debated relationship between R&D subsidies and SEEs' general innovation. Some have claimed that R&D subsidies stimulate SEEs' innovation performance [9][10][11], while others have found the opposite [12][13][14]. Beyond the directly intended impacts, interventions typically also have indirect (unintended) impacts on organizations. However, it is regrettable that prior studies focused more on the direct impact of R&D subsidies on innovation output (a perspective of output additionality) while rarely discussing the internal mechanisms. In the scant literature, the mechanism is mainly discussed from the perspective of the influencing factors of R&D investment (a perspective of input additionality), and there is little discussion of external collaborative networks that reflect the behavioral changes of SEEs (a perspective of behavioral additionality), especially in emerging economies.
This line of research reveals that studies of the behavioral additionality of subsidies are primarily concentrated in developed countries, and it should be expanded to emerging economies with caution. On the one hand, in emerging economies, formal institutions, policies, and regulations have not yet been established, but may develop and vary over time. Thus, it is difficult for enterprises to conform to such a complex institutional system [15]. This challenge may be one of the reasons why the effects of R&D subsidies vary. On the other hand, in emerging economies such as China, where the government is the most powerful actor and a major source of resources [16,17], governments usually have a relatively strong and unpredictable influence on enterprises' development. Therefore, compared to developed countries, the behavioral additionality of subsidies is more complicated in emerging countries.
To develop our understanding of the relationship between R&D subsidies and sustainable innovation performance, further efforts can be made regarding the following aspects. First, in terms of variable measurement, several studies, such as Wu et al. [18], used the total amount of general subsidies to approximately replace R&D subsidies by including the subsidies that do not belong to R&D and innovation. At present, there are many kinds of government subsidies in China, including R&D subsidies for innovation, as well as non-R&D subsidies, such as local government investment attraction and capital introduction, financial contribution awards, pollution control, demolition compensation, and assistance for enterprises with poor operations and management [19]. The use of mixed general subsidies as proxies for R&D subsidies may cause inconsistent and inaccurate estimations. It is necessary to judge the category of subsidies and identify the amounts of R&D subsidies used to stimulate enterprise innovation as a proxy variable [19]. Second, in light of the relationship between R&D subsidies and sustainable innovation performance, especially for countries such as China which are transforming from factor-driven to innovation-driven, the additionality of subsidies must be discussed within a complete framework. This is because a single additionality of subsidies may underestimate the real effect of subsidies [20], and it is difficult to completely analyze the mechanism. Particularly in the context of open innovation, constructing external collaborative networks as an innovation behavior is an important factor affecting sustainable innovation performance [2,8]. Constructing these networks also provides ways to explore the mechanism of R&D subsidies from the perspective of behavioral additionality. Therefore, based on R&D investment, external collaborative networks should also play an important mediating role between subsidies and sustainable innovation performance. With this in mind, it is necessary to consider the mediating role of R&D investment and external collaborative networks within the same framework. Finally, in the research on the impact of external collaborative networks on sustainable innovation performance, R&D subsidies reflect support and intervention at the macro government level. R&D subsidies are a form of financial support provided by the government to encourage the development of an industry or enterprise. Their purpose is to reduce the costs and risks of innovation and to motivate enterprises to improve their innovation performance [11,18]. With increasing external collaborative networks, R&D subsidies may change SEEs' internal and external innovation environment. It follows that R&D subsidies also play an essential role in the relationship between external collaborative networks and sustainable innovation performance. Moreover, due to the heterogeneity of the political contexts and innovation environments that SEEs face, the moderating role of government subsidies also deserves further attention.
Therefore, to extend our insights into the behavioral additionality of subsidies, this paper takes Chinese SEI A-share listed enterprises from 2010-2019 as a sample and seeks to investigate the relationship among R&D subsidies, external collaborative networks, R&D investment, and the sustainable innovation performance of SEEs using the fixed effects model. Overall, this paper makes the following contributions. (1) The independent variable of R&D subsidies in this paper is stripped away from the other types of subsidies, which can help to effectively measure the impact of R&D subsidies on SEEs' sustainable innovation performance. Simultaneously, by taking SEEs as the object of policy effect evaluation, relevant evidence for making full use of the promotive effect of subsidies can be provided. (2) Based on exploring the relationship between R&D subsidies and SEEs' sustainable innovation performance, this paper also brings the input, output, and behavioral additionality of subsidies into the unified framework, and explores the interrelations among them, which can help to further illuminate the mechanism of the policy tool in promoting SEEs' sustainable innovation performance. (3) This paper verifies that input, output, and behavioral additionality can occur simultaneously and that the moderating effects of R&D subsidies have different relationships with differences in ownership and life cycle. After doing so, the relationships among R&D subsidies, external collaborative networks, R&D investment, and sustainable innovation performance of China's SEEs can be fully identified, which can serve as a reference to optimize R&D subsidy policies and provide guidance to improve support for other relevant policies.

Theoretical Analysis and Research Hypothesis
The following aspects are critical to analyze the impact of China's R&D subsidies on SEEs' sustainable innovation performance. First, the characteristics of sustainable innovation activities in SEIs, including high investment, precise technology, uncertain markets, and high risk [5,6], make SEEs' innovation decisions more complicated [21]. Second, SEEs are mostly SMEs that lack innovation resources, urgently requiring them to use external support [22,23]. Third, China has a unique and complex institutional environment, with its strong government [15].

