Depth and Width of Collaborative Innovation Networks and High-Quality Development

Abstract

The key driving force for high-quality development is innovation, and collaborative innovation is an important form of organizing and realizing innovation. However, the impact of collaborative innovation networks on high-quality regional development remains unclear. At the city cluster level, this study analyzes more than 300,000 patent data based on the data of prefecture-level cities in China from 2012 to 2020 using the crawler method and social network analysis. The results show that, first, collaborative innovation in China is characterized by growth, network, and structural stability. Second, collaborative innovation can significantly improve the high-quality development of urban economies by reducing human resource mismatch and increasing the “intensive margin” and “expansive margin” of innovation. Third, at the national level, increased urban collaboration in terms of width and depth has contributed to the economy’s high-quality development. However, the two have not yet demonstrated complementarity, although at the level of urban agglomerations, the two are significantly complementary. Fourth, heterogeneity analysis shows that collaborative innovation is more effective in promoting high-quality development for highly matured city clusters and cities with robust innovation capacity. It can considerably overcome geographical constraints. From the regional heterogeneity perspective, the promotion of high-quality development through collaborative innovation is stronger in southern and central China. It is recommended that emerging market countries and city clusters focus on constructing and developing collaborative innovation networks and promoting high-quality economic development through measures such as increasing network density, enhancing the breadth and depth of synergies among cities, and developing differentiated policies.

1. Introduction

High-quality development strikes a balance between the quality and quantity of economic development, enabling low-carbon, sustainable economic development [1]. From a theoretical perspective, technological progress is the core of economic growth [2]. From a realistic perspective, innovation is the core driving force for a country’s high-quality development [3]. In an open innovation environment, innovation is not a closed and isolated system. Innovative subjects establish cooperative innovation networks through cooperative activities [4]. Such networks do not turn cities into “islands”. Cities share risks and accelerate the emergence of innovations through knowledge spillover, technology transfer, and industry–university–research cooperation [5,6]. Various countries have proposed several policies to support collaborative innovation. For example, the US government has advocated for the establishment of collaborative networks among enterprises [7]. European countries have proposed strengthening multilateral collaborative innovation in the EU Framework Program; China has proposed the regional synergy of scientific and technological innovation and industrial innovation across city clusters. Collaborative innovation emphasizes deep collaboration and resource integration between different innovation subjects, breaking the limitations of the traditional innovation model and creating more efficient open innovation. Moreover, collaborative innovation networks serve as broad platforms for fostering innovation collaboration. Through various exchanges and cooperation, they facilitate the flow of innovation resources and allocation across a wider scope, thereby promoting innovation upgrading and economic development throughout the region [8,9]. However, existing research has not sufficiently examined the impact of collaborative innovation or its networks on high-quality development.

Policymakers and researchers have been interested in collaborative innovation [7,10], but research on collaborative innovation is still lacking compared to its rapid development at the reality level and the vast attention it receives at the policy level. Most studies on collaborative innovation have focused on industry, academia, and research, i.e., limiting the main body of innovation to include only enterprises, universities, and research institutions [11], and some to individual industries, such as the nanoenergy and nanowire industries [12,13]. Collaborative innovation and development among cities should be a key focus in regional or urban economics because of their focus on cities, but few have focused on city clusters. The limited studies have only sampled one city cluster [14] and did not analyze each city cluster at the national level.

Research has confirmed that innovation can improve the efficiency of green development [15] and promote economic [9] and high-quality development [16]. However, this aspect has been understudied, while most studies on collaborative patenting have focused on its influencing factors [14,16], spatio-temporal evolution patterns [17,18], and its impact on innovation performance [4,19]. Few studies place collaborative innovation and economic growth or high-quality development in the same analytical framework. In their study on the Beijing–Tianjin–Hebei city cluster, Deng et al. [20] used the spatial Durbin model to show that collaborative innovation can promote high-quality development. Crawler methods and social network analysis should be used while exploring national collaborative innovation and networks to analyze a large amount of patent data, whereas econometric methods are used for studying the relationship between collaborative innovation and high-quality development. As such studies involve the use of multidisciplinary knowledge, there is a lack of clarity regarding the impact of collaborative innovation on large-scale high-quality development, the relationship between collaborative innovation networks and high-quality development, and collaborative innovation’s contribution to the high-quality development of the economy. In the context of globalization, countries and city clusters are trying to drive economic development through innovation. Studying the relationship between collaborative innovation and the high-quality development of cities within Chinese city clusters helps in constructing and sustaining collaborative innovation networks across various countries and city clusters.

In summary, what is the characteristic spatio-temporal distribution of collaborative innovation in China? Does collaborative innovation promote high-quality economic development? If so, how does it promote such development, and what is its underlying mechanism? These questions are crucial for understanding the context of innovation-driven development. These questions can identify China’s collaborative innovation network and evaluate the degree of the prefecture-level high-quality development of cities, which can provide insights for formulating and implementing strategies and theoretical and empirical references for further promoting high-quality development. Therefore, this study focuses on urban cooperative innovation networks, which refer to networks with cities as nodes and cross-city invention patent cooperation as connecting edges. Accordingly, as shown in Figure 1, this study uses crawler technology to identify collaborative innovations and their networks generated from more than 300,000 collaborative patent data from 2012 to 2020. The use of the social network analysis method also allows for analyzing the characteristics of a collaboration network and incorporating them into the econometric model. Moreover, a multi-indicator system was constructed to measure the degree of high-quality development of prefecture-level cities. This study found significant improvement in China’s level of collaborative innovation and stability among the core cities of collaborative innovation. City collaborative innovation helps promote high-quality economic development and is heterogeneous in many aspects. Collaborative innovation can reduce the degree of human resource mismatch, increase the intensive and expansive margins of innovation [21,22], and thus contribute to high-quality development. Collaboration at the national level can promote high-quality development, but the width and depth of such collaboration have not yet formed a complementary situation. This study further analyzes the collaborative innovation network of city clusters.

There are few studies in the existing literature on collaborative innovation and high-quality development, and even fewer studies that involve the integration of network characteristics into empirical analyses. Based on the existing literature, the contributions of this study are as follows. First, most existing studies have considered each city as a separate “black box” [19], ignoring the interactions between cities, and the few studies that consider the spatial impacts are based on the strong assumption that their impacts are only related to geographic or economic distance. Therefore, drawing from these studies, this study analyzes the relationships between cities through city collaborative networks and between collaborative innovation and high-quality development. Second, this study uses the crawler method and social network analysis to identify all effective collaborative invention patents in China. This is a more accurate measure of the current status of collaborative innovation than, for example, questionnaire data in related studies. Third, high-quality development is characterized by its multidimensionality and obvious epochal characteristics [23]. Some studies use total factor productivity [24,25] or GDP per capita [26,27] as indicators, although these are not fully consistent with the multidimensional character of high-quality development [23]. Therefore, this study measures the degree of high-quality development of Chinese prefecture-level cities across six dimensions. This measurement is an attempt to integrate information about the latest policies of prefecture-level cities. Fourth, resolving these issues will help developed countries and mature city clusters to leverage collaborative innovation to achieve synergistic development. It will also help late-developing countries and emerging city clusters to form effective collaborative networks, optimize innovation resource allocation and efficient usage, and achieve high-quality economic development.

The rest of the study is presented as follows. Section 2 provides a literature review. Section 3 outlines the theoretical framework and develops the research hypotheses. Section 4 constructs the quantitative economic model, elucidates the calculation methods of each index, and examines the present state of collaborative innovation in China. Section 5 conducts tests, analyses, and discussions on the hypotheses. Section 6 develops the heterogeneity analysis, and Section 7 further analyzes the city cluster network. Section 8 draws conclusions and indicates directions for future research.

2. Literature Review

In an open innovation environment, cities form a cooperative innovation network and depend on and influence each other through cooperative innovation [8]. Scholars have carried out a lot of research on collaborative innovation. A part of this study explores the current status of collaborative innovation in a particular industry and the factors influencing it. Lee et al. investigated the patent network characterization of information and communication technologies, by using data from the United States Patent and Trademark Office (USPTO) and the Lotka–Volterra equation method [6]. Liu et al. analyzed the collaborative innovation evolution network of Chinese wind energy by using complex network theory and social network analysis methods [17]. Using data from the Derwent Innovation Index, Guan et al. investigated the structural characteristics of collaborative networks in the field of nanoenergy. They also explored the impact of networks on innovation in terms of development and exploration [11]. Ozcan et al. use data on global collaboration in the nano industry to explore how patent collaboration occurs and how key players interact to support the process [14]. Yang et al. confirmed that the opening of high-speed rail would promote cross-regional collaborative innovation [16]. Another part of the research focuses on the relationship between collaborative innovation and innovation performance. Fan et al. used the spatial Durbin model to confirm that collaborative innovation can promote the improvement of innovation efficiency in local and other regions, but found that this effect has a lagging effect [4]. Gao et al. constructed a collaborative innovation index to measure the degree of collaborative innovation using Chinese provinces as their research object. They found that collaborative innovation can improve innovation performance through spatial econometric modeling [18]. In summary, the role of innovation in promoting economic development has been proven, and innovation can further promote high-quality development.

High-quality development is a development approach that balances the quality and quantity of economic development. Green development and sustainable development are important elements of high-quality development. Many studies have been conducted to measure the degree of high-quality development in different dimensions using different data and methods. Yang et al. measured the degree of high-quality development at the level of prefecture-level cities from six aspects and analyzed the temporal and spatial evolution patterns [16]. Mlachila et al. selected six indicators from growth fundamentals and social outcomes. They calculated the quality of development in more than 90 countries during the period 1990–2011 [24]. Jahanger directly measured high-quality development by TFP and found that foreign investment has no significant effect on China’s economic development, but can promote high-quality development in the eastern and central regions [25]. Chen et al. measured high-quality development by GDP per capita and verified that air pollution will inhibit high-quality development [26]. Deng et al. established a high-quality development evaluation system from five aspects and explored the relationship between collaborative innovation and high-quality development using the spatial Dubin model [20]. In general, in terms of measuring the degree of high-quality development, a single indicator was dominant in the early days, i.e., total factor productivity and GDP per capita as indicators. As the multidimensional character of high-quality development was recognized [23], it gradually developed into a composite indicator system.

Among the studies on collaborative innovation and high-quality development, only Deng et al. conducted a study with a sample of one city cluster [24]. Through spatial Durbin modeling, they confirmed that cooperative innovation can promote high-quality development. This leaves room for our research. Firstly, the results of the spatial Durbin model depend on the spatial weight matrix and cannot solve the endogeneity problem. For example, the use of a distance weight matrix assumes that the impact between two cities is inversely proportional to the distance between them. This strong assumption obviously ignores many influences. In addition, the spatial Durbin model cannot solve the endogeneity problem through the instrumental variables approach. Therefore, the spatial Durbin model is no longer used in this paper. Secondly, it is difficult to reveal universal phenomena by using only one city cluster as a sample. Therefore, this paper uses all city clusters in China. In general, the existing literature rarely puts collaborative innovation and high-quality development under the same research framework. Even fewer studies incorporate co-innovation network characteristics into econometric models. On the one hand, this study uses the crawler method to obtain cooperative innovation data and analyzes the current situation of cooperative innovation using social network analysis. On the other hand, this study assesses the degree of the high-quality development of prefecture-level cities using a multi-indicator evaluation system with 26 indicators selected from six aspects. Based on these, this study uses econometric models to explore the relationship between collaborative innovation and high-quality development. This study innovatively conducts interdisciplinary analysis, and the findings provide useful references for innovation development and high-quality development in countries around the world.

3. Theoretical Hypothesis

As shown in Figure 2, this study verifies the role of collaborative innovation in promoting high-quality development and its mechanism from two dimensions: the city itself and the national collaborative innovation network.

First, city-level competition can stimulate a city’s potential. However, it often worsens the divergence between stronger and weaker cities, thereby widening the regional development gap [28]. Conversely, collaborative innovation among cities can generate a synergistic effect of 1 + 1 > 2, which enhances the efficiency and overall competitiveness of regional innovation [4]. Therefore, Friedman opposes competition between cities [29] as it does not foster a win–win development model [28]. As innovation is increasingly characterized by nonlinearity and networking, the traditional model of independent, linear innovation is gradually being replaced by collaborative innovation approaches [2]. Collaborative innovation is based on close cooperation among various innovators to promote knowledge sharing and transfer [30]. This not only accelerates the horizontal diffusion of information, knowledge, and technology among industries and regions [31,32] but also enables regional talents to directly enhance the level of innovation and economic development through learning and applying new knowledge [33]. Accordingly, this study proposes Hypothesis 1 as follows:

H1. 

Urban collaborative innovation contributes to high-quality development.

Second, collaborative innovation helps reduce the barrier of poor information availability and promotes talent mobility [34] across different cities, fields, and sectors. During collaborative innovation, knowledge about experience, benefits, salaries, and so on is shared among different innovation subjects. This enables talents to find better positions and development opportunities [35] and reduces human resource mismatch arising from talent solidification or poor mobility. Human capital is a key player in innovation activities and economic development [36], and reductions in human capital mismatch boost productivity and promote high-quality development.

Collaborative innovation helps save on innovation costs by preventing innovation duplication, which often arises from information asymmetry [34]. Cities can build on existing foundations to innovate further and generate scale effects. By integrating different “knowledge pools” [8], collaborative innovation also facilitates knowledge collisions and industry exchanges between cities, thereby increasing the likelihood of cities entering new industries and technology fields [22]. Therefore, from the binary margin perspective, in technology fields, collaborative innovation not only enhances cities’ scale effects in existing technology fields (i.e., innovation-intensive margin), but it also opens up new growth avenues (i.e., innovation-expansive margin) by increasing the categories of innovations, thereby comprehensively promoting high-quality development. Hence, this study proposes Hypothesis 2:

H2. 

City collaborative innovation promotes high-quality development by reducing human resource mismatch and increasing the innovation-intensive and innovation-expansive margins.

Third, the theory of social network analysis posits that innovators, such as enterprises and individuals, do not exist in isolation but form networks through various relationships. Among them, collaborative innovation plays a key role in establishing connections in innovation networks. When two or more patent holders jointly research and develop the same patent, they form a collaborative relationship, forming a collaborative innovation network [17]. Asheim [37] found that collaborative innovation networks not only provide innovators with quick access to specific knowledge but also facilitate communication and interaction among various participants, thereby increasing the chances of knowledge spillovers. This network structure has a profound impact on improving the innovation capacity and economic development of the entire region. In the context of open innovation, building an efficient and collaborative regional innovation network has become essential for promoting high-quality economic development [38,39].

As key nodes in the national innovation network, the effective performance of cities in collaborative innovation is crucial, and it can be measured based on the width and depth of collaboration. Width refers to the number of different innovation participants with whom the city has established collaborative relationships, whereas depth reflects the closeness of these collaborative relationships. Specifically, collaborative width reflects the breadth and diversity of the city’s collaborative innovation with other cities across the country [40]. From the resource allocation perspective, if a city establishes collaborative relationships with several cities, it can integrate richer resources [41]. Optimal resource allocation further improves the level of innovation and development of the city. Enhanced depth of collaboration implies that cities have formed closer and more stable relationships in innovation collaboration. Cities occupying the core positions of the innovation network often have more voice and collaboration opportunities [42] and are more likely to benefit from collaborative innovation. Hence, this study proposes Hypothesis 3:

H3. 

Both the width and depth of collaborative innovation in cities can contribute to the degree of high-quality development.

Finally, according to the rules of urban development and the Matthew effect, resources, including talents, capital, and technology, are typically concentrated in large cities, leading to the development of core cities [43]. Through abundant resources, large market sizes, diverse suppliers, and a highly concentrated labor force, large cities provide favorable conditions for an accurate matching of technology and other aspects between partners, which effectively boosts efficient collaborative relationships [44]. Moreover, existing studies confirm that collaborations established in large cities lead to higher productivity [45,46]. Therefore, the more central a city’s position is in a national collaborative innovation network, the more likely it is to attract and have more partners [47]. This position not only brings the city more development opportunities but also strengthens its innovation competitiveness. Through risk sharing and resource integration in collaborative innovation [4], core cities achieve higher innovation efficiency and further economic development. Hence, this study proposes Hypothesis 4:

H4. 

The depth and width of collaboration are complementary, and both can jointly promote high-quality development.

4. Data and Methods

4.1. Data and Sample

This study is based on cities within Chinese city clusters, with 2012–2020 as the observation period. The data were obtained from the Zhihuiya database, China’s city and industry innovativeness report, and the statistical yearbooks of various provinces and cities. If a prefecture-level city had a few missing values during the statistical year, the data were supplemented using interpolation. If the data had many missing values (more than half), the sample was excluded. Continuous variables had no extreme values and did not need to be truncated. Data cleaning resulted in 1231 observations for 182 prefectural cities.

