The Impact of a Multilevel Innovation Network and Government Support on Innovation Performance—An Empirical Study of the Chengdu–Chongqing City Cluster

Abstract

A national strategy has been deployed for the development of China’s western region. The Chengdu–Chongqing city cluster is an important platform for collaborative regional innovation. In this empirical study, we constructed multilevel innovation networks for each of the 16 cities in the Chengdu–Chongqing city cluster and the inter-city networks for these 16 cities based on a panel of data on applications for invention patents by industry–university–research collaborators in the city cluster. We used social network analysis and a negative binomial regression model with fixed effects to examine the impact of the multilevel innovation networks on the innovation performance of the 16 cities. The moderating effect of government support was also analyzed. The results show that the average weighted degree of the intra-city innovation network has significant positive effects on the innovation performance of the 16 cities. For the inter-city innovation networks, the network density and cooperation intensity have significant positive effects on the innovation performance of the 16 cities. Regarding the moderating effect, our results show that a high level of government support enhances the positive effects of the average weighted degree of the intra-city innovation networks and the network density of the inter-city innovation networks on the innovation performance.

1. Introduction

With the globalization of the economy and the rapid development of science and technology, innovation has become the core driving force of regional economic development [1]. Narrowing the gap in the level of economic development among regions and achieving coordinated regional development through innovation are the keys to solving the problem of imbalanced regional economic development in China [2]. The innovation network is important to regional innovation and enhancing innovation performance [3]. According to the strategy for the development of the western region, the Chengdu–Chongqing city cluster is an important platform for collaborative regional innovation [4]. Improving the efficiency of the innovation network of the Chengdu–Chongqing city cluster may improve the level of economic development in the western regions [5].

During the early stage of collaborative innovation, geographical proximity can reduce communication costs and improve the efficiency of an innovation network. Innovators within a city tend to cooperate with one another to obtain knowledge and enhance the efficiency of the absorption and diffusion of knowledge within the city [6]. Social proximity and cultural proximity can facilitate collaboration among innovators within a city. Gobbo and Olsson [7] point out that closed network structures accelerate the sharing of information among innovators. However, with the rapid development of transportation and computer technology, cross-city collaborative innovation is occurring more frequently, and a city’s innovation needs can no longer be met by the resources within the city alone [8,9]. A region’s innovation performance depends not only on the resources within one city but also on the resources in other cities. Cooperation among the 16 cities in the Chengdu–Chongqing city cluster may produce new and heterogeneous information and knowledge in a broader range of fields. In this study, we constructed multilevel innovation networks, including intra-city and inter-city innovation networks, and analyzed their impact on the innovation performance of these 16 cities.

Innovation activities are characterized by high costs, high risks, strong spillover, and information asymmetry. These characteristics provide a theoretical basis for governmental intervention in the field of innovation [10]. Government support can guarantee that the construction of a region’s innovation network and innovation activities will go smoothly [11]. On the one hand, the government can provide funding to reduce the risks and costs borne by innovators and encourage them to engage in innovation activities [12,13]. Freeman [14] argues that basic research should be funded by the government. If the government were to stop funding scientific research, the consequences would be unthinkable, and private investment would not be able to fill the gap in funding created by the government. On the other hand, by setting up an innovation platform, the government can reduce for innovators the time and costs involved in obtaining knowledge and cultivating professional skills, improving the efficiency of the innovation network [15,16].

According to the above analysis of innovation networks, the flow of knowledge among the 16 cities in the Chengdu–Chongqing city cluster has a significant impact on the innovation performance of the region [4]. Therefore, a holistic view is needed that takes the intra-city and inter-city innovation networks into account. In addition, as a factor that has an influence on the innovation environment, government support is important to the promotion of collaboration among innovators [17]. This raises the following questions: What types of intra-city and inter-city network structure can enhance a city’s innovation performance? Does the moderating effect of government support differ between intra-city innovation networks and inter-city innovation networks? The purpose of this study is to investigate the impact of intra-city and inter-city innovation networks on the innovation performance of the 16 cities in the Chengdu–Chongqing city cluster.

The remainder of this paper is organized as follows. Section 2 presents a review of the literature on innovation networks and government support. Section 3 presents our theoretical hypotheses. Then, in Section 4, we use the data of collaborative invention patent applications of the Chengdu–Chongqing city cluster to construct intra-city innovation networks for each of the 16 cities in the Chengdu–Chongqing city cluster, and inter-city innovation networks among the 16 cities. We calculated multilevel innovation network characteristics by using the social network analysis method. Considering the moderate effect of government support, an empirical model is proposed to evaluate the impact of multilevel innovation networks on innovation performance with the moderating effect of government support. In Section 5, we use a negative binomial regression model with fixed effects to examine the impact of multilevel innovation network structure on city innovation performance with the moderating effect of government support. In Section 6, we summarize the research conclusions and propose some suggestions on how to improve the innovation performance of the 16 cities.

2. Literature Review

Previous studies on regional innovation networks focused on different spatial scales, including countries [18], well-developed city clusters [19,20], and cities [21]. The innovation networks of the developing city clusters such as Chengdu–Chongqing need further investigation. Kimh D et al. [22,23,24] study the characteristics of innovation networks and their spatial and temporal evolutionary characteristics by using social network analysis. To illustrate the impact of innovation networks on regional innovation performance more clearly, regression analysis was used by Ter Wal to study the relationships between them [25]. Zheng concludes that the high network density accelerates the flow and sharing of knowledge between innovators, and improves the innovation ability of products [26], while Innocentin [27] argues that network density is associated with a negative effect on invention productivity. Du et al. [28] believe that the centrality of the IUR network has a positive effect on the performance of corporate knowledge co-creation. Thomas ritter [29] contends that the high cooperation intensity of the enterprises is helpful to acquiring the knowledge and improving their innovation performance. Therefore, the impact of innovation networks of the Chengdu–Chongqing city cluster on innovation performance needs to be further investigated.

The existing studies indicate that multilevel networks provide insights into a broader perspective of innovation helping us to understand innovation phenomena at and across different levels [26]. Innovators are embedded in multilevel networks and the acquisition capabilities of innovation resources may be different [30]. In the intra-city innovation networks, close relationships among innovators can accelerate information diffusion, and improve the efficiency of recombination of knowledge [31]. In the inter-city innovation network, cross-city cooperation of innovators facilitates the acquisition of heterogeneous knowledge [32]. Huggins et al. [33] contend that the ability of regions to access external knowledge is largely determined by their position in a network. A central position offers the city advantages information collection and processing [34]. Guan [3] argues that the high centrality of the inter-city collaboration network has the advantage of accessing unique information and improves innovation performance. The inter-city innovation networks compensate for the limitations of intra-city innovation resources [35], acquiring and integrating external knowledge and improving the innovation performance of the city [36]. In this study, the innovators include industries, universities, and research institutes. Collaboration among the innovators within a city formed the intra-city innovation networks. Each node represents an innovator and the edges represent their collaborative relations. Collaboration among the 16 cities in the city cluster formed the inter-city innovation networks. Each node represents a city and the edges represent collaborative relations among cities. (Collaboration is established by the joint applications for invention patents among innovators.)

As a very important factor in the innovation environment, government support can guide and coordinate regional innovation activities through relevant policies such as tax incentives and R&D subsidies [37]. Szucs and Du [12,13] point out that R&D subsidies have a positive impact on enterprise innovation. Zhang et al. [10] study the impact of coupling coordination degree of government support, financial support, and innovation on economic development by using panel data from 28 provinces in China. The results show that the coupling coordination degree of government support, financial support, and innovation has significantly promoted the economic development of the eastern regions, but has no significant impact on the economic development of the central and western regions. However, existing studies on government support have primarily focused on the direct impact on innovation. The moderating effect of government support on the innovation of regions needs to be further explored. Therefore, it is necessary to consider the moderating effect of government support, while analyzing the impact of the intra-city and the inter-city innovation networks on the innovation performance of the 16 cities in the Chengdu–Chongqing city cluster.

In summary, previous studies on regional innovation networks focused on their impact on innovation performance from a single perspective and lacked a comprehensive analysis of the characteristics of innovation networks. With the economic development of the Chengdu–Chongqing city cluster, cross-city collaboration is increasing and accelerates the flow of heterogeneous knowledge in the inter-city innovation networks. Therefore, it is necessary to study the impact of characteristics of the intra-city and inter-city innovation networks on innovation performance from a multilevel network perspective. In addition, as a part of the innovation environment, government support also has an influence on collaborative innovation activities. However, previous studies focused on the direct impact of government support on innovation performance. The moderating effect of government support needs to be further explored. The Chengdu–Chongqing city cluster has become the principal platform for promoting the economic development of the western regions. Therefore, it is imperative to study the multilevel innovation networks to improve the innovation performance of the cities in the Chengdu–Chongqing city cluster and the economic development of the western regions.

3. Theoretical Hypothesis

3.1. Characteristics of the Innovation Network and the Innovation Performance of the 16 Cities in the Chengdu–Chongqing City Cluster

The overall and individual network characteristics describe innovation network characteristics from different perspectives. The overall network characteristics include the average weighted degree, network density, and so on, which reflect the impact of the tightness and connectivity among innovators on innovation performance. The innovation performance is influenced by the network position of the city, which can be measured by the individual network characteristics, such as the between centrality, cooperation intensity, and so on. In previous studies on innovation networks, these network characteristics are the most commonly used. However, their effects on innovation performance haven’t come to consistent conclusions [26,27,28,29,38,39].

To investigate the characteristics of the innovation network of the Chengdu–Chongqing city cluster more comprehensively. This study constructed intra-city and inter-city innovation networks and selects overall and individual network characteristics to examine the impact of multilevel innovation networks on innovation performance. We select the network density of the inter-city networks and the average weighted degree of the intra-city networks as the overall network characteristics. The betweenness centrality and cooperation intensity of the inter-city networks as individual network characteristics.

3.1.1. The Average Weighted Degree of Intra-City Innovation Networks and the City’s Innovation Performance

The average weighted degree is defined as the average linkages of the network among all innovators. It reflects the contact intensity of the overall innovation network [40]. A high average weighted degree of intra-city innovation networks accelerates the flow and sharing of resources between innovators in the same city [41]. On one hand, a higher average weighted degree suggests more collaboration in the intra-city network and contributes to establishing trust between industries, universities, and research institutes [42]. Grosser et al. [43] point out that trust between innovators is helpful to reduce innovation costs and risks. On the other hand, a high average weighted degree promotes complementary and utilization efficiency of innovation resources within a city, helping innovators to explore and expand new innovation resources [44]. This study contends that a high average weighted degree indicates high accessibility in the network, and accelerates the information flow and resource sharing between innovators. Therefore, it is helpful to establish collaborative innovation relationships between innovators and improves the city’s innovation performance. Hence then, our theoretical Hypothesis 1 is proposed:

Hypothesis 1.

The average weighted degree of intra-city innovation networks positively affects the city’s innovation performance.

3.1.2. The Network Density of Inter-City Innovation Networks and the City’s Innovation Performance

Network density is measured by the number of actual relationships between nodes in the network to the maximum possible number of relationships among nodes [44]. In this study, we constructed inter-city networks by using 16 cities in the Chengdu–Chongqing city cluster as nodes. Coleman [45] highlights that a dense and connected network would facilitate knowledge exchange and diffusion. Almeida [46] argus that a high density of inter-city networks means more direct connections between cities, which contributes to reducing communication time and innovation costs. Meanwhile, high-density networks indicate a large number of collaborations among cities, which improves the efficiency of innovation [47]. Li et al. [48,49] also conclude that high-density innovation networks provide cities with more innovation resources, accelerating knowledge flow, promoting knowledge transfer, and increasing the city’s innovation performance. Accordingly, Hypothesis 2 was proposed:

Hypothesis 2.

The network density of inter-city innovation networks positively affects the city’s innovation performance.

3.1.3. The Betweenness Centrality of Inter-City Innovation Networks and the City’s Innovation Performance

The betweenness centrality reflects the extent to which a node acts as an intermediary, the degree of access to resources, or the way it controls them [43]. Nodes occupying high intermediary positions are in a better situation for sharing, integrating, and utilizing complementary, heterogeneous resources. In the inter-city innovation networks, cities with different network positions have different opportunities to acquire new knowledge, which is essential to innovation activities [50]. Cities with high betweenness centrality have an information advantage. Such cities have access to unique information and become information databases, increasing the diversity of information [51,52]. Meanwhile, these cities enjoy the opportunity to bridge the information gap between tripartite relationships [53]. The higher the betweenness centrality of the city in the network, the shortest paths are created, reducing the distribution time of resources and facilitating the exchange of innovative ideas [54]. Finally, in the inter-city innovation networks, cities with a high betweenness centrality have the unique advantage to determine the flow of resources. The higher the betweenness centrality of the city, the stronger the ability to control the diffusion of resources, and the more facilitate to accelerate the flow of resources [55]. Therefore, we propose the following hypotheses:

Hypothesis 3.

The betweenness centrality of the inter-city innovation networks positively affects the city’s innovation performance.

3.1.4. The Cooperation Intensity of Inter-City Innovation Networks and the City’s Innovation Performance

The cooperation intensity refers to the average number of cooperation between this node and other nodes, reflecting its ability to obtain innovation resources [47]. In the inter-city innovation networks, the high cooperation intensity will increase the resources of the city, and enhance the ability to address complex problems [56]. In general, cities prefer to cooperate with those they previously worked, as they have already established common guidelines for cooperation [57]. A high cooperation intensity can strengthen trust and commitment among cities, and reduce the conflicts in cooperation and coordination costs [58]. Therefore, in the inter-city innovation networks, cities with high cooperation intensity indicate that they establish trust with other cities. It is helpful to transfer resources across city boundaries and improves the innovation performance of the cities in the Chengdu–Chongqing city cluster. Accordingly, Hypothesis 4 is proposed:

Hypothesis 4.

The cooperation intensity of inter-city innovation networks positively affects the city’s innovation performance.

3.2. The Moderating Effect of Government Support

Government support can make up for the funding gap caused by a market failure in innovation activities, and mainly includes R&D subsidies, and project funding [37,59]. In this study, government support is measured by the proportion of government expenditures on science and technology in government fiscal expenditures [60]. Shu et al. [61] indicate that government support could provide necessary resources for firms and enhance a firm’s opportunities for developing new collaborations. For region innovation, the government hosts and participates in basic knowledge and common technology R&D, creating a favorable knowledge environment for innovators to carry out commercial and practical R&D activities, which helps to enhance regional innovation efficiency [62]. In innovation activities with long-term and high uncertainty, government support can alleviate the risk of insufficient R&D expenditure for innovators stabilize innovators’’ confidence, and facilitate cooperative innovation within a city [63]. In the inter-city innovation networks, the government support can provide specialized services such as knowledge acquisition, technology diffusion, and management consulting for innovators in the city cluster. This helps to reduce innovation costs for innovators to find effective knowledge and develop professional skills, to improve the efficiency of innovation [64]. In addition, government support can promote industry-university-research collaboration by building a collaborative innovation platform and increasing the scale of collaborative innovation funds [65,66]. Therefore, government support would have a moderating effect on the relationship between innovation networks and the innovation performance of 16 cities in the Chengdu–Chongqing city cluster. Accordingly, the following hypotheses are proposed:

Hypothesis 5(a).

Government support positively moderates the relationship between the average weighted degree of intra-city innovation networks and the city’s innovation performance.

Hypothesis 5(b).

Government support positively moderates the relationship between the network density of inter-city innovation networks and the city’s innovation performance.

Hypothesis 5(c).

Government support positively moderates the relationship between the betweenness centrality of the inter-city innovation networks and the city’s innovation performance.

Hypothesis 5(d).

Government support positively moderates the relationship between the cooperation intensity of inter-city innovation networks and the city’s innovation performance.

The theoretical model is proposed in this paper in Figure 1.

4. Data and Methods

4.1. Patent Data

The State Intellectual Property Office (SIPO) grants three types of patents, including invention patents, utility patents, and design patents. It is generally acknowledged that invention patents are of greater value than utility or design patents. Each patent in SIPO contains the names and addresses of the inventors. Therefore, based on the data of collaborative applications for invention patents by industry-university-research in the Chengdu–Chongqing city cluster published by the SIPO, this study constructed intra-city and inter-city innovation networks for overlapping 5-year (t-5–t-1) rolling time windows from 2006 to 2018 (2006–2010, 2007–2011, 2008–2012, 2009–2013, 2010–2014, 2011–2015, 2012–2016, 2013–2017, 2014–2018) [52]. The UCINET6.0 software was used to analyze the characteristics of multilevel innovation networks. Data of the dependent variable and control variables were adopted from the China City Statistical Yearbook, China Statistical Yearbook, and China Statistical Yearbook on Science and Technology.

4.2. Constructing Networks

Figure 2 illustrates five innovators (a1, a2, b1, c1, c2) from three cities in the city cluster (A, B, C) in cooperation with three patents (P1, P2, P3). P1 is a cooperation of a1, a2, and b1; P2 is a cooperation of b1 and c1; P3 is a cooperation of c1 and c2. Then, according to the cooperation relationship of Figure 2, Figure 3 describes the multilevel innovation network diagram, including the intra-city and inter-city innovation networks. ● represents the innovators, including industries, universities and research institutes The edges represent their collaborative relations, and the intra-city innovation networks were constructed by the innovators within a city. The dotted line box represents the inter-city innovation network, in which nodes represent 16 cities and the edges represent collaborative relations among cities in the Chengdu–Chongqing city cluster.

4.3. Method and Variables

4.3.1. Dependent Variable

Patent data is often used to reflect the innovation performance of a region and represents the actual number of regional innovation performances. In this study, we use the number of invention patent grants of each city to measure the city’s innovation performance. Compared to utility patents, and design patents, invention patents are often considered the better indicator of knowledge transformation and innovation achievements [67]. We use the number of invention patents granted in the year following the innovation network period as the measure of innovation performance. For example, the city’s innovation performance in the innovation network from 2006 to 2010 is measured by the number of the city’s invention patents granted in 2011 [3].

4.3.2. Independent Variables

(1) Average Weighted Degree (AWD)—the overall network characteristics. The average weighted degree is measured by the number of cooperation between nodes to the number of nodes in the network. It is used to describe the characteristics of the intra-city innovation networks in this study. As described in Equation (1).

$$AWD=\frac{1}{N}\left({\displaystyle \sum _{i=1}^N{\displaystyle \sum _{j=1}^N{w}_{ij}}}\right)$$

(1)

where N is the number of nodes in the network, $w_{ij}$ is the number of cooperation between i and j.

(2) Network Density (D)—the overall network characteristics. It is measured by the number of actual relationships between nodes in the network ratio to the maximum possible number of relationships among nodes. Network density reflects the tightness of the overall network. It is used to describe the characteristics of the inter-city innovation networks in this study. As described in Equation (2).

$$D=\frac{2l}{N\left(N-1\right)}$$

(2)

where l represents the actual number of connections in the collaborative innovation network, and N represents the number of nodes in the innovation network.

(3) Betweenness Centrality (BC)—the individual network characteristics. The betweenness centrality of a node represents the extent to which this node controls the linkages among the other nodes. It is also used to describe the characteristics of the inter-city innovation networks in this study. As described in Equation (3).

$$BC\left(i\right)=\frac{g_{jk}\left(i\right)}{g_{jk}}$$

(3)

where BC(i) represents the betweenness centrality of the node i, g_jk represents the number of shortcuts existing between node j and k, g_jk(i) represents the number of shortcuts passing through node i between node j and k.

(4) Cooperation Intensity (CI)—the individual network characteristics. It refers to the ratio of the total cooperation times of a node to the degree centrality of this node. It is also used to describe the characteristics of the inter-city innovation networks in this study. As described in Equation (4).

$$CI\left(i\right)=\frac{{\displaystyle \sum _{j=1}^N{w}_{ij}}}{d}$$

(4)

where ${\displaystyle \sum _{j=1}^N{w}_{ij}}$ is the number of cooperation between i and other nodes. Where d represents the degree centrality of i.

4.3.3. Moderating Variable

Government support refers to the funding support and policy guarantee provided by the government for innovation activities. Government support (GOV) can be measured by the proportion of science and technology expenditures in government fiscal expenditures [60]. Fiscal expenditures include expenditures for science and technology and expenditures for education and other expenditures. Expenditure for science and technology is an important source of funding for innovation activities among innovators. It can better reflect the direct impact of government on local innovation activities.

4.3.4. Control Variables

The existing studies indicate that innovation performance is also a function of other socioeconomic factors [68,69]. We include the following control variables.

GDP reflects the economic development level of the city. Therefore, we selected the GDP per capita to reflect the effect of economic development on innovation performance.

The expenditure of research and development was selected to reflect the investment intensity of innovation. In this study, the expenditure on research and development is measured by the internal expenditure of R&D.

The openness of a city is measured by the total amount of foreign investment actually utilized.

Government intervention is essential for local innovation. In this study , government intervention is measured by the proportion of local general public budget expenditure in the gross regional product.

A city’s knowledge base is measured by the number of patent grants in the city during the past five years.

Specific variable definitions and measurements are shown in

Table 1. Description and coincidence of variables.

Variable	Symbolic Representation	Definition Specification
Innovation performance of city	Pat	Number of invention patents granted
Network average weighted degree	AWD	Collaboration among innovators in the intra-city network/Number of innovators
Network density	D	Actual relationships/Possible relationships among cities in the inter-city network
Betweenness centrality	BC	The intermediary capability of the cities
Cooperation intensity	CI	Collaboration of the city/Degree centrality of the city
Government support	GOV	Expenditure for science and technology/Government fiscal expenditures
The economic development level of the city	PGDP	Per capita gross regional product(logarithmic)
Expenditure of R&D	RD	The internal expenditure of R&D (logarithmic)
Openness of the city	OP	The total amount of foreign investment actually utilized (logarithmic)
Government intervention	GI	Local general public budget expenditure/Gross regional product (logarithmic)
Knowledge accumulation in the city	CKB	The number of city patents granted during the past 5 years (logarithmic)

.

4.4. Statistical Approach

The innovation performance is measured by the number of invention patent grants of the city and the negative binomial regressions are often used to deal with patents as the dependent variable [70]. Equation (5) was used to examine the impact of innovation networks on the innovation performance of the 16 cities in the Chengdu–Chongqing city cluster.

$$Pa{t}_{i,t}={\beta }_0+{\beta }_{1}AW{D}_{i,t}+{\beta }_2{D}_{i,t}+{\beta }_{3}BC{(i)}_{i,t}+{\beta }_{4}CI{(i)}_{i,t}+{\beta }_6{Z}_{i,t}+{\mu }_i+{\epsilon }_{i,t}$$

(5)

To further examine the moderating effect of the government support, the interaction term between the moderating variable of the government support and the characteristics of intra-city and inter-city innovation networks are introduced based on Equation (5), as shown in Equation (6):

$$\begin{array}{cc}\hfill Pa{t}_{i,t}=& {\gamma }_0+{\gamma }_{1}GO{V}_{i,t}+{\gamma }_{2}AW{D}_{i,t}+{\gamma }_3{D}_{i,t}+{\gamma }_{4}BC{(i)}_{i,t}+{\gamma }_{5}CI{(i)}_{i,t}+{\gamma }_{6}AW{D}_{i,t}\times GO{V}_{i,t}\hfill \\ & +{\gamma }_7{D}_{i,t}\times GO{V}_{i,t}+{\gamma }_{8}BC{(i)}_{i,t}\times GO{V}_{i,t}+{\gamma }_{9}CI{(i)}_{i,t}\times GO{V}_{i,t}+Z_{i,t}+{\mu }_{i,t}+{\epsilon }_{i,t}\hfill \end{array}$$

(6)

The dependent variable Pat_i,t stands for total invention patents in the city i during period t; AWD_i,t, D_i,t, BC(i)_i,t, CI_i,t(i) stand for the average weighted degree, network density, betweenness centrality, and the cooperation intensity of inter-city innovation networks for node i during period t; AWD_i,t × GOV_i,t, D_i,t × GOV_i,t, BC(i)_i,t × GOV_i,t, CI_i,(i)_t × GOV_i,t stands for the interaction between innovation network characteristics and government support; Z_i,t represents the control variables, including the economic development level of the city, expenditure of R&D, the openness of the city, government intervention and knowledge accumulation of the city; μ_i is the fixed-effects; ε_i,t is the error term.

5. Results

5.1. Descriptive Statistics and Correlation Analysis

The descriptive statistics of the variables are presented in

Table 2. Descriptive statistics of variables.

Variable	N	Mean	SD	Min.	Max.
Pat	144	734.1	1801	2	9179
AWD	144	0.949	1.127	0	4.556
D	144	0.270	0.060	0	0.314
BC	144	0.564	0.158	0	1
CI	144	6.520	6.221	0	26.67
PGDP	144	10.18	0.948	6.585	11.55
RD	144	12.12	1.574	9.680	15.32
OP	144	9.382	1.870	6.215	14.09
GI	144	0.197	0.0690	0.118	0.675
BKN	144	8.185	1.516	5.347	12.28
GOV	144	0.010	0.009	0.002	0.063

. The average number of invention patent grants is 734.1, while the standard deviation is 1801. The difference between the mean and standard deviation suggests an over-dispersion in the count data of invention patent grants. Therefore, a negative binomial model was used to examine our hypotheses. Meanwhile, fixed effect and random effect should be considered when using a negative binomial regression model to process panel data. According to the Hausman test, the results show that the p-value is less than 0.05, so we select the fixed effect model. In addition, for the consideration of model endogeneity, the fixed-effect model should also be selected, and the independent variables should be delayed by one stage during data processing.

The correlation analysis of the variables is presented in

Table 3. Correlation analysis.

	Pat	AWD	D	BC	CI	PGDP	RD	OP	GI	BKN	GOV
Pat	1
AWD	0.511 ***	1
D	0.145 *	0.274 ***	1
BC	0.644 ***	0.504 ***	0.655 ***	1
CI	0.591 ***	0.330 ***	0.353 ***	0.463 ***	1
PGDP	0.337 ***	0.133	−0.0480	0.224 ***	0.147 *	1
RD	0.680 ***	0.457 ***	0.134	0.566 ***	0.584 ***	0.278 ***	1
OP	0.711 ***	0.358 ***	0.0510	0.517 ***	0.469 ***	0.182 **	0.695 ***	1
GI	−0.156 *	0.218 ***	−0.0220	−0.0520	−0.215 ***	−0.0960	−0.184 **	−0.186 **	1
CKB	0.824 ***	0.568 ***	0.321 ***	0.686 ***	0.682 ***	0.224 ***	0.774 ***	0.733 ***	−0.220 ***	1
GOV	0.600 ***	0.320 ***	0.160 *	0.512 ***	0.581 ***	0.212 **	0.529 ***	0.379 ***	−0.232 ***	0.561 ***	1

Note: * p < 0.1, ** p < 0.05, *** p < 0.01.

. The result shows that all variables are positively correlated with the dependent variable. The correlation between the key explanatory variables is less than 0.6 in absolute values, except for the correlation between network density and betweenness centrality. Furthermore, to assess the severity of multicollinearity, we computed variance inflation factors (VIFs), with an average VIF value of 3.02 and the maximum VIF value of 5.78, which are well below the cut-off point of 10, implying that multicollinearity does not pose a problem to our regression [71].

The STATA/SE 16.0 software (It was created by the StataCorp: College Station, TX, USA) was used to analyze a negative binomial regression.

5.2. Characteristics of the Innovation Network and Innovation Performance of the 16 Cities in the Chengdu–Chongqing City Cluster

This study tested four hypotheses by entering all control variables in Model 1, and independent variables separately in Models 2–5.

Table 4. Panel negative binomial regression of the impact of innovation networks on innovation performance.

	Model 1	Model 2	Model 3	Model 4	Model 5
	Pat	Pat	Pat	Pat	Pat
AWD		0.172 ***
		(3.63)
D			3.510 ***
			(3.19)
BC				0.145
				(0.53)
CI					0.037 ***
					(6.97)
PGDP	0.099 ***	0.078 **	0.097 ***	0.098 ***	0.060 **
	(2.78)	(2.31)	(3.03)	(2.78)	(2.24)
RD	−0.024	−0.022	0.098	−0.098	0.142 **
	(−1.21)	(−1.22)	(1.06)	(−1.30)	(1.97)
OP	0.727 ***	0.636 ***	−0.020	−0.025	−0.031 **
	(9.84)	(8.81)	(−1.17)	(−1.25)	(−2.21)
GI	1.841 ***	1.158 *	1.536 **	1.847 ***	2.066 ***
	(2.72)	(1.70)	(2.11)	(2.76)	(3.62)
CKB	−0.099	−0.055	0.604 ***	0.722 ***	0.526 ***
	(−1.32)	(−0.71)	(7.67)	(9.65)	(9.19)
Constant	−3.796 ***	−3.325 **	−5.988 ***	−3.845 ***	−4.546 ***
	(−2.81)	(−2.49)	(−4.47)	(−2.86)	(−4.89)
Observations	144	144	144	144	144
N	16	16	16	16	16
city FE	YES	YES	YES	YES	YES
Wald chil 2	190.46	236.56	245.4	172.34	621.49
Log LH	−657.477	−650.660	−650.535	−656.635	−634.521

Note: * p < 0.1, ** p < 0.05, *** p < 0.01.

provides results for Models 1–5 using fixed-effects negative binomial regression. Model 1 is the basic model, which includes only control variables. The coefficient for the level of economic development, the degree of openness, and government intervention are positive and significant. However, the impact of internal expenditure of R&D on innovation performance is negative but insignificant. Internal expenditure of R&D includes the expenditure of basic research, applied research, and experimental development. The innovation performance of the city is measured by the number of invention patent grants, therefore, increasing the expenditure on applied research can effectively improve the innovation performance of the city [35]. In addition, compared with developed city clusters, the Chengdu–Chongqing city cluster has less internal expenditure of R&D and leads to no significant impact on innovation performance [72]. As shown in Model 2, the average weighted degree of intra-city innovation networks has a significant positive effect on innovation performance (β = 0.172, p < 0.01). Thus, Hypothesis 1 is supported. As shown in Model 3, the network density of inter-city innovation networks has a significant positive effect on innovation performance(β = 3.510, p < 0.01). Thus, Hypothesis 2 is supported. As shown in Model 4, the betweenness centrality of inter-city innovation networks have a negative effect on innovation performance but is insignificant. This may be caused by the high betweenness centrality of the city, which increases the redundant information and processing costs [34]. Therefore, Hypothesis 3 is not supported. As shown in Model 5, the cooperation intensity of inter-city innovation networks has a significant positive effect on innovation performance (β = 0.037, p < 0.01). Therefore, Hypothesis 4 is supported.

5.3. The Impact of the Interaction between the Government Support and the Characteristics of the Innovation Network on Innovation Performance

As shown in Table 4, it is found that the betweenness centrality of the innovation network has no significant effect on the innovation performance of the cities in the Chengdu–Chongqing city cluster. Therefore, the impact of betweenness centrality on the city’s innovation performance with moderating effect of government support is not included. As shown in

Table 5. Regression results of moderating effects of government support.

	Model 6	Model 7	Model 8
	Pat	Pat	Pat
AWD	0.180 ***
	(3.85)
D		2.951 ***
		(3.28)
CI			0.041 ***
			(6.49)
GOV	−10.302	−0.601	2.277
	(−1.46)	(−0.15)	(0.28)
AWD × GOV	12.682 ***
	(2.88)
D × GOV		233.861 ***
		(2.58)
CI × GOV			−0.235
			(−0.61)
PGDP	0.042	0.084 ***	0.064 **
	(1.35)	(2.85)	(2.36)
RD	0.004	0.091	0.174 **
	(0.06)	(1.19)	(2.22)
OP	−0.018	−0.019	−0.029 **
	(−1.20)	(−1.22)	(−2.17)
GI	1.160 *	1.592 **	2.115 ***
	(1.84)	(2.44)	(3.66)
CKB	0.580 ***	0.572 ***	0.518 ***
	(9.33)	(8.05)	(9.22)
Constant	−2.960 ***	−4.465 ***	−4.672 ***
	(−2.74)	(−4.28)	(−4.70)
Observations	144	144	144
N	16	16	16
city FE	YES	YES	YES
Wald chi2	475.65	427.92	665.25
Log LH	−639.958	−641.784	−633.865

Note: * p < 0.1, ** p < 0.05, *** p < 0.01.

, models 6–8 involved the interaction terms of the innovation networks with government support in the innovation performance of the cities. As shown in Model 6, government support has a significant positive moderating effect on the average weighted degree of intra-city innovation networks and innovation performance of the cities (β = 12.682, p < 0.01). This indicates that, with increased government support, the average weighted degree of the intra-city innovation network has a stronger promotion effect on the city’s innovation performance. To illustrate exactly how government support moderates the relationship between the average weighted degree and innovation performance of the cities. we plot the moderating effect by using a drawing template. Following a common method, we take one standard deviation below the mean of the average weighted degree to represent its low and high values (as shown in Figure 4a). As shown in Model 7, government support has a significant positive moderating effect on the network density of inter-city innovation networks and the innovation performance of the cities (β = 233.861, p < 0.01). This indicates that with the increase in government support, the network density of inter-city innovation networks in the promoting effect of innovation performance can be enhanced. Therefore, Hypothesis 5(b) is supported. Similarly, we plot the moderating effect (as shown in Figure 4b). As shown in Model 8, the government has no significant moderating effect on the cooperation intensity of inter-city innovation networks and the innovation performance of the cities. Therefore, Hypothesis 6(d) is not supported. Government support can facilitate collaboration among innovators, accelerates the flow of innovation resources, and improves the efficiency of innovation. However, the analysis indicates that the Chengdu–Chongqing city cluster is a core-edge structure, and collaboration is mainly concentrated in Chengdu and Chongqing [73]. When these cities with high betweenness centrality will increase the cost of processing redundant information and decrease the innovation performance of the city.

5.4. Robust Check

In this study, a negative binomial model was used to examine the impact of innovation networks on the innovation performance of the 16 cities in the Chengdu–Chongqing city cluster. To ensure the stability and universality of the research results, this study puts the logarithm of the patent grants number as the dependent variable, and then uses ordinary least squares (OLS) analysis to re-estimate the model. The results are consistent with the findings in Table 4.

6. Conclusions and Suggestions

6.1. Conclusions

Previous studies showed that different city clusters have different network characteristics and innovation capabilities [4,5,20,21]. There is a gap between the Chengdu−Chongqing city cluster and other developed city clusters in innovation capability [74]. Therefore, the conclusions of developed city clusters may not be suitable for the Chengdu–Chongqing city cluster. Studying the innovation network of the Chengdu−Chongqing city cluster is imperative to improve the innovation performance of cities as well as the economic development of the western regions. In this study, based on a panel of data on applications for invention patents by industry-university-research collaborators in the Chengdu−Chongqing city cluster, we constructed intra-city innovation networks for each of the 16 cities, and inter-city innovation networks among the 16 cities. The social network analysis and a negative binomial regression model with fixed effects were used to examine the impact of multilevel innovation networks on the innovation performance of the cities. Considering government plays an important role in promoting collaboration among innovators, this study further analysis the moderating effect of government support on innovation networks and the innovation performance of the cities. The following research conclusions are drawn.

The average weighted degree of intra-city networks has a significant positive effect on the innovation performance of the cities. The network density and cooperation intensity of inter-city networks have significant positive effects on the innovation performance of cities. However, the betweenness centrality of inter-city networks has no significant effect on the city’s innovation performance and even shows a negative effect. Therefore, cooperation among innovators within a city can reduce communication costs and improve innovation performance. Cross-city cooperation among innovators helps to obtain heterogeneous knowledge and improves innovation performance. However, the high betweenness centrality of the city will lead to the high cost of processing redundant information and lower innovation performance of the cities.

The impact of the average weighted degree of intra-city networks and network density of inter-city networks on the city’s innovation performance with moderating effect of government support has a significant positive effect. While moderating effect of government support on the relationship between the cooperation intensity of inter-city networks and the city’s innovation performance is insignificant. Therefore, government support improves innovation performance by promoting collaboration within and across cities. This will increase the closeness of networks, accelerate the flow of resources in innovation networks, and improve innovation efficiency.

6.2. Suggestions

(1) Accelerate the construction of the innovation system of intra-city and inter-city innovation networks.

Since the Chengdu–Chongqing city cluster is developing, the first step is to encourage industry-university-research cooperation within a city to improve the innovation performance of the city. For example, taking advantage of the geographical proximity of innovators within the city construct strategic alliances of industry-university-research. For inter-city innovation networks, other cities in the city cluster should exploit the leading role of the Chengdu–Chongqing to improve innovation performance. For example, the Chengdu–Chongqing city cluster should build an innovative resource-sharing platform to solve the problem of an increasing gap in innovation capacity and alleviate the dilemma caused by the “central collapse area”.

(2) Coordinate government support for science and technology in different cities.

Government departments need to coordinate innovation policies of different cities. The local government focused on improving their city’s innovation performance, which lead to the imbalanced distribution of innovation resources among cities in the Chengdu–Chongqing city cluster. Therefore, it is necessary to establish coordination mechanisms and provide a coherent innovative environment for cities in the city cluster. For example, government departments should set up innovation collaboration platforms to encourage cross-city cooperation among industries, universities, and research institutes. These innovators can absorb and integrate the unique innovation resources of other cities in the city cluster to improve their innovation performance.