Direct Impact of R&D Subsidies and the Sustainable Innovation Performance of SEEs
Different views are put forward on the role of R&D subsidies in promoting innovation. Zhao et al. generated the conventional error component model using firms' R&D expenditure as the dependent variable and government R&D subsidies as the independent variable. They obtained a positive net effect when the subsidy amount is large with significant direct (spillover) and indirect (crowding-out) effects, revealing that two types of effects exist simultaneously. Thus, overall, subsidies effectively promote enterprise innovation [11]. By analyzing subsidy data from southern Italy over the period 1996-2004 under the regional policy, Law 488/1992, Cristina and Guido found a smaller increase in total factor productivity in subsidized firms than in unsubsidized firms [12]. However, in the Chinese context, many studies agree with the positive effect of R&D subsidies. Liao et al. used provincial panel data of large-and medium-sized industrial enterprises in China to analyze the effect and influencing factors of government R&D funding from the perspective of R&D investment. The results show that there is a leverage effect of government R&D funding on enterprises' R&D investment, and this leverage effect increases with the progress of the industrialization stage [24]. Guo [19] and Wu et al. [18] obtained consistent results by using different samples; in other words, R&D subsidies encourage enterprises to increase technological innovation. This paper argues that the effect of R&D subsidies should be analyzed by integrating input, output, and behavioral additionality. Specifically, it may promote SEEs' sustainable innovation performance through the direct resource acquisition mechanism, the indirect signal transmission mechanism, and the management decision change mechanism. First, R&D subsidies can provide funding sources through the mechanism of direct resource acquisition to enrich the cash flow of enterprises [25] and relax capital constraints in SEEs' sustainable innovation process, effectively internalizing innovation positive externalities [26]. With the support of government funds, the costs of sustainable innovation are reduced, as are the risks. In this way, SEEs will be more willing to invest in R&D activities, thus improving their sustainable innovation performance.
Second, through an indirect signal transmission mechanism, R&D subsidies contribute to acquiring high-quality talent, technology, information, and other innovation elements for enterprises [19]. On the one hand, R&D subsidies send a signal of healthy development for enterprises. R&D subsidies represent the guidance of government policy [24], which means that the more subsidies enterprises receive, the more recognition they will receive from the government, including recognition of products and market prospects. In the case of information asymmetry, favorable information can become an important basis for stakeholders to judge enterprises' reputation and development; to guide capital, talent, advanced management technology, and business philosophy for SEEs; and to drive other organizations and market resources to SEIs, while simultaneously promoting enterprises' innovation performance. For example, support for investors and banks can provide stable financial guarantees for enterprises' innovation activities [27], support for collaborators can improve the efficiency of enterprise innovation activities [28], and support for hightech talent can provide enterprises with the impetus for innovation [29]. Conversely, R&D subsidies provide a signal of closeness between enterprises and the government. Numerous related studies have pointed out that enterprises with closer ties to the government can receive more "attention" from the government [30]. Previous studies have found that politically connected enterprises are more likely to obtain loans from banks [31], favor investors [19,32], and support collaborators [33,34], which will reduce uncertainty and improve the enterprises' sustainable innovation performance.
Finally, R&D subsidies will lead to higher sustainable innovation performance for SEEs by changing managers' risk decisions about innovation activities. SEEs' sustainable innovation has higher decision-making risk, but the acquisition of government resources will spread the risks of R&D innovation activities to an extent, directly affect enterprises' decision-making on sustainable innovation, and increase enterprises' confidence in sustainable innovation [35].
Therefore, according to the perspective of input, output, and behavioral additionality, we put forward the following hypothesis: Hypothesis 1 (H1). R&D subsidies promote the sustainable innovation performance of SEEs.

Mediating Effect of External Collaborative Networks
To further analyze the mechanism by which R&D subsidies promote sustainable innovation performance in the context of open innovation, it is necessary to open the "black box" of enterprises and explore the behavioral changes of SEEs after they receive subsidies [33,34]. The literature notes that the risk of innovation is shared when SEEs receive R&D subsidies [36,37], therefore strengthening innovation risk tolerance [38] and risk-taking [39], leading to change innovation decisions and more involvement in sustainable innovation activities. In the context of open innovation, enterprises collaborate with external partners to actively expand external collaborative networks, which indicates that "enterprises invest in innovation". Expanding external collaborative networks will provide innovation directions for SEEs with limited resources and capabilities because SEEs can not only obtain diversified resources from different partners [40] but also improve their own technological abilities through the establishment of innovation networks, using a variety of mechanisms to create and capture value innovation [41].
Moreover, some scholars in Western countries propose that R&D subsidies help develop external partners through establishing networks and "bridging" [33,42], which indirectly improve innovation performance. However, the mechanism of external collaborative networks has not been discussed in the Chinese context. Therefore, from the perspective of behavioral additionality and views of open innovation and innovation networks, we propose that the positive relationship between R&D subsidies and the sustainable innovation performance of SEEs may be caused by a change in behavior-the expansion of external collaborative networks.
Our reasons are as follows. On the one hand, R&D subsidies encourage SEEs to expand their external collaborative networks by supplementing their financial resources. The establishment of external collaborative networks requires a great deal of investment [21,22]. As one of the funding sources for SEEs, R&D subsidies can appropriately alleviate financing constraints and provide financial support for the development of external partners [21]. In addition, the "signaling effect" is helpful to obtain more external financing from banks and external investors, expanding the external collaborative network [19,30]. On the other hand, R&D subsidies expand external collaborative networks by reducing costs. Establishing external collaborative networks entails a series of costs, including search [43], coordination [44], and risk costs [43]. R&D subsidies, with the government "endorsement" effect, not only help SEEs attract external finance but also increase the legitimacy of enterprises [45,46], which effectively addresses the legitimacy cognitive dysfunction of potential partners [42,47]. Such legitimacy provides a positive collaboration signal for potential partners, somewhat reducing the cost of creating external collaborative networks. Especially in the Chinese context, government "endorsement" builds trust among organizations advantageously and reduces the costs of search and cooperation, thus supporting the formation of external collaborative networks [19]. Therefore, R&D subsidies expand collaborative networks by providing financial resources and reducing costs.
Expanding external collaborative networks always improves sustainable innovation performance. According to the relevant literature [22], the larger the network is, the more complete the innovation knowledge acquired is, which improves SEEs' sustainable innovation performance [43,48,49]. Moreover, expanding external collaborative networks indicates that the external environment is diverse and that the sources of innovation are increasingly extensive. It is advantageous for SEEs to acquire key information and perceive changes in the external environment, thereby improving their sustainable innovation performance [50][51][52][53]. Therefore, R&D subsidies promote SEEs' sustainable innovation performance by expanding external collaborative networks. Hence, we propose Hypothesis 2: Hypothesis 2 (H2). The relationship between R&D subsidies and sustainable innovation performance is mediated by external collaborative networks.

Mediating Effect of R&D Investment
R&D subsidies signify that the government voluntarily provides unpaid financial support for enterprises' sustainable innovation activities. Such financial support reduces the risks and costs of enterprise innovation investment in SEIs and stimulates more innovation investments from the perspective of innovation input. According to the previous analysis, SEEs' sustainable innovation is a high-risk activity with a longer investment time, greater uncertainty, and much higher failure rates. Resource constraints and insufficient incentives are important barriers to SEE innovation, and the institutional environment in China further restricts the opportunities for SEEs to use market mechanisms to obtain external innovation resources. Therefore, government R&D subsidies can help enterprises reduce innovation risks and costs through the effect of resource acquisition.
First, R&D subsidies spread the risk of SEEs' investment in sustainable innovation. Enterprises usually lack motivation for R&D because the process of R&D investment has great spillover and extremely high risk [36,37]. Especially for SEIs, on the one hand, the direction of industry development and government policies is more uncertain; on the other hand, the technical problems faced by enterprises in such industries are also more challenging [5,6]. Government subsidies, in the form of financial subsidies for enterprise innovation activities, can spread the risk of innovation investment and encourage enterprises to invest more in sustainable innovation [54][55][56].
Second, R&D subsidies reduce the cost of SEEs' investment in sustainable innovation. As a direct incentive method, government R&D subsidies can encourage enterprises to increase R&D investment in the form of financial injection by increasing marginal revenue after successful R&D or reducing marginal costs when R&D fails [57]. In SEIs, the initial investment required by enterprises to explore the industry frontiers is very large, and it is difficult to recover funds in the short term. At this time, R&D subsidies can alleviate the financial pressure of enterprises and effectively promote continuous investment in sustainable innovation.
Third, R&D subsidies can also guide SEEs to invest more in sustainable innovation. There are two types of R&D subsidies in China [18]. One is for public technical service institutions and enterprises' sustainable innovation activities in the form of innovation funds [18]. The other is policy guidance programs, which determine the development direction for major state projects and promise to provide large-scale subsidies for the participating enterprises, such as the China Torch Program and The National New Products Program [18]. The development of SEIs are typical examples of policy guidance programs. Under policy guidance, enterprises are often more willing to invest in sustainable innovation to seize development opportunities and obtain R&D subsidies continuously.
The positive relationship between R&D investment and sustainable innovation performance has been verified in a large number of studies [58][59][60]. Thus, R&D investment activities in enterprises can create high value-added output (such as new products, processes, technologies, and designs), thereby improving the technological level and efficiency. This not only contributes to product upgrades and updates, but also improves the sustainable innovation performance represented by patents. Thus, we believe that R&D subsidies encourage SEEs to invest in sustainable innovation through resource acquisition effects, thereby improving sustainable innovation performance. Therefore, we propose Hypothesis 3:

Hypothesis 3 (H3).
The relationship between R&D subsidies and sustainable innovation performance is mediated by R&D investment.

Data and Sample
The research objects of this paper are SEEs. This paper selects A-share listed SEEs from 2010-2019 as samples. The specific screening conditions are set as follows. (1) In view of Zhao et al. [61], the samples are SEIs, which are selected according to the classification of the SEI concept stock in the WIND database, the "High-tech Industry Classification Catalog", and the "Strategic Emerging Industry Key Products and Services Guidance Catalog 2018", and 179 concepts are identified, such as 3D sensing, 4G, 5G, 3D printing, large aircraft, semiconductor materials, graphene, biological vaccines, biological breeding, innovative drugs, charging piles, electric vehicles, shale gas, geothermal energy, clean development mechanism (CDM) projects, solid waste treatment, and animation. (2) ST, ST*, or other financial and special treatment enterprises are not included in this paper.
(3) Enterprises with missing values, such as R&D subsidies, R&D investment, external collaborative networks and sustainable innovation performance, or other core variables, are not included. The final dataset used in this paper is an unbalanced panel that includes 4953 firm-year records from 2010-2019. The data processing software is Stata 16.0.
The financial data of enterprises are obtained from the WIND database and CSMAR database. The information on R&D subsidies comes from the notes of the annual reports of listed enterprises. The patent data of listed enterprises come from the State Intellectual Property Office (SIPO) website.

Measurement of Variables
Sustainable innovation performance: The indicators for measuring enterprise innovation usually include R&D investment, sales revenue from new products, and the number of patents. Because the dependent variable in this paper is the innovation output of SEEs, the number of patents has higher data quality than the former indicators, reflecting the actual results of enterprise innovation activities [62]. As innovation performance in this paper emphasizes the continuity and sustainability of time, referring to Xu et al. [63], the authorized patents refer to the patents granted by administrators to the applicants during the reporting period; these are traffic and sequential data reflecting time continuity [63]. Therefore, the number of authorized patents is used to measure SEEs' sustainable innovation performance, which is denoted as patent. A logarithmic transformation is finally adopted to linearize the variable and reduce its skewness.

R&D subsidies:
The key independent variable is sub, which is measured as the total amount of R&D subsidies belonging to R&D projects in the current year. It is assessed by keywords, technical terms, local science, and technology plans in the annual reports of listed enterprises [64]. To avoid the problem of heteroscedasticity, it was processed in logarithm.
External collaborative networks: The patent information of enterprises is usually used for empirical studies on innovation collaborative networks [7]. According to Gao et al. [65], we retrieved and downloaded the joint application patent information of listed enterprises. Data on the collaboration of sample enterprises are gathered to identify their external collaborative networks after further screening and sorting, and the logarithm of the number of partners linked to SEEs (namely, the number of network nodes) plus 1 is used to measure the external collaborative network, denoted as col.
R&D investment: Li [66] pointed out that enterprise innovation investment includes capital investment and personnel investment, and only one of these must be considered to avoid multicollinearity when measuring innovation investment. Therefore, R&D investment is measured by the natural logarithm of the amount of R&D expenditures plus 1, denoted as invest.
Control variables: Considering the factors that may affect SEEs' sustainable innovation performance in the process and referring to the literature [19,67], the control variables include enterprise size (size), enterprise age (age), R&D intensity (rd), liquidity (liq), return on total assets (roa), and shareholding concentration (shrcr).
Detailed definitions of and descriptive statistics for the variables are presented in Table 1.

Relationship between R&D Subsidies and Sustainable Innovation Performance
The dependent variable in this paper is measured by computing the number of authorized patents for each SEE with logarithmic processing; consequently, a linear panel model specification is recommended. After running poolability tests (F test) and checking for the presence of random effects (Hausmann test), we adopt a panel fixed effect model with time effects and individual effects through Stata 16.0 because we expect a significant individual effect over time on the sustainable innovation performance of SEEs related to the macroeconomic impact and industry differences. In addition, SEEs' sustainable innovation performance is unlikely to be randomized; rather, it is expected to be influenced by observed and time-invariant features. Moreover, fixed effect models are the safest choice to eliminate possible omitted variable bias. Based on the above statistical considerations and following Guo [21], the baseline regression model (1) is used to test H1: where the subscripts i and t represent the firm and year, respectively, and patent it is the sustainable innovation performance of SEEs as the dependent variable. The symbol and value of β 1 are used to identify the effect of R&D subsidies. controls it include all the control variables. λ i is firm-level fixed effects, τ t is year fixed effects, and ε it is the error term. Table 2 shows the regression results of R&D subsidies on SEEs' sustainable innovation performance. In column (1) of Table 2, sustainable innovation performance (patent) is directly used to regress R&D subsidies (sub) without any control variables. The results show that the coefficient on R&D subsidies is significantly positive. This indicates that SEEs' sustainable innovation performance increases with the increase in R&D subsidies. In column (2), six control variables are included, and the regression results are similar to those in column (1), which somewhat indicates that the impact of R&D subsidies on SEEs' sustainable innovation performance does not change with the control variables. Specifically, as shown in the regression results in column (2), the coefficient on R&D subsidies is 0.0865, with significance at the 1% level. Specifically, a 1% increase in R&D subsidies results, on average, in a 0.09% increase in authorized patents. Therefore, H1 is supported.
For other control variables, column (2) of Table 2 shows that the coefficients on size (size) are significantly positive. This indicates that large enterprises have somewhat better sustainable innovation performance. The coefficient on firm age (age) is significantly positive, indicating that the older the enterprise, the better its sustainable innovation performance. The possible reasons for this are as follows. First, enterprises may effectively improve their innovation abilities through learning by doing with increasing age. Second, older enterprises tend to have more knowledge reserves and thus have better R&D experience [68,69]. The coefficient on R&D intensity (rd) is also significantly positive, which indicates that the higher the R&D expenditure ratio of an enterprise, the better its sustainable innovation performance. The impacts of enterprise liquidity (liq), return on total assets (roa), and shareholding concentration (shrcr) are not obvious.
Considering R&D subsidies as an external policy shock may present issues with endogeneity, such as mutual causation and omission of variables. Instrumental variable (IV) estimation is used to correct for potential endogeneity in this paper. The first IV is the mean value of R&D subsidies based on the year, province, and industry [70,71], denoted as v 1 . The second is the total GDP of the province where the enterprise is located [30], which reflects the local resources of the enterprise and is represented by v 2 . The results with IV estimation are shown in columns (3) and (4) of Table 2. In the first stage, the coefficients of v 1 and v 2 are statistically significant and positive (Coef. = 0.5588, p < 0.01; Coef. = 0.2324, p < 0.05), suggesting that the IVs are appropriate. The results in the second stage are consistent with the previous results. In addition, the underidentification, weak identification, and overidentification tests are all verified, indicating that core H1 still holds after considering the potential endogeneity issue. Note: *, **, and *** indicate that the significance levels are 10%, 5%, and 1%, respectively, and the standard deviations of each coefficient are in parentheses.

Mediating Effect on the Relationship between R&D Subsidies and Sustainable Innovation Performance
Our main analysis shows that R&D subsidies improve SEEs' sustainable innovation performance. Furthermore, we examine the mediating effect (external collaborative networks and R&D investment) between R&D subsidies and sustainable innovation performance. Referring to Baron and Kenny [72] and Wen et al. [73], the following mediating effect models (equation set) are constructed based on model (1) to test the mediating effect of external collaborative networks (behavioral additionality) and R&D investment (input additionality), namely, H2 and H3: where a 1 reflects the effect of R&D subsidies (sub) on the mediating variables (col and invest) and the effect of the mediating variables (col and invest) on the sustainable innovation performance of SEEs-a 1 c 2 -is obtained by substituting model 3 based on model 2.
The results regarding external collaborative networks are shown in columns (1) and (2) of Table 3. The coefficient of R&D subsidies on external collaborative networks is significantly positive (a 1 = 0.0321, p < 0.05), which indicates that R&D subsidies can help SEEs expand their external collaborative networks. This is consistent with Beck et al. [74] and Chapman et al. [35] and confirms the existence of behavioral additionality for R&D subsidies. The coefficient of external collaborative networks is also significant (c 2 = 0.1697; p < 0.01), which indicates that the expansion of external collaborative networks is beneficial to SEEs' sustainable innovation performance. Therefore, the mediating effect of external collaborative networks holds; namely, H2 is supported. Sobel test 0.0055 ** 0.0240 *** Note: *, **, and *** indicate that the significance levels are 10%, 5%, and 1%, respectively, and the standard deviations of each coefficient are in parentheses. When the variable of R&D investment (invest) is added to the model, the ratio of technical personnel to the total number of employees in the current year (human) is controlled, the control variable of R&D intensity (rd) is discarded conversely, and the subsequent step is along the same lines.
Columns (3) and (4) show the results for R&D investment. The coefficient of R&D subsidies on R&D investment is positive and significant at the 1% level (a 1 = 0.1197, p < 0.01), suggesting that R&D subsidies can increase SEEs' confidence in investing in innovative technologies, thereby increasing their internal R&D investment. Meanwhile, increased R&D investment significantly promotes SEEs' sustainable innovation performance (c 2 = 0.2005; p < 0.01), which confirms the mediating effect of R&D investment. H3 is supported.
Furthermore, the Sobel test indicates that the mediating effect of R&D investment is more significant. Thus, R&D subsidies play a particularly important role in promoting R&D investment in SEEs, possibly because the collaborative innovation strategy is an alternative plan implemented by enterprises to overcome a lack of innovation resources [75] rather than a sustainable innovation strategy. When SEEs' financial situation is relatively slack, the safer and easier strategy, i.e., internal R&D, will be used [76].

Robustness Tests
Replacement of the regression method. The dependent variable in this study is the number of authorized patents, with a discrete distribution of nonnegative integers. Therefore, negative binomial regression is used to re-estimate the model as a robustness check, and the estimated coefficients are 0.1459 (p < 0.01), as shown in column (1) of Table 4, which reveals the robustness of the conclusion.
Replacement of the measure. In the above analysis, R&D subsidies are measured by the logarithm of the number of R&D subsidies. For robustness, R&D subsidies are measured by the proportion of R&D subsidies received by SEEs to their total assets (sub1). The regression results are shown in column (2) of Table 4. Similar to the benchmark regression results in column (3) of Table 2, the coefficient of R&D subsidies is significantly positive. This again indicates that R&D subsidies significantly increase SEEs' sustainable innovation performance. Thus, the regression result is robust. Note: *, **, and *** indicate that the significance levels are 10%, 5%, and 1%, respectively, and the standard deviations of each coefficient are in parentheses.