4.2. Model Construction

4.2.1. Benchmark Regression Model

To test H1, we develop the following panel regression model:

$${\mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h}\_\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y}}_{\mathrm{i},\mathrm{t}}={\mathsf{\beta }}_0+{\mathsf{\beta }}_1{\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}}_{\mathrm{i},\mathrm{t}}+{\mathsf{\beta }}_2{\mathrm{X}}_{\mathrm{i},\mathrm{t}}+{\mathrm{n}}_{\mathrm{i}}+{\mathsf{\lambda }}_{\mathrm{t}}+{\mathsf{\epsilon }}_{\mathrm{i},\mathrm{t}}$$

(1)

where ${\mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h}\_\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y}}_{\mathrm{i},\mathrm{t}}$ is the explanatory variable, indicating the level of high-quality development, excluding the innovation score. ${\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}}_{\mathrm{i},\mathrm{t}}$ is the core explanatory variable, indicating the number of patent collaborations (in thousands) between city i and other cities in year t. ${\mathrm{X}}_{\mathrm{i},\mathrm{t}}$ is a series of control variables. This study chose the degree of industrial development, GDP per capita, the level of regional synergistic development, the level of invention patent authorization, the proportion of science and technology expenditures of the financial sector, green development, and the level of actual foreign investment to control for the city characteristics. Furthermore, this study chose city-fixed effects ${\mathrm{n}}_{\mathrm{i}}$ to absorb other unobservables and control for year-fixed effects, ${\mathsf{\lambda }}_{\mathrm{t}}.$ ${\mathsf{\epsilon }}_{\mathrm{i},\mathrm{t}}$ denotes the error term.

4.2.2. Mechanism Analysis Model

To test H2, we develop the following econometric model:

$${\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}}_{\mathrm{i},\mathrm{t}}={\mathsf{\beta }}_0+{\mathsf{\beta }}_1{\mathrm{P}\mathrm{a}\mathrm{t}\mathrm{h}}_{\mathrm{i},\mathrm{t}}+{\mathsf{\beta }}_2{\mathrm{X}}_{\mathrm{i},\mathrm{t}}+{\mathrm{n}}_{\mathrm{i}}+{\mathsf{\lambda }}_{\mathrm{t}}+{\mathsf{\epsilon }}_{\mathrm{i},\mathrm{t}}$$

(2)

where ${\mathrm{P}\mathrm{a}\mathrm{t}\mathrm{h}}_{\mathrm{i},\mathrm{t}}$ is the mechanism variable of city i in year t.

4.2.3. Model of Collaborative Innovation Width, Depth, and High-Quality Development

To test H3, model (3) is established

$${\mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h}\_\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y}}_{\mathrm{i},\mathrm{t}}={\mathsf{\beta }}_0+{\mathsf{\beta }}_1{\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{W}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}}_{\mathrm{i},\mathrm{t}}{+\mathsf{\beta }}_2{\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{D}\mathrm{e}\mathrm{p}\mathrm{t}\mathrm{h}}_{\mathrm{i},\mathrm{t}}+{{\mathsf{\beta }}_3\mathrm{X}}_{\mathrm{i},\mathrm{t}}+{\mathrm{n}}_{\mathrm{i}}+{\mathsf{\lambda }}_{\mathrm{t}}+{\mathsf{\epsilon }}_{\mathrm{i},\mathrm{t}}$$

(3)

where, ${\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{W}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}}_{\mathrm{i},\mathrm{t}}$ denotes city i’s collaborative width in year t. It is expressed by the number of cooperative cities of city i in the national cooperative innovation network. ${\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{D}\mathrm{e}\mathrm{p}\mathrm{t}\mathrm{h}}_{\mathrm{i},\mathrm{t}}$ denotes the collaborative depth of city i in year t. It is denoted by the proximity centrality of city i in the national cooperative innovation network.

To test H4, model (4) was obtained by including the cross-multiplication terms of $\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{W}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}$ and $\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{D}\mathrm{e}\mathrm{p}\mathrm{t}\mathrm{h}$ in model (3):

$${\mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h}\_\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y}}_{\mathrm{i},\mathrm{t}}={\mathsf{\beta }}_0+{\mathsf{\beta }}_1{\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{W}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}}_{\mathrm{i},\mathrm{t}}{+\mathsf{\beta }}_2{\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{D}\mathrm{e}\mathrm{p}\mathrm{t}\mathrm{h}}_{\mathrm{i},\mathrm{t}}+{{\mathsf{\beta }}_3{\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{W}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}\mathrm{D}\mathrm{e}\mathrm{p}\mathrm{t}\mathrm{h}}_{\mathrm{i},\mathrm{t}}+{\mathsf{\beta }}_4\mathrm{X}}_{\mathrm{i},\mathrm{t}}+{\mathrm{n}}_{\mathrm{i}}+{\mathsf{\lambda }}_{\mathrm{t}}+{\mathsf{\epsilon }}_{\mathrm{i},\mathrm{t}}$$

(4)

where the positivity, negativity, and significance of ${\mathsf{\beta }}_3$ are used to determine whether the depth and width of collaboration represent a complementary mechanism.

4.3. Definitions of Key Variable

4.3.1. High-Quality Development

To obtain a precise measure of high-quality economic development, this study refers to existing studies [23,27] to establish the evaluation system (

Table 1. Evaluation system for high-quality development.

First-Level Indicator	Second-Level Indicator	Details
Marketization	Share of the market in allocating economic resources	Fiscal expenditure/GDP
	Size of government	Number of employees in public administration and social organizations/Resident population at the end of the year
	Degree of credit market activity	Total deposits and loans at the end of the year/GDP
	Supply of human resources	Resident population/Household population
	Intellectual property protection	Number of patents granted/GDP
Modernized industrial system	Degree of industrial structure advancement	Ratio of output value of secondary to tertiary industries
	Transportation convenience	Miles of highway
	Greening of industry	Comprehensive utilization rate of general industrial solid waste
Regional coordinated development	Regional development gap	Gini index of regional per capita GDP (income)
		Ratio of value added of industry to total employees of all enterprises in the city
	City livability	Road area per capita
		Hospital beds per capita
		Length of urban drainage pipes per capita
	Coordinated development of urban and rural areas	Urban per capita disposable income/Rural per capita disposable income
		Urban per capita consumption expenditure/Rural per capita consumption expenditure
	Urbanization rate	Urban household population/Total household population
Opening up	Foreign trade	Ratio of total imports and exports to GDP
	Utilization of foreign capital (capital dependence)	Ratio of total actual utilized foreign capital to GDP
	Number of foreign enterprises	Number of foreign-invested enterprises
Scientific and technological innovation	Science and technology input	Number of full-time teachers in general higher education institutions/Year-end resident population
		Percentage of employed persons in scientific research and technological services (%)
		Share of local financial expenditure on science and technology in local financial expenditure (%)
	Science and technology output	Number of invention patents owned by 10,000 people
Green development	Green space	Greening coverage rate of built-up areas, including park green space, protective green space, production green space, and so on
	Air quality	Number of days that air quality statistics meet the standard
	Water environment quality	Centralized treatment rate of sewage treatment plants
	Solid waste disposal	Harmless treatment rate of domestic garbage

Note: organized by the authors.

). Compared with the five development concepts, this study revises the evaluation system based on the report of the 20th Party Congress. The six first-level indicators are marketization, a modernized industrial system, regional coordinated development, opening up, scientific and technological innovation, and green development.

The high-quality development indicator was measured using principal component analysis and the equalization method [23]. The specific measurement process is shown in Appendix A.

4.3.2. Collaborative Innovation

Studies that have measured collaborative innovation have utilized multiple indicator evaluation systems [19], questionnaire data [48], collaborative papers [49,50], gravity models [21], or collaborative patents [51,52] for their analysis. Patent data are among the indicators that are open, relatively objective, and frequently used [53]. With the advancement in data analysis technology and the theory of “flow space”, scholars have considered cities as nodes in the network and applied social network analysis to identify collaborative networks [54]. This study is based on the Wisdom Sprout database that reviews valid Chinese invention patents with patent application dates from January 2012 to December 2020 that had two or more collaborators. This study finally obtained 318,577 sample data. Given that invention patent information only includes the geographic location information of the first inventor, it is difficult to determine the information of other individual applicants. Therefore, this study excludes all individual applicants and collaborative patents where only the first applicant is a company while the rest are individuals, ultimately yielding 244,012 collaborative patents. Taking patents α and β as examples (Figure 3), the crawler method is used to match the geographic location of each inventor and determine the inventor’s region. The tracking region of this study focuses on 337 prefecture-level units in China (including 4 municipalities directly under the central government and 333 prefecture-level cities, regions or autonomous states, leagues, and units under provincial jurisdiction). After matching, the data (network) of city-level collaborative innovation at the prefecture level could be obtained. Furthermore, using the social analysis method, the current status of collaborative innovation was analyzed, and the indicators needed for this study were calculated.

• Number of collaborative innovations

$${\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}}_{\mathrm{i}}={\sum }_{\mathrm{j}=1}^{337}{\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}}_{\mathrm{i}\mathrm{j}}$$

(5)

${\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}}_{\mathrm{i}}$ is the number of collaborative innovations of city i, derived by adding the number of collaborative innovations of city i and city j.

2.

Width and depth of collaboration

Centrality is an indicator in social network analysis that represents the importance of a node in the network. This study uses degree and betweenness centralities. Degree centrality is the most direct measure. The centrality degree of node i is the number of nodes to which it is connected. It is calculated as follows:

$${\mathrm{D}\mathrm{C}}_{\mathrm{i}}=\frac{{\mathrm{k}}_{\mathrm{i}}}{\mathrm{N}-1}$$

(6)

where ${\mathrm{k}}_{\mathrm{i}}$ is the number of connected edges of node i in network G. In this study, the degree of centrality of city i is the number of cities with which it cooperates. The collaborative width in the national network is represented by $\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{W}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}$.

Betweenness centrality is the number of shortest paths through node i in a network, which is calculated as follows:

$${\mathrm{B}\mathrm{C}}_{\mathrm{i}}={\sum }_{\mathrm{s}\ne \mathrm{i}\ne \mathrm{t}}\frac{{\mathrm{n}}_{\mathrm{s}\mathrm{t}}^{\mathrm{i}}}{{\mathrm{g}}_{\mathrm{s}\mathrm{t}}}$$

(7)

where ${\mathrm{n}}_{\mathrm{s}\mathrm{t}}^{\mathrm{i}}$ is the number of shortest paths through node i, and ${\mathrm{g}}_{\mathrm{s}\mathrm{t}}$ is the number of shortest paths connecting s and t. This study uses this indicator in the national network to represent the collaborative depth of city i in the national network, denoted as $\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{D}\mathrm{e}\mathrm{p}\mathrm{t}\mathrm{h}$.

4.3.3. Mechanistic Variables

According to H2, this study includes the following three mechanism variables:

$\mathrm{M}\mathrm{i}\mathrm{s}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{c}\mathrm{h}$ represents the degree of human resource mismatch, measured by micro-enterprise data. Specifically, this study refers to Chen [55] to measure the enterprise resource mismatch and takes the mean value of all enterprises to determine the human resource mismatch at the prefecture level. The indicators of human resource mismatch at the enterprise level are as follows:

$${\mathrm{m}\mathrm{i}\mathrm{s}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{c}\mathrm{h}}_{{\mathrm{L}}_{\mathrm{i}}}=\left(\frac{{\mathrm{L}}_{\mathrm{i}}}{\mathrm{L}}\right)/\left(\frac{{\mathrm{s}}_{\mathrm{i}}{\mathsf{\beta }}_{{\mathrm{L}}_{\mathrm{i}}}}{{\mathsf{\beta }}_{\mathrm{L}}}\right)$$

(8)

where ${\mathrm{L}}_{\mathrm{i}}/\mathrm{L}$ denotes the actual ratio of human capital used by firm i to the total amount of human capital in the city, and ${\mathrm{s}}_{\mathrm{i}}$ is the share of the total output value of firm i in the city’s GDP. To ensure that the data are comparable across years, GDP is deflator-adjusted. β is the labor output elasticity measured by the C-D production function. ${\mathrm{s}}_{\mathrm{i}}{\mathsf{\beta }}_{{\mathrm{L}}_{\mathrm{i}}}/{\mathsf{\beta }}_{\mathrm{L}}$ measures the theoretical proportion of human capital used by firm i when human capital is efficiently allocated. A $\mathrm{m}\mathrm{i}\mathrm{s}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{c}\mathrm{h}$ larger than 1 indicates that firm i overuses human capital; conversely, a $\mathrm{m}\mathrm{i}\mathrm{s}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{c}\mathrm{h}$ less than 1 indicates a lack of human capital.

To test the binary margin mechanism in technology fields, this study follows the study by Alberto and Denisse [56] to measure the current state of innovation in year n by taking the existing innovative industries in Chinese cities in year n − 1 as the base period. The specific measures are as follows: Based on China’s city and industry innovativeness report, we calculate the innovation level of the existing innovative industries. We take their sum as the innovation-intensive margin ($\mathrm{I}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{v}\mathrm{e}$). Similarly, we take the sum of the innovation levels of the new innovative industries as the extensive margin of innovation ($\mathrm{E}\mathrm{x}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{v}\mathrm{e}$).

4.3.4. Description of Variables

Table 2. Description of variables.

Variable Type	Variable Symbols	Variable Definition
Explained Variables	$\mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h}\_\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y}$	Degree of high-quality development of the city
Explanatory variables of H1	$\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}$	Collaborative innovation, number of patent collaborations with other prefecture-level cities in China
Mechanism variables of H2	$\mathrm{m}\mathrm{i}\mathrm{s}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{c}\mathrm{h}$	Degree of human resource mismatch
	$\mathrm{I}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{v}\mathrm{e}$	Innovation-intensive margin
	$\mathrm{E}\mathrm{x}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{v}\mathrm{e}$	Innovation-expansive margin
Explanatory variables of H3 and H4	$\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{W}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}$	Collaboration width, degree centrality of the city in the national collaborative innovation network
	$\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{D}\mathrm{e}\mathrm{p}\mathrm{t}\mathrm{h}$	Collaboration depth, betweenness centrality of cities in the national collaborative innovation network
	$\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{W}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}\mathrm{D}\mathrm{e}\mathrm{p}\mathrm{t}\mathrm{h}$	Interaction terms for depth and width
Control variables	$\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{y}\_\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}$	Tri-industry/secondary industry ratio
	$\mathrm{l}\mathrm{n}\mathrm{g}\mathrm{d}\mathrm{p}\mathrm{p}\mathrm{e}\mathrm{r}$	Logarithm of real GDP per capita
	$\mathrm{c}\mathrm{o}\mathrm{o}\_\mathrm{d}\mathrm{e}\mathrm{v}$	Degree of regional coordinated development
	$\mathrm{l}\mathrm{n}\mathrm{P}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{s}$	Logarithm of total invention patents
	$\mathrm{t}\mathrm{e}\mathrm{c}\mathrm{h}\_\mathrm{i}\mathrm{n}$	Share of fiscal expenditure on science and technology
	$\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{e}\mathrm{n}\_\mathrm{d}\mathrm{e}\mathrm{v}$	Degree of green development
	$\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{v}\_\mathrm{r}\mathrm{e}$	Amount of real foreign investment

Note: organized by the authors.

shows all variables used in this study to prove the four hypotheses.

4.4. State of Collaborative Innovation

4.4.1. Growth Characteristics

Figure 4 shows the growth characteristics of collaborative innovation in China. At the national level, both city clusters and prefecture-level cities show a rising trend in the degree of collaborative innovation. Despite a slight decrease in the share of city cluster collaborative innovation across the country, it always remains above 96%, affirming their dominance in collaborative innovation. This trend shows the increasing activity and importance of city clusters and prefecture-level cities in collaborative innovation, giving a strong impetus to the country’s high-quality development.

Figure 5 shows intra- and non-intra-city cluster collaboration. The number of intra-city cluster collaborations increased from 10,076 in 2012 to 30,096 in 2020, reflecting an increase of 198.7%; the number of non-internal collaborations increased from 29,898 in 2012 to 92,294 in 2020, marking an increase of 208.7%. The total number of patents of collaborative innovation between city clusters and external cities is about three times that of intra-city cluster collaboration. This relationship further emphasizes the key role of city clusters in promoting open innovation. Through extensive collaborative innovation with external cities, cities can overcome geographic limitations and accelerate innovation, thereby promoting their own innovative development and economic growth.

4.4.2. Growth Characteristics

From a national perspective, collaborative innovation network density shows a trend of continuous enhancement (

Table 3. Density of national collaborative innovation networks.

	2012	2016	2020
Network Density	0.0832	0.0908	0.1069

). Specifically, collaborative innovation network density grew from 0.0832 in 2012 to 0.1069 in 2020. This 28.5% increase indicates the strengthening of collaborative innovation links between Chinese cities, with consistent innovation resource sharing and flow. However, there is a higher network density at the city cluster level; for example, the network densities of the Beijing–Tianjin–Hebei and Yangtze River Delta city clusters in 2020 were 0.4286 and 0.3875, respectively, which is significantly larger than the national network. This indicates that small networks within city clusters show a higher degree of linkage closeness.

Figure 6, Figure 7 and Figure 8 show the results of visualizing the structure of the national collaborative innovation network in 2012, 2016, and 2020, respectively. On one hand, the degree of connectivity between cities shows a clear trend of strengthening, indicating China’s growing and strengthening collaborative innovation network. On the other hand, Beijing and Shanghai consistently maintain their status as the country’s key innovation cities. They are not only central nodes in the collaborative innovation network but also important drivers of national innovation development. Owing to space constraints, the results of the collaborative innovation network visualization at the city cluster level are presented in Appendix B.

4.4.3. Structural Characteristics

Core–edge analysis is a method for identifying network structure in social networks [54]. The core–edge network relationship describes the connections between nodes at the edge of the network, with lower centrality, and those at the core, with higher centrality. By fitting the data network to a continuous core–edge model, the core–edge method can determine the importance of each node, which is one of the methods for identifying core cities. The Chinese collaborative innovation network was analyzed in depth using this method.

Table 4. Results of the core–edge analysis of the national network.

Year	2012		2016		2020
Rank	City	Coreness	City	Coreness	City	Coreness
1	Zhuhai	0.70	Beijing	0.97	Beijing	0.98
2	Beijing	0.64	Zhuhai	0.12	Nanjing	0.10
3	Shanghai	0.20	Shanghai	0.10	Zhuhai	0.08
4	Fushun	0.15	Nanjing	0.09	Tianjin	0.06
5	Nanjing	0.11	Jinan	0.06	Chengdu	0.06
6	Tianjin	0.07	Xuchang	0.05	Jinan	0.06
7	Shenyang	0.04	Hangzhou	0.05	Hangzhou	0.05
8	Chengdu	0.04	Tianjin	0.04	Shanghai	0.04
9	Changzhou	0.04	Hefei	0.04	Xi’an	0.04
10	Shenzhen	0.03	Changsha	0.03	Shijiazhuang	0.04
11	Hefei	0.03	Fuzhou	0.03	Hefei	0.04
12	Hangzhou	0.03	Shijiazhuang	0.03	Changsha	0.03
13	Guangzhou	0.03	Wuhan	0.03	Wuhan	0.03
14	Dongying	0.03	Chengdu	0.03	Chongqing	0.02
15	Xi’an	0.03	Pingdingshan	0.02	Zhengzhou	0.02
16	Suzhou	0.03	Chongqing	0.02	Guangzhou	0.02
17	Qingdao	0.03	Shenzhen	0.02	Shenzhen	0.02
18	Ningbo	0.03	Xi’an	0.02	Pingdingshan	0.02
19	Fuzhou	0.02	Shenyang	0.02	Qingdao	0.02
20	Chongqing	0.02	Zhengzhou	0.02	Fuzhou	0.01

Note: organized by the authors.

shows the results of the core degree of the top 20 cities. Overall, the national collaborative innovation network is relatively stable, with Beijing, Zhuhai, Shanghai, Nanjing, Tianjin, Shenzhen, Hefei, Hangzhou, Guangzhou, and Chengdu as the core. With its extensive collaborative innovation network, Beijing has emerged as one with a leading core degree score in the national innovation collaborative network.

By analyzing the centrality of the collaborative innovation network of the city clusters (

Table 5. Core cities of the city cluster.

Rank	Core Cities List
First	Shanghai, Urumqi, Lanzhou, Beijing, Nanning, Hohhot, Harbin, Taiyuan, Guangzhou, Kunming, Wuhan, Shenyang, Jinan, Fuzhou, Xi’an, Guiyang, Zhengzhou, Chongqing, and Yinchuan
Second	Foshan, Baotou, Beihai, Nanjing, Xiamen, Daqing, Dalian, Tianjin, Baoji, Kaifeng, Chengdu, Changji Hui Autonomous Prefecture, Jinzhong, Qujing, Baiyin, Shizuishan, Zunyi, Qingdao, and Huangshi

Note: organized by the authors.

), the cities ranking first and second in the betweenness centrality of the city clusters remain unchanged. This finding reveals the solid position of core cities in collaborative innovation networks. However, this study finds significant differences in innovation capability among core cities in different city clusters, indicating an imbalance in innovation potential and development dynamics across city clusters.

5. Results and Discussions

5.1. Urban Collaborative Innovation Is Beneficial to High-Quality Economic Development

Table 6. Benchmark regression results.

Variables	(1)	(2)	(3)
	$$\mathbf{H}\mathbf{i}\mathbf{g}\mathbf{h}\_\mathbf{Q}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{i}\mathbf{t}\mathbf{y}$$	$$\mathbf{H}\mathbf{i}\mathbf{g}\mathbf{h}\_\mathbf{Q}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{i}\mathbf{t}\mathbf{y}$$	$$\mathbf{H}\mathbf{i}\mathbf{g}\mathbf{h}\_\mathbf{Q}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{i}\mathbf{t}\mathbf{y}$$
$\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}$	0.04 ***	0.04 ***	0.02 ***
	(0.009)	(0.010)	(0.004)
$\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{y}\_\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}$		0.26 ***	0.09 **
		(0.040)	(0.038)
$\mathrm{l}\mathrm{n}\mathrm{g}\mathrm{d}\mathrm{p}\mathrm{p}\mathrm{e}\mathrm{r}$		−0.05	−0.14 ***
		(0.036)	(0.020)
$\mathrm{c}\mathrm{o}\mathrm{o}\_\mathrm{d}\mathrm{e}\mathrm{v}$		0.26 ***	0.16 ***
		(0.030)	(0.047)
$\mathrm{l}\mathrm{n}\mathrm{P}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{s}$		0.06 *	0.00
		(0.033)	(0.025)
$\mathrm{t}\mathrm{e}\mathrm{c}\mathrm{h}\_\mathrm{i}\mathrm{n}$		0.98 **	1.26 ***
		(0.384)	(0.355)
$\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{e}\mathrm{n}\_\mathrm{d}\mathrm{e}\mathrm{v}$		0.15 ***	0.16 ***
		(0.020)	(0.018)
$\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{v}\_\mathrm{r}\mathrm{e}$		0.00 **	0.00 ***
		(0.000)	(0.000)
Constant	−0.07 ***	−0.02	1.28 ***
	(0.014)	(0.285)	(0.280)
Year-fixed effects	YES	YES	NO
Individual-fixed effects	YES	YES	YES
Observations	1231	1231	1231
Number of city_id	182	182	182
R-squared	0.212	0.371	0.426

Note: ***, **, and * are significant at the 1%, 5%, and 10% significance levels, respectively, and robust standard errors are shown in parentheses.

shows the results of the benchmark regressions. Column 1 shows the regression results without control variables. Columns 2 and 3 show the regression results for year- and city-fixed effects without and with control variables, respectively. The regression results show that the coefficient of $\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}$ is significantly positive, hence proving H1. Specifically, an increase of one unit in $\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}$ increases the $\mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h}\_\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y}$ degree by 0.04 points, indicating that for every 1000 increase in the number of domestic collaborations, the city’s high-quality development level increases by 0.07 standard deviations (the standard deviation of the explanatory variable is 0.5454; therefore, 0.04 is 0.04/0.5454 ≈ 0.07 standard deviations). From the theoretical perspective, the improvement in overall regional competitiveness and the level of economic development are highly correlated with high-quality development. Collaborative innovation can promote the improvement of overall regional competitiveness and the level of economic development [4,33], so collaborative innovation will also promote high-quality development. From the empirical results, this conclusion is consistent with the findings of Deng et al. [20].

5.2. Results of Mechanism Analysis

Table 7. Mechanism inspection results.

	(1)	(2)	(3)
Variables	$\mathbf{M}\mathbf{i}\mathbf{s}\mathbf{m}\mathbf{a}\mathbf{t}\mathbf{c}\mathbf{h}$	$\mathbf{I}\mathbf{n}\mathbf{t}\mathbf{e}\mathbf{n}\mathbf{s}\mathbf{i}\mathbf{v}\mathbf{e}$	$\mathbf{E}\mathbf{x}\mathbf{t}\mathbf{e}\mathbf{n}\mathbf{s}\mathbf{i}\mathbf{v}\mathbf{e}$
$\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}$	−0.2980 **	0.5791 ***	0.0037 ***
	(0.111)	(0.025)	(0.001)
Control variables	Yes	Yes	Yes
Year-fixed effects	Yes	Yes	Yes
Individual-fixed effects	Yes	Yes	Yes
Observations	1231	1231	1231
Number of city_id	182	182	182
R-squared	0.120	0.564	0.240

Note: ***, ** are significant at the 1%, 5% significance levels, respectively, and robust standard errors are shown in parentheses.

shows the regression results of the mechanism test. Column 1 shows that the coefficient of $\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}$ is −0.2980 at the 5% level of significance, implying that for every 1000 increase in the number of collaborative innovations, the degree of human resource mismatch decreases by 0.2980 points. This indicates that for every 1000 increase in the number of domestic collaborations, the degree of human resource mismatch decreases by 0.48 standard deviations (the standard deviation of the explanatory variable is 0.6268; therefore, 0.2980 is 0.2980/0.6268 ≈ 0.48 standard deviations). This conclusion is in agreement with the findings of the existing research. The existing research confirms that the innovation capacity of enterprises, universities, or institutions depends largely on the knowledge reserve and innovation capacity of the innovation subject [57]. Therefore, human capital mismatch inhibits innovation [58], while an insufficient level of innovation makes it difficult to promote high-quality development. Collaborative innovation can reduce information barriers and eliminate problems such as market failure, thus helping human resources better match market and high-quality development needs.

Columns 2 and 3 show the regression results for the intensive and expansive margins of innovation, respectively. Column 2 shows that the $\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}$ coefficient is 0.5791 at the 1% level of significance, indicating that for every 1000 increase in co-innovation, the intensive margin increases by 0.48 standard deviations (the standard deviation of the explanatory variable is 1.2092; therefore, 0.5791 is 0.5791/1.2092 ≈ 0.48 standard deviations). This implies that collaborative innovation creates significant scale effects within existing technology areas. Column 3 shows that the $\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}$ coefficient is 0.0037 at the 1% level of significance, indicating that for every 1000 increase in collaborative innovation, the extensive margin of innovation increases by 0.07 standard deviations (the standard deviation of the explanatory variable is 0.0496; therefore, 0.0037 is 0.0037/0.0496 ≈ 0.07 standard deviations). Thus, by collaborating, cities could jointly explore new technological paths and market opportunities. This extended approach to innovation helps in diversifying and differentiating innovation, thereby promoting high-quality development. Theoretically, this finding is consistent with the binary margin perspective in technology fields. Further, this is confirmed by Zhang et al.’s study on domestic and international collaborative innovation [22].

In summary, the mechanism test confirms H2, which states that collaborative innovation promotes high-quality development by reducing the degree of human resource mismatch and increasing the intensive and expansive margins of innovation.

5.3. Depth and Width of Collaborative Innovation in Cities Can Improve the Level of High-Quality Development

The regression results in Column 1 of

Table 8. Test results for H3 and H4.

	(1)	(2)
Variables	$\mathbf{H}\mathbf{i}\mathbf{g}\mathbf{h}\_\mathbf{Q}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{i}\mathbf{t}\mathbf{y}$	$\mathbf{H}\mathbf{i}\mathbf{g}\mathbf{h}\_\mathbf{Q}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{i}\mathbf{t}\mathbf{y}$
$\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{W}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}$	0.24 ***	0.23 ***
	(0.074)	(0.075)
$\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{D}\mathrm{e}\mathrm{p}\mathrm{t}\mathrm{h}$	0.13 **	0.13 **
	(0.062)	(0.061)
$\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{W}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}\mathrm{D}\mathrm{e}\mathrm{p}\mathrm{t}\mathrm{h}$		0.10
		(0.099)
Control variables	YES	YES
Year-fixed effects	YES	YES
Individual-fixed effects	YES	YES
Observations	1231	1231
Number of city_id	182	182
R-squared	0.424	0.424

Note: ***, ** are significant at the 1%, 5% significance levels, respectively, and robust standard errors are shown in parentheses.

show that at the national level, increases in both the width and depth of city cooperation positively contribute to high-quality development. Specifically, for every 1000 increase in the average number of a city’s collaborations in the country, the degree of high-quality development increases by 0.24 points, that is, 0.44 standard deviations (0.24/0.5454 ≈ 0.44); concurrently, for every one-degree increase in the depth of collaboration in the country, the degree of high-quality development also increases by 0.13 points, that is, 0.24 standard deviations (0.13/0.5454 ≈ 0.24), hence proving H3, which states that in the national collaborative innovation network, the width of collaboration promotes high-quality development more than the depth. Column 2 of Table 8 shows that the coefficient of the cross-multiplier term is positive but not significant, indicating that the depth and width of collaboration at the national level have not had a significant complementary effect. Therefore, H4 is invalid.

5.4. Endogenous Treatment and Robustness Test

This study constructed instrumental variables based on the shift-share method. As the base case, the ratio of the number of collaborative patents to all patents in city i in 2011 was used, and the growth rate of collaborative innovation in all prefecture-level cities in the country was used as the rate of potential growth for city i. The predicted value of the share of the number of collaborative patents in year t was calculated using an instrumental variable, which in turn was obtained by cross-multiplying the initial state and the exogenous national collaborative innovation growth rate. It was not correlated with the residual term and was correlated with the original core explanatory variables after controlling for fixed effects [59]. Column 1 of

Table 9. Endogenous treatment and robustness test.

	(1)	(2)		(3)	(4)
Variables	$$\mathbf{H}\mathbf{i}\mathbf{g}\mathbf{h}\_\mathbf{Q}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{i}\mathbf{t}\mathbf{y}$$	$$\mathbf{H}\mathbf{i}\mathbf{g}\mathbf{h}\_\mathbf{Q}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{i}\mathbf{t}\mathbf{y}$$		$$\mathbf{H}\mathbf{i}\mathbf{g}\mathbf{h}\_\mathbf{Q}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{i}\mathbf{t}\mathbf{y}$$	$$\mathbf{H}\mathbf{i}\mathbf{g}\mathbf{h}\_\mathbf{Q}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{i}\mathbf{t}\mathbf{y}$$
Panel A: first stage Y:$\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}$
IV	0.325 **
	0.030
Panel B: second stage
$\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}$	0.046 **	0.02 ***		0.03 ***	0.13 ***
	(0.021)	(0.007)		(0.010)	(0.045)
$\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{y}\_\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}$	−0.288	0.10 **		0.12 ***	0.25 ***
	(0.338)	(0.038)		(0.034)	(0.024)
$\mathrm{l}\mathrm{n}\mathrm{g}\mathrm{d}\mathrm{p}\mathrm{p}\mathrm{e}\mathrm{r}$	−0.141 **	−0.13 ***		−0.19 ***	−0.07 *
	(0.063)	(0.021)		(0.058)	(0.035)
$\mathrm{c}\mathrm{o}\mathrm{o}\_\mathrm{d}\mathrm{e}\mathrm{v}$	0.323 ***	0.15 ***		0.22 **	0.28 ***
	(0.025)	(0.048)		(0.096)	(0.021)
$\mathrm{l}\mathrm{n}\mathrm{P}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{s}$	0.027	0.00		−0.03	0.04
	(0.026)	(0.025)		(0.031)	(0.025)
$\mathrm{t}\mathrm{e}\mathrm{c}\mathrm{h}\_\mathrm{i}\mathrm{n}$	1.461 **	1.22 ***		1.04 **	0.72 *
	(0.548)	(0.347)		(0.423)	(0.369)
$\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{e}\mathrm{n}\_\mathrm{d}\mathrm{e}\mathrm{v}$	0.217 ***	0.16 ***		0.10 ***	0.15 ***
	(0.027)	(0.018)		(0.022)	(0.020)
$\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{v}\_\mathrm{r}\mathrm{e}$	0.000	0.00 ***		0.12 ***	0.00 **
	(0.000)	(0.000)		(0.034)	(0.000)
Year-fixed effects	YES	YES		YES	YES
Individual-fixed effects	YES	YES		YES	YES
Under-identification test: H0: under-identified
p-Value	0.0462
Weak identification test: H0: weakly identified
F-value			38.168
Observations	1184	1231		1231	1065
Number of city_id		182		182	158
R-squared		0.424		0.610	0.344

Note: ***, **, and * are significant at the 1%, 5%, and 10% significance levels, respectively, and robust standard errors are in parentheses.

shows the regression results of re-estimating model (1) using the 2SLS method. The results of the under-identification test show that the p-value is 0.0462 < 0.05, which rejects the original hypothesis of under-identification. The F-value of the weak identification test is 38.168, which far exceeds the 10% significance level (16.38) proposed by Stoch and Yogo. The $\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}$ coefficient is significant at the 95% confidence level at 0.046, indicating that for every 1000 increase in the number of domestic collaborations, there is a corresponding increase of 0.08 standard deviations (0.046/0.5454 ≈ 0.08) in the city’s degree of quality development. This result confirms the robustness of the benchmark regression findings.

To ensure the robustness of the estimation results, three additional treatments were applied in this study. First, we replaced the core explanatory variable with the number of cooperating cities as the new explanatory variable. Second, we replaced the explanatory variables with the results derived from the domain-wide principal component analysis. Third, we deleted the core city sample. The core cities identified using the core–edge method have a stronger innovation capacity, a comprehensive complete economic base, a more favorable business environment, and sufficient resource endowment, making it easier for these cities to attract more collaborative partners. To prevent collaborative innovation from only working in cities with a strong innovation capacity, this study excluded these cities. The results of the robustness regression tests after the above treatment are shown in Table 9. The results show that the coefficients of the core explanatory variables are always significantly positive in the three robustness tests. Regardless of whether explanatory or interpreted variables were replaced or samples were excluded, the results confirm that collaborative innovation contributes to high-quality development. The results also confirm that increases in the numbers of both participants in collaborative innovation and collaborative cities help in promoting high-quality development. This robustness test reconfirms H1, which states that collaborative innovation in cities contributes to high-quality economic development.

6. Heterogeneity Analysis

6.1. Whether Collaborative Innovation Leads to Cooperation within the City Cluster

Depending on the innovation subject, collaborative innovation can be divided into intra-city and non-intra-city cluster cooperation. To ensure comparability of both categories, they were normalized in this study. Column 1 of

Table 10. Heterogeneity: whether it is intra-city cluster cooperation.

Variables	(1)	(2)
$\mathrm{I}\mathrm{N}\_\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}$	0.11 **	0.14 ***
	(0.049)	(0.040)
$\mathrm{E}\mathrm{X}\_\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}$	0.68 **	0.50 **
	(0.248)	(0.213)
$\mathrm{I}\mathrm{N}\_\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{e}$		−0.25 ***
		(0.074)
$\mathrm{E}\mathrm{X}\_\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{e}$		1.18 ***
		(0.321)
Control variables	Yes	Yes
Year-fixed effects	Yes	Yes
Individual-fixed effects	Yes	Yes
Observations	1231	1231
Number of city_id	182	182
R-squared	0.426	0.435

Note: ***, ** are significant at the 1%, 5% significance levels, respectively, and robust standard errors are in parentheses.

shows that cities can effectively promote high-quality development regardless of whether they engage in collaborative innovation with cities within or outside city clusters. The p-value of the coefficient test is 0.0491, which passes the F-test. This means that cooperation with cities outside the city cluster can more significantly promote local development than that within the city cluster. This implies that collaborative innovation can overcome the limitation of geographical proximity and confirms the significance of open innovation for high-quality development. From the perspective of multidimensional proximity, geographical proximity is one of the important influencing factors [60]. However, in reality, entrepreneurs do not like to cooperate with neighboring firms [61]. It has been confirmed that geographic proximity reduces social proximity and, thus, hinders cooperation [62].

To further examine the underlying reasons for these findings, this study refers to Wei’s study and categorizes collaborative innovation into hierarchical and wide-ranging cooperation from the perspective of innovation diffusion [63]. The former refers to cooperation between cities of the same rank, for example, between large cities or between small cities. The latter refers to cooperation between different hierarchies, such as the cooperation between large cities and small cities. If there is a serious division within the city cluster, it cannot realize the hierarchical cooperation between megacities and large cities. In this case, these cities choose to cooperate across city clusters. Using the variance of high-quality development to represent the city cluster score index, the regression results in Column 2 of Table 10 show that the coefficient of $\mathrm{I}\mathrm{N}\_\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{e}$ is significant at −0.25 at the 99% confidence level, implying that the number of intra-city cluster cooperations decreases when the degree of city cluster differentiation increases. The coefficient of $\mathrm{E}\mathrm{X}\_\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{e}$ is significant at 1.18 at the 99% confidence level. This implies that the number of intra-city cluster cooperations decreases when the degree of city cluster differentiation increases. The number of collaborations outside city clusters increases as the degree of differentiation of city clusters increases. This explains the regression results in the first column, where the inability to achieve a high level of cooperation represents a limitation of the driving effect of cooperation within city clusters.

6.2. Heterogeneity of Urban Innovation Capabilities

Urban innovation capacity limits choice in terms of partners and affects the benefits that cities receive from cooperation. Cities with high urban innovation capacity tend to obtain higher benefits from their innovative elements. Therefore, the heterogeneity is divided based on the number of invention patents.

Table 11. Heterogeneity results.

Variables	Innovation Capacity		Degree of Development of City Cluster
	High	Low	High	Low
$\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}$	0.01 ***	0.09	0.05 **	0.02 ***
	(0.004)	(0.064)	(0.021)	(0.004)
Control variables	Yes	Yes	Yes	Yes
Year-fixed effects	Yes	Yes	Yes	Yes
Individual-fixed effects	Yes	Yes	Yes	Yes
Observations	266	965	861	370
Number of city_id	52	161	127	55
R-squared	0.578	0.366	0.439	0.439
p-Value of Fisher’s permutation test	0.013		0.001

Note: ***, ** are significant at the 1%, 5% significance levels, respectively, and robust standard errors are in parentheses.

shows that collaborative innovation cannot significantly drive high-quality development for those cities with weak innovation capacity (0.09). However, in cities with strong innovation capacity, collaborative innovation can effectively contribute to high-quality development (0.01 ***).

6.3. Heterogeneity of City Clusters

The top 10 city clusters are more mature, and the internal collaborative mechanisms of these city clusters are relatively more complete. Thus, does collaborative innovation have different impacts on high-quality development for city clusters with various degrees of development? Table 11 shows that although in highly developed city clusters, for every 1000 increase in collaborative innovation, the degree of high-quality development per city increases by 0.05 points, in the less developed city clusters, for every 1000 increase in collaborative innovation, the degree of high-quality development of each city increases by 0.02 points. This means that collaborative innovation promotes the high-quality development of city clusters regardless of their degree of development. However, the coefficient test between groups shows that city clusters with a high degree of development evidence a greater impact of collaborative innovation on high-quality development.

6.4. Regional Heterogeneity

China’s vast land area exhibits regional heterogeneity, and this study categorizes it into two or three major regions. The regression results of north–south heterogeneity in

Table 12. Regional heterogeneity results.

Variables	North–South Heterogeneity		Heterogeneity of the Three Regions
	South	North	East	Middle		West
$\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}$	0.01 ***	0.09	0.03 ***	0.04 **		0.19 *
	(0.004)	(0.064)	(0.006)	(0.016)		(0.095)
Control variables	Yes	Yes	Yes	Yes		Yes
Year-fixed effects	Yes	Yes	Yes	Yes		Yes
Individual-fixed effects	No	No	No	No		No
Observations	266	965	523	478		230
Number of city_id	52	161	75	69		38
R-squared	0.578	0.366	0.517	0.434		0.465
p-Value of Fisher’s permutation test			East vs. Others Middle vs. Other West vs. Other		0.448 0.079 0.483

Note: ***, **, and * are significant at the 1%, 5%, and 10% significance levels, respectively, and robust standard errors are in parentheses.

show that the coefficient of $\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}$ for southern cities is 0.09 at the 99% confidence level, whereas that for northern cities is not significant. This indicates that the southern region is more conducive to the role of collaborative innovation in high-quality development. From the regression results of the three regions, the $\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}$ coefficients of the east, center, and west are positive at the 99%, 95%, and 90% significance levels, respectively. This indicates that collaborative innovation enhances high-quality development in all these regions. Fisher’s permutation test shows that the p-value of the central region is 0.079, implying that it has a stronger ability to drive collaborative innovation.

7. Further Analysis

Co-innovation networks of city clusters are an important part of national co-innovation networks, and they have a greater network density than national networks. To test H3, which states that both the width and depth of collaborative innovation in cities can contribute to the degree of high-quality development, this study focuses on the city cluster level and constructs the following regression model:

$${\mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h}\_\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y}}_{\mathrm{i},\mathrm{t}}={\mathsf{\beta }}_0+{\mathsf{\beta }}_1{\mathrm{I}\mathrm{N}\_\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{W}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}}_{\mathrm{i},\mathrm{t}}{+\mathsf{\beta }}_2\mathrm{I}\mathrm{N}\_{\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{D}\mathrm{e}\mathrm{p}\mathrm{t}\mathrm{h}}_{\mathrm{i},\mathrm{t}}+{{\mathsf{\beta }}_3\mathrm{X}}_{\mathrm{i},\mathrm{t}}+{\mathrm{n}}_{\mathrm{i}}+{\mathsf{\lambda }}_{\mathrm{t}}+{\mathsf{\epsilon }}_{\mathrm{i},\mathrm{t}}$$

(9)

where $\mathrm{I}\mathrm{N}\_{\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{W}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}}_{\mathrm{i},\mathrm{t}}$ denotes the collaborative width of city i in the city cluster in year t, expressed by the average amount of cooperation between city i and each city in the city cluster. ${\mathrm{I}\mathrm{N}\_\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{D}\mathrm{e}\mathrm{p}\mathrm{t}\mathrm{h}}_{\mathrm{i},\mathrm{t}}$ denotes the depth of collaborative innovation of city i in city cluster in year t, expressed by the betweenness centrality of city i in the collaborative innovation network of this city cluster.

Meanwhile, earlier studies have also proposed H4, that is, there is complementarity in the collaboration depth and width, and both can jointly promote high-quality development. To test the validity of H4 at the city cluster level, this study includes the cross-multiplication term $\mathrm{I}\mathrm{N}\_\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{W}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}\mathrm{D}\mathrm{e}\mathrm{p}\mathrm{t}\mathrm{h}$ in model (9) and builds model (10):

$${\mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h}\_\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y}}_{\mathrm{i},\mathrm{t}}={\mathsf{\beta }}_0+{\mathsf{\beta }}_1{\mathrm{I}\mathrm{N}\_\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{W}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}}_{\mathrm{i},\mathrm{t}}{+\mathsf{\beta }}_2{\mathrm{I}\mathrm{N}\_\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{D}\mathrm{e}\mathrm{p}\mathrm{t}\mathrm{h}}_{\mathrm{i},\mathrm{t}}+{{\mathsf{\beta }}_3\mathrm{I}\mathrm{N}\_\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{W}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}\mathrm{D}\mathrm{e}\mathrm{p}\mathrm{t}\mathrm{h}+{\mathsf{\beta }}_4\mathrm{X}}_{\mathrm{i},\mathrm{t}}+{\mathrm{n}}_{\mathrm{i}}+{\mathsf{\lambda }}_{\mathrm{t}}+{\mathsf{\epsilon }}_{\mathrm{i},\mathrm{t}}$$

(10)

Column 1 of

Table 13. Results of city cluster network.

Variables	(1)	(2)
$\mathrm{I}\mathrm{N}\_\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{W}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}$	1.09 ***	1.49 ***
	(0.323)	(0.362)
$\mathrm{I}\mathrm{N}\_\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{D}\mathrm{e}\mathrm{p}\mathrm{t}\mathrm{h}$	0.09 **	0.09 **
	(0.041)	(0.041)
$\mathrm{I}\mathrm{N}\_\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{W}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}\mathrm{D}\mathrm{e}\mathrm{p}\mathrm{t}\mathrm{h}$		0.11 ***
		(0.036)
Control variables	Yes	Yes
Year-fixed effects	Yes	Yes
Individual-fixed effects	Yes	Yes
Observations	1231	1231
Number of city_id	182	182
R-squared	0.425	0.425

Note: ***, ** are significant at the 1%, 5% significance levels, respectively, and robust standard errors are in parentheses.

shows that an increase in the width and depth of collaboration boosts high-quality development. The coefficient of $\mathrm{I}\mathrm{N}\_\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{W}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}$ is significant at 1.09 at a 99% confidence level, indicating that for every 1000 increase in the width of collaboration within the urban agglomeration, the degree of a city’s high-quality development increases by 2 standard deviations (1.09/0.5454 ≈ 2). The coefficient of $\mathrm{I}\mathrm{N}\_\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{D}\mathrm{e}\mathrm{p}\mathrm{t}\mathrm{h}$ is significant at the 95% confidence level at 0.09, indicating that for every unit increase in the depth of collaboration within a city cluster, the degree of high-quality development of the city increases by 0.26 standard deviations (0.09/0.3462 ≈ 0.26). This shows that in the city cluster collaborative innovation network, the width of collaboration promotes high-quality development more than the depth of collaboration. This finding contradicts the finding at the national level. This shows that the driving role of node collaboration depth is more important in collaborative networks with fewer nodes and higher network density. Column 2 of Table 13 shows that the coefficient of the cross-multiplier term is significantly positive, implying that the depth and width of collaboration within city clusters are complementary and can synergize to promote high-quality development. This shows that low network density and poor node connectivity make it difficult for collaboration to play a complementary role in depth and width.

8. Conclusions and Limitations

From the theoretical perspective, the endogenous growth model confirms that technological improvement promotes economic development. From the perspective of cooperation and competition, cooperation promotes common development better than competition [4,28,29]. In the open innovation generation, the traditional model of independent, linear innovation is gradually being replaced by collaborative innovation approaches [2]. With all countries seeking sustainable development, it is of practical significance to explore the relationship between collaborative innovation and high-quality development. Based on the data of prefecture-level cities within 182 city clusters in China from 2012 to 2020, this study finds the following results.

First, collaborative innovation in China is characterized by growth, network, and structural stability. Specifically, collaborative innovation among Chinese cities is characterized by growth in terms of increasing numbers, an increase in the density of collaborative innovation networks, and the establishment of closer collaborative relationships among cities. Collaborative networks have the structural characteristic of having a relatively fixed core city.

Second, collaborative innovation among cities promotes high-quality development. An increase in the number of participants in collaborative innovation or collaborative cities positively contributes to high-quality development. This study also shows the robustness of the findings, including through shift-share instrumental variables. This result is also based on human capital allocation. The results of the mechanism test indicate that collaborative innovation drives high-quality development by reducing the degree of human resource mismatch and increasing the intensive and expansive margins of innovation.

Third, based on the binary margin theory of technology, this study proposes two mechanism variables, “intensive margin” and “expansion margin”. The “intensive margin” refers to strengthening the scale effect of existing technologies, while the “expansive margin” refers to opening up innovation avenues in new fields. The mechanism test proves that collaborative innovation plays a leading role in high-quality development by reducing the degree of human resource mismatch and increasing the “intensive margin” and the “expansive margin” of innovation.

Fourth, national-level and city cluster collaborative innovation networks differ in terms of the width and depth of collaboration driving high-quality development. In the national collaborative innovation network, an increase in the width and depth of city synergy contributes to the economy’s high-quality development. However, there is no obvious complementary effect from the depth and width of collaboration. Further analysis found that improving the width and depth of collaboration within city clusters promotes high-quality development, and the two are complementary. Collaboration width is more significant at the national level, while collaboration depth is more significant at the city cluster level.

Fifth, there is multifaceted heterogeneity in the impact of collaborative innovation on high-quality development. Cooperation with cities outside city clusters tends to contribute more significantly to local high-quality development than cooperation within city clusters. This is because city clusters have serious internal differentiation and cannot realize the “powerful combination”. For mature city clusters and cities with strong innovation capacity, collaborative innovation can better promote their high-quality development. The regional heterogeneity analysis shows that the driving effect of collaborative innovation is stronger in southern than in northern cities. At the level of the three regions, collaborative innovation has the greatest driving effect on high-quality development in the middle region.

The findings provide policy recommendations for the development of city clusters and latecomer cities. Emerging countries and city clusters can further optimize the structure of collaborative innovation networks, drive collaborative innovation, and promote high-quality development. Meanwhile, policymakers should create differentiated collaborative innovation strategies for various regions and networks.

First, in regions with low network density, the focus should be on improving the collaboration width and promoting the sharing and flow of innovation resources by expanding the scope of cooperation and increasing the number of partners to promote high-quality development. In regions with high network density, emphasis should be placed on deepening collaboration by enhancing the centrality of cities in the network and facilitating the efficient flow and sharing of innovative resources, such as information, technology, and talent, to promote the high-quality development of the entire region.

Second, the government should promote collaborative innovation between cities to optimize human resource allocation, strengthen the scale effect of technology, and develop innovation paths in new areas. This will promote high-quality development by reducing human capital mismatches and balancing the binary margins of technology.

Third, city clusters with mature development and cities with a strong innovation capacity should leverage their advantageous position to strengthen cooperation with other regions. By building collaborative platforms, promoting industrial docking, and sharing innovation resources and technologies, they can expand their market influence, increase their level of innovation, and realize mutual benefits and win–win situations.

Fourth, to address the problem of serious divisions within city clusters, which affect the role of collaborative innovation, policies should focus on promoting balanced development within city clusters. On the one hand, less developed regions must receive greater support to improve their innovation capacity and industrial level through fiscal, tax, financial, and other policy tools to narrow the gap with developed regions. On the other hand, policymakers should maintain an open and collaborative attitude, broaden cooperation channels, and establish collaborative innovation mechanisms with cities outside the city cluster and even with foreign cities. Overall, the role of collaborative innovation should be used as a driver of high-quality development.

A great deal of work has been done in this study, but there are some limitations. First, this study has not yet been analyzed at the firm level, which could be further analyzed in the future. Second, this study has not yet fully explored the synergistic relationship between the width and depth of cooperation at the city cluster and national level, as well as possible policy implications. In the future, policy implementation effects can be further explored.