Technology Spillovers, Collaborative Innovation and High-Quality Development—A Comparative Analysis Based on the Yangtze River Delta and Beijing-Tianjin-Hebei City Clusters

Abstract

Exploring the mechanism of science and technology innovation spillover effect and collaborative innovation on the high-quality development of urban agglomerations is of great practical significance for implementing the innovation-driven development strategy. Based on the panel data of prefecture-level cities from 2012 to 2020, this study uses web crawler technology to obtain cooperative invention patent data, combines the social network analysis method to construct collaborative innovation networks, constructs a high-quality development indicator system from six dimensions such as the degree of marketization and the industrial system, and adopts the spatial Durbin model to reveal the regional innovation spillover effect. The comparative study based on the Yangtze River Delta (YRD) and Beijing-Tianjin-Hebei (BTH) urban agglomerations found the following: (1) There is significant spatial heterogeneity in science and technology innovation, with the YRD showing a positive spillover trend and BTH showing a significant negative spillover trend; (2) The collaborative innovation network shows differentiated characteristics, with the YRD having a higher density of the network and forming a multi-centered structure, and BTH maintaining the pattern of single-core radiation; (3) There is a horse-tracing effect in high-quality development, with the average score of YRD The average score of YRD is significantly higher than that of Beijing-Tianjin-Hebei, and the indicators of several dimensions are better. Based on these conclusions, city clusters should further strengthen the construction of collaborative innovation networks among cities and enhance the capacity of neighboring cities to undertake innovation, to give full play to the spillover effect and driving effect of innovation on high-quality development.

1. Introduction

Science and technology innovation (S&T innovation), as the first driving force for the formation of new productive forces and the promotion of high-quality development, is related to the overall situation of the country’s modernization [1]. Jin systematically explained this concept in the Economic Research on “High-Quality Development”, pointing out that high-quality development is the organic unity of the quality of economic development, efficiency power, social benefits and ecological benefits, with multidimensional characteristics such as innovation, coordination, greenness, openness and sharing [2]. Chen et al. further emphasized that high-quality development needs to break through the traditional GDP orientation and build a comprehensive evaluation system that includes dimensions such as optimization of economic structure, innovation-driven development, and sustainability of resources and environment [3].

From the realistic dimension, high-quality development is reflected in the practical deepening of the five development concepts: at the economic level, it calls for the establishment of a modernized economic system [4], whereas at the innovation level, it emphasizes scientific and technological self-reliance and self-improvement [5], at the coordination level, it focuses on balanced regional development [6], at the green level, it highlights the goal of carbon peaking and carbon neutrality [7], and promotes a high level of institutionalized openness at the openness level [8]. This multidimensional character is further strengthened in the report of the 20th Party Congress, which calls for the construction of an economic system with “effective market mechanisms, dynamic micro-entrepreneurs, and moderate macro-control”. City clusters centered on large cities play a very important role as innovation growth poles due to their strong scientific and technological resource advantages. At the city cluster level, China implemented the Yangtze River Delta (YRD) Regional Integration Development Strategy and the Beijing-Tianjin-Hebei (BTH) Synergistic Development Strategy in 2012 and 2014, respectively. The policy emphasizes the need for the Yangtze River Delta region to strengthen cross-regional synergies in science and technology innovation and industrial innovation, linking the Yangtze River Economic Belt and radiating across the country. This reflects the strategic deployment of the city clusters to jointly promote high-quality development with science and technology innovation as the leader and collaborative innovation as the booster. Such a development model not only helps to realize the optimal allocation and efficient use of scientific and technological resources, but also accelerates the transformation and application of scientific and technological innovation achievements through the model of collaborative innovation, thus further enhancing the role of scientific and technological innovation in promoting high-quality development.

From a practical point of view, on the one hand, scientific and technological talents, equipment and other innovation factors are constantly gathering in large cities, forming a strong innovation capacity and power; with the depth of scientific and technological innovation activities, the innovative technology formed spills over to the surrounding cities through a variety of channels and mechanisms, improving the overall innovation capacity of the entire city cluster. On the other hand, the introduction of city cluster planning helps to improve inter-city collaboration and exchanges, and promotes collaborative innovation; through resource sharing and complementary advantages between cities, the formation of science and technology innovation networks further improves the efficiency of innovation [9]. Figure 1 shows that the average S&T innovation capacity, degree of collaborative innovation and high-quality development level of the Beijing-Tianjin-Hebei and Yangtze River Delta city clusters all show growth. However, what still needs to be further explored in depth behind this is what kind of correlation exists among the three. What is the impact of S&T innovation and technology spillover on Beijing-Tianjin-Hebei and the Yangtze River Delta as the two city clusters with the strongest S&T innovation strength? What is the role of collaborative innovation in technology spillover and high-quality development? The two most representative city clusters in China will be empirically and comparatively analyzed.