Considering lag effect.
As subsidies could impact the sustainable innovation performance of SEEs with some lag, for robustness, Equation (1) is re-estimated when considering R&D subsidies at time t − 1 and not t. As shown in column (3) of Table 4, the coefficient on R&D subsidies (L.sub) remains significantly positive, which again indicates that R&D subsidies significantly increase SEEs' sustainable innovation performance. Therefore, even if we consider the lag effect, the benchmark regression results are robust.
Controlled industry-fixed effect. In the basic regression model mentioned above, the firm-fixed effect and the year-fixed effect are included in the model. Considering the possible impact of industry differences, the industry-fixed effect is further controlled, and the re-examination results in column (4) of Table 4 show that the coefficient of R&D subsidies is significantly positive, which is consistent with the previous.
Winsorized at the 2% and 98% levels for continuous variables. To avoid the interference of outliers on the regression results, all the continuous variables are winsorized at the 2% and 98% levels. As shown in column (5) of Table 4, the coefficient of R&D subsidies is positive and significant, thus supporting the reliability of the conclusion.
Mediation test for bootstrapping method. Based on the above Sobel test, the bootstrapping method with a 95% confidence interval is used to re-estimate the two indirect mechanisms. Table 5 shows the results of bootstrapping analysis, which indicate that external collaborative networks and R&D investment play a partial mediating role in the relationship between R&D subsidies and SEEs' sustainable innovation performance, thus supporting H2 and H3. Note: *, **, and *** indicate that the significance levels are 10%, 5%, and 1%, respectively, P is for the percentile confidence interval, and BC is for the bias-corrected confidence interval.

Further Analysis: The Moderating Effect of R&D Subsidies on the Relationship between External Collaborative Networks and Sustainable Innovation Performance
In the previous sections, we assessed the impact of R&D subsidies on SEEs' sustainable innovation performance and its mechanism from the perspectives of input additionality, output additionality, and behavioral additionality. The findings show that R&D subsidies significantly improve SEEs' sustainable innovation performance through external collaborative networks and R&D investment. Moreover, the mediating effect of R&D investment is significantly stronger than that of external collaboration networks, which indicates that R&D subsidies have a limited effect on SEEs' external collaboration networks. However, building external collaboration networks is crucial for SEEs, especially in the context of the complex and changing international and domestic competition environment, and open innovation and the construction of external collaboration networks have gradually become important ways for SEEs to break through organizational boundaries and acquire rich external resources to improve their technical capabilities. Therefore, public policies play a critical role in promoting the adoption of open innovation among enterprises [77]. Another question that we wish to explore is whether R&D subsidies affect the relationship between external collaborative networks and sustainable innovation performance, that is, in the context of the large-scale increase in subsidies and open innovation, whether R&D subsidies promote the effect of external collaborative networks although the impact of R&D subsidies on external collaboration networks is limited. Do the effects of subsidies differ for SEEs with different enterprise characteristics?
R&D subsidies are an important way for the government to support and intervene in the development of enterprises at the macro level; as R&D subsidies received by SEEs increase, the internal and external innovation environments will change accordingly. From the perspective of enterprises' internal innovation environment, an increase in subsidies generates more innovation resources for enterprises [78], affecting SEEs' interaction initiatives with external partners. After external collaborative networks are established, deep interaction and close collaboration among network subjects are needed to improve sustainable innovation ability [79,80]. However, as SEEs' own innovation resources increase, SEEs are likely to reduce interaction due to knowledge leakage, potential competition risks, or partners' opportunistic behaviors [75,76,81], which is not conducive to sustainable innovation. This eventually weakens the positive relationship between external collaborative networks and sustainable innovation performance. From the perspective of enterprises' external innovation environment, R&D subsidies represent stronger political connections between enterprises and the government [78]. In other words, the more R&D subsidies that an enterprise receives, the stronger the links between the enterprise and the government become. As a result, enterprises receiving larger subsidies pay more attention to the government than others. However, manager attention is limited [82,83], and it naturally shifts from partners to the government, which weakens enterprises' relationships with different external partners and increases the probability of distortions in enterprises' innovation behaviors caused by political connections [78,84]. Especially if network construction is increased in response to application requirements, rather than as a consequence of deepening preexisting networks, it is likely to become a cost rather than an asset for enterprises [77]. Moreover, the demands of the government and innovation partners are difficult to coordinate effectively [85], and balancing the needs of both parties will affect the relationship between external collaborative networks and sustainable innovation performance. All of these factors have a negative impact on sustainable innovation performance.
Similarly, because different types of enterprises have different characteristics and face different innovation environments, we believe that under the differences in enterprise ownership type and life cycle stage, the moderating role of R&D subsidies in the relationship between external collaborative networks and sustainable innovation performance of SEEs also differs.
Based on the above analysis, model 4 is constructed to further analyze the moderating effect of R&D subsidies on the relationship between external collaborative networks and the sustainable innovation performance of SEEs: where the coefficient of d 3 is the basis for identifying the moderating effect of R&D subsidies.
Column (1) of Table 6 reports the moderating effect of R&D subsidies (sub) for the full sample. The interaction term (sub × col) is −0.0516 (p < 0.01), indicating that R&D subsidies have a negative impact on the relationship between external collaborative networks and SEEs' sustainable innovation performance. In other words, as R&D subsidies increase, the positive effect of external collaborative networks on sustainable innovation performance gradually weakens. As discussed above, on the one hand, obtaining R&D subsidies can dramatically alleviate the innovation resource constraints of sustainable innovation, thus reducing the enthusiasm for interaction between the partners-an effect that is unfavorable to SEEs' sustainable innovation. On the other hand, the close political connection between SEEs and the government maintained by R&D subsidies makes it difficult for SEEs to balance the needs of the government and external partners. Many enterprises will pay substantial attention to meeting the needs of the government to obtain public support in the short term but will neglect the needs of innovation partners, leading to innovationdistorting behavior. In this context, R&D subsidies will reduce the promotion of external collaborative networks on SEEs' sustainable innovation performance. In the subsample studies, the estimated results of SOE and NSOE enterprises are shown in columns (2) and (3) in Table 6. The estimated coefficient of sub × col is less than 0 for both SOEs and non-SOEs, although it is only statistically significant in non-SOEs. Compared to NSOEs, SOEs have closer connections with the government and do not need R&D subsidies to improve their relationship. In addition, NSOEs are more profit-oriented, which makes them less willing to establish interactive relations with external partners when innovation resources are abundant because of high relationship maintenance costs and information disclosure risks. This also largely explains why the negative moderating effect of R&D subsidies on the relationship between external collaborative networks and SEEs' sustainable innovation performance is significant only in non-SOEs.
According to the results in columns (4)- (6) in Table 6, whether SEEs are in the mature stage or declining stage, the coefficients of sub × col are not statistically significant. In the growing stage, the coefficient of sub × col is significantly negative (d 3 = −0.0425, p < 0.1), which shows that R&D subsidies play a significant and negative moderating role in the impact of external collaborative networks on sustainable innovation performance in SEEs' growth stage. In comparison, enterprises in the growth stage have somewhat stronger demand for innovation resources and hope to take a certain position in market competition; thus, they have a stronger motivation to allocate R&D subsidies as a way to maintain political connections and quickly gain market recognition by government power. Therefore, the negative moderating effect of R&D subsidies is significant in SEEs' growth stage.

Discussion
With R&D subsidies expanding in recent years in combination with the background of SEEs' open innovation, this paper explores the effect and mechanism of R&D subsidies on SEEs' sustainable innovation performance. It reveals the multiple relationships among R&D subsidies, external collaboration networks, R&D investment, and SEEs' innovation performance. Based on Xu et al. [63], who found significant evidence for a positive effect of public funds on sustainable patent output at the regional level, we find evidence supporting the relationship between R&D subsidies and SEEs' sustainable innovation performance at enterprises' micro level. Unlike the extant literature, this paper focuses on SEEs' sustainable innovation performance rather than general innovation. However, the positive impact of R&D subsidies on SEEs' sustainable innovation performance is congruent with results regarding general innovation [10], which showed that R&D subsidies positively influence the R&D intensity of Jiangsu high-tech manufacturing firms. Cotti and Skidmore [9] and Guo [19] also found that the crowding-out effects with regard to innovation subsidies were not present for specific enterprise types, such as SEEs, which is similar to our findings but different from those of Bernini and Pellegrini [12] and Yu et al. [13]. We confirm that R&D subsidies can improve SEEs' sustainable innovation performance from the perspective of input, output, and behavioral additionality.
R&D subsidies can improve SEEs' sustainable innovation performance by expanding their external collaboration networks and increasing internal R&D investment. Compared with R&D investment, the mediating role of external collaborative networks in the relationship between R&D subsidies and sustainable innovation is rarely discussed. We know very little about the behavioral additivity of subsidies, except that studies by Cerulli et al. [33] and Chapman et al. [34] showed that R&D subsidies positively influence the breadth of external collaborative networks, which is an important factor affecting sustainable innovation. In this context, we put forward a complete theoretical framework from the perspectives of input, output, and behavioral additionality based on Cerulli et al. [33], and the results show that both external collaborative networks and R&D investment are important mediators of the relationship between R&D subsidies and sustainable innovation. The empirical results reinforce the existing black box research on the impact of R&D subsidies on enterprise innovation [9,10,19]. In contrast to the method used by Ahn et al., the Sobel test with secondary data led to a consistent conclusion in our study; that is, R&D subsidy effects, such as input, output, and behavioral additionality, can occur simultaneously [76].
In addition, we find that the mediating effect of R&D investment is more significant than that of external collaborative networks. The interaction effect of R&D internal investment and external collaboration networks has been investigated by Cerulli et al. [33] and Ahn et al. [76]. However, little research has attempted to compare the two types of mechanisms during the effect of R&D subsidies. This paper fills this gap by exploring the differences between the two additionalities in the relationship between R&D subsidies and SEEs' sustainable innovation performance.
Because the moderating effect of R&D subsidies has not drawn sufficient attention, through the innovative introduction of R&D subsidies in the analysis, this paper provides new insights into the positive relationship between external collaborative networks and sustainable innovation from the perspective of changes in the internal and external innovation environment of emerging enterprises that receive R&D subsidies. The results show that the more R&D subsidies SEEs receive, the weaker the positive relationship between the external collaborative networks and SEEs' sustainable performance is. This result is similar to that of D'Ambrosio et al. [77], who suggested that the applications for subsidies could change the selection criteria for R&D partners. Costa et al. [26] also pointed out that the role of public funding is limited and only partially enhances eco-innovation adoption. In addition, the effective boundary between R&D subsidies and the relationship between external collaboration networks and sustainable innovation performance fills the gap by probing the heterogeneity of the moderating effect of R&D subsidies. These significant research findings are conducive to a more developed understanding of the relationships among R&D subsidies, external collaborative networks, and SEEs' sustainable innovation performance.

Conclusions
To explore the relationships among R&D subsidies, external collaboration networks, R&D investment, and SEEs' sustainable innovation performance, this paper establishes a research model based on the perspectives of input, output, and behavioral additionality and selects A-share SEEs listed in the Shanghai and Shenzhen stock exchanges from 2012 to 2016 as samples to conduct the panel data multiple regression analysis. The main conclusions are as follows. (1) R&D subsidies have a significant promoting effect on SEEs' sustainable innovation performance. This conclusion holds even when endogeneity is considered. (2) External collaborative networks and R&D investment act as mediators in the relationship between R&D subsidies and SEEs' sustainable innovation performance. (3) R&D subsidies weaken the positive relationship between external collaborative networks and sustainable innovation performance, and the moderating effect of R&D subsidies varies in the sign, statistical significance, and impact magnitude of the heterogeneous samples. Specifically, the negative moderating effect of R&D subsidies is statistically significant in non-SOE enterprises and enterprises in the growth stage, but it is insignificant in SOEs and enterprises in the mature and declining stages.
This study provides a complete framework for understanding the microperformance of R&D subsidies from the three types of perspectives of subsidy additionality, indicating the importance of applying multiple theories and perspectives to explain how R&D subsidies affect SEEs' sustainable innovation performance. Examining the contribution of R&D subsidies to SEEs' sustainable innovation performance in terms of multiple concepts and perspectives is vital, as it helps expand our understanding of R&D subsidies. In addition, research on the mediating role of internal R&D investment and external collaboration networks and the moderating role of R&D subsidies resolves the controversy regarding the mechanism of the effect of R&D subsidies on innovation performance. The difference between the impact of internal R&D investment and external collaboration networks on sustainable innovation performance, which has attracted little attention from scholars, is investigated in this paper. Finally, this paper emphasizes the importance of the moderating effect of R&D subsidies and includes it in a theoretical framework of external collaborative networks and sustainable innovation performance, providing a new perspective to explore the role of R&D subsidies and supplementing academic research on innovation network theory and open innovation theory.
Our findings have practical implications for policy-makers. On the one hand, full leverage of government subsidies should be encouraged, and the government should explore and formulate R&D subsidy policies aimed at complying with the law of open innovation for SEEs. The research shows that R&D subsidies not only promote innovation input and output directly, but also serve as an effective tool for building diversified external networks. Therefore, based on effective policy design and implementation, such as optimizing R&D subsidies in terms of subsidy amounts, objects, models, and implementation methods, subsidies must be guided to play a role in building cross-organizational external collaboration networks to aid open innovation. On the other hand, more networked/collaborated policy tools should be added to China's innovation policy toolbox to better fulfill the role of R&D subsidy policy, creating a new open innovation system. Direct R&D support and indirect network/coordination support are two kinds of important policy tools for innovation in China [86]. The former is mostly aimed at addressing "market failure" for enterprise innovation resources, although it also somewhat promotes the construction of external collaborative networks. However, the findings show that a single policy intervention is not sufficient to trigger deeper interactive cooperative behavior, and more concerningly, largescale subsidies may have negative effects. To this end, the government should develop more policy tools to enrich our innovation support policy system to solve the problem of interaction or network failure of enterprises in the process of external collaborative network construction and operation.
Although this study contributes to the literature on the R&D subsidies and sustainable innovation performance of SEEs, it has certain limitations. First, the government's stimulus policies for sustainable innovation performance not only include R&D subsidies but also tax credits and other policies. Further research is needed to determine whether there is an interaction effect between the policy combinations, such as whether the policy combinations affect sustainable innovation performance or whether the effect of policy combinations is stronger than that of a single policy instrument. Second, this paper uses only authorized patents to reflect SEEs' sustainable innovation performance, which is a relatively limited data source. Future studies could select a number of indicators to measure sustainable innovation performance considering innovation, development, the environment, and other aspects to establish a comprehensive evaluation system. In addition, future studies can use the principal component analysis method to calculate the comprehensive score function of SEEs' sustainable innovation performance. Finally, this research is limited by only studying a single country and industry. Future research could extend this study to other emerging countries or types of industries, which is sure to provide insights for policy-makers and enterprise managers interested in this issue.