Existing studies have formed an important consensus on collaborative innovation and innovation performance, innovation and high-quality development: most scholars confirm that collaborative innovation can promote innovation performance [10], and at the same time, innovation also has a significant role in promoting high-quality development [11,12]. At the level of metrics, the existing literature mainly presents two paths: for the measurement of high-quality development, some scholars use a single indicator such as total factor productivity (TFP) or GDP per capita [3,13]; while for the assessment of collaborative innovation, it generally relies on a multi-indicator evaluation system or questionnaire data [10,14]. However, there are still significant shortcomings in existing studies: firstly, in terms of research perspectives, there is little literature on innovation, collaborative innovation and high-quality development into a unified analytical framework, and cities are generally regarded as independent “black box” [13], ignoring inter-city interactions, which is fundamentally conflicting with the first theorem of geography and the reality; secondly, in terms of high-quality development metrics, it is difficult to comprehensively reflect the multidimensional characteristics of high-quality development by relying on a single proxy; and finally, regarding the measurement of collaborative innovation, existing evaluation systems either lack theoretical support or have subjective bias, while questionnaire methods face problems of limited sample size and selection bias. Characteristics [2]; and finally, regarding collaborative innovation measurement, the established evaluation system either lacks theoretical support or has a subjective bias, while the questionnaire method faces the problems of limited sample size and selection bias.

The rest of this study is formed as follows. Section 2 provides a literature review. Section 3 develops a theoretical model. Section 4 establishes the econometric model and explains the calculation method of each indicator. Section 5 analyzes the current situation of high-quality development and collaborative innovation in the two city clusters and shows the regression results of the econometric model. Section 6 discusses the reasons for the different results for the two city clusters. Finally, Section 7 summarizes the research conclusions and provides policy recommendations.

2. Literature Review

S&T innovation is an effective way to address the negative externalities generated by vicious competition and crowding effects when industries are over-aggregated [15]. In regional economics, Marshall first proposed that industrial agglomeration externalities are important for economic development. Currently, research has concluded that S&T innovation has a “core-edge” distribution [16], and the spillover effect of innovation has been confirmed by scholars from many countries [17,18,19]. In addition, in terms of research methodology, the current research on S&T innovation is mainly divided into two main categories: one is research based on the gravity model and the breaking point formula [20], and the other one is studies using the panel model and spatial econometrics model [21,22]. Regarding the relationship between S&T innovation and high-quality development, Yang et al. [23] confirmed that S&T innovation factors are the main driving force for high-quality development. However, their study did not consider the role of cooperative innovation.

Many scholars have also carried out relevant studies on the measurement and role mechanism of collaborative innovation. In terms of measurement, existing studies, respectively, started from the multi-indicator evaluation system [10], questionnaire data [14], and network analysis of collaborative papers or collaborative patents [24]. Most studies on collaborative innovation have focused on its influencing factors [25,26], the trend of temporal and spatial evolution [27,28] and the impact of collaborative innovation on other things [10,29]. In terms of the effects of collaborative innovation on innovation, studies by Bai et al. and Fan et al. use spatial econometric modeling to confirm the facilitating effect of collaborative innovation on regional innovation performance [10,28]. Fan et al. also formalize that this facilitating effect has a lag [29]. In terms of the impact of collaborative innovation on high-quality development, Deng et al. used a spatial Durbin model to confirm the facilitating effect of collaborative innovation on high-quality development [21]. Dai et al.’s study uses the spatial panel model with Chinese city clusters as an example and confirms that both the depth and the width of collaborative innovation can promote high-quality development [30]. In summary, the contribution of innovation and collaborative innovation to high-quality development has been proved, but whether there is a complementary relationship between innovation and collaborative innovation has not yet been explored.

High-quality development is a development approach that balances the quality and quantity of economic development. Green and sustainable development are important elements of high-quality development. Many studies have used different data and methods to measure the degree of high-quality development from different dimensions. Some scholars directly use a single indicator to measure high-quality development, e.g., Jahanger directly uses total factor productivity to measure high-quality development [13], and Chen et al. use per capita GDP to measure high-quality development [3]. Other scholars use the evaluation system approach to measure. For example, Deng et al. established a high-quality development evaluation system from five aspects [31], and Dai et al. measured it from six aspects [30]. Li et al.’s study assessed the extent of high-quality development in Chinese prefecture-level cities from the perspective of five dimensions and 15 indicators [32]. Overall, as it is recognized that high-quality development is multidimensional [33], high-quality development has gradually developed into a comprehensive indicator system. In general, in studies on the national, city cluster, and province levels, the evaluation system usually contains at least five dimensions and 20 indicators; while in studies on the measurement of prefecture-level cities, the number of years, indicators, or cities in the relevant empirical research samples is relatively small due to the difficulty of data collection. Such limitations may affect the accuracy of regional comparative analysis.

In summary, a large number of studies have examined S&T innovation and its spillovers, collaborative innovation and high-quality development, but few studies have included all three in the same analytical framework. Yang et al.’s study confirms that the flow of innovation factors can lead to the improvement of the level of high-quality development of neighboring regions through the spatial spillover effect of high-quality development of the economy [25]. Deng et al.’s study confirms the role of collaborative innovation in high-quality development using a city cluster as an example [21]. Based on these, this study further deepens the understanding of the mechanism of how collaborative innovation in city clusters affects S&T innovation, and in turn, promotes high-quality development.

Based on existing studies, the marginal contribution of this study is mainly reflected in the following aspects: First, it innovatively constructs a three-dimensional linkage framework of “scientific and technological innovation-collaborative innovation-high-quality development” and uses spatial econometric models to capture the spillover phenomenon of scientific and technological innovation. Second, it improves the measurement system for high-quality development through six dimensions, breaking the one-dimensional limitation of TFP. Third, this study uses crawler technology to obtain all cooperative invention patents and combines social network analysis methods to more accurately quantify collaborative innovation. Empirical results show that scientific and technological innovation has a direct promotional and spatial spillover effect on high-quality development (positive in the Yangtze River Delta city cluster and negative in the Beijing-Tianjin-Hebei city cluster), and that collaborative innovation has a direct driving effect but does not produce significant spatial spillover.

3. Theoretical Model

From the perspective of new economic geography, the phenomenon of spatial overflow of technological level between regions is common in the process of S&T innovation and development of city clusters. Increasing research and development investment and encouraging city innovation can greatly enhance the spread of S&T innovation among neighboring cities. This will further promote rapid economic growth. This model builds upon the spatial economic framework proposed by Fujita and Thisse [34] and integrates Romer’s [35] knowledge-driven growth mechanism to explore the mechanism by which the technological progress growth rate of urban agglomerations influences economic growth through the spatial spillover effects of technological innovation.

The significance of this model lies in two aspects of expansion: (1) incorporating the intensity of technological spillovers into the growth rate of R&D, and (2) quantifying the marginal effect of innovation spillovers on total output ($\mathsf{\partial }E/\mathsf{\partial }g$), thereby addressing the shortcomings of the original model in analyzing the relationship between spillovers and economic performance. The specific analysis is as follows:

It is assumed that there are only two regions in the whole economy, A and B, with three types of production sectors: the traditional product sector (T), the modern product sector (M) and the research and development sector (R).

Both T and M sectors use unskilled personnel (L) and R&D sector (R) uses skilled personnel (H) for scientific and technological research, development and innovation. The T sector produces homogeneous products and the modern product sector (M) produces differentiated products using diversified R&D and innovations from the R&D sector (R). Here, the total number of technicians (H) is constant and normalized to 1, and they are free to move between A and B but with migration costs; non-technicians (L) are not mobile.

3.1. Household Department

Assume that any consumer $j$ in the economy as a whole makes the following behavioral decisions in time and space: for time $t\in [0,\infty ]$, $j$ will choose a consumption path ${\epsilon }_j\left(t\right)\ge 0$ and a location path $r_j\left(t\right)\in \left\{A,B\right\}$. Then, the indirect utility of $j$ at time $t$ is

$$v_j\left(t\right)={\epsilon }_j\left(t\right){\left[P_{r_j\left(t\right)}\left(t\right)\right]}^{-\mu }$$

(1)

where, $P_{r_j\left(t\right)}\left(t\right)$ is the price index of commodity $M$ in region $r_j\left(t\right)$ at time $t$, and then:

$$P={\left[{\displaystyle {\int }_0^{M}p{(i)}^{-(\sigma -1)}di}\right]}^{-1/(\sigma -1)}$$

(2)

$M$ is the total number of $M$ modern products available in the entire economy at time $t$, ${\epsilon }_j\left(t\right)$ is the expenditure of $j$ at a given moment $t$, $p\left(i\right)$ is the price of product $i$, $i\in \left[0,M\right]$. $\sigma$ is the constant elasticity of substitution between different types of final products. If $r_j\left(t\_\right)\ne r_j\left(t\right)$, then the product relocates its geographic position at time $t$. Denote the sequence of such movements by $t_h\left(h=1,2,3\cdots \right)$. Here, the price index for differentiated products is described using an integral form, following the Dixit-Stiglitz monopolistic competition framework [36]. When the number of product types M is large enough, the discrete sum can converge to a continuous integral and can more clearly characterize the elasticity of substitution between products. In order to focus on the role of innovation spillovers in economic growth, the model assumes that consumer utility comes only from differentiated modern products (M). Traditional products (T) are homogeneous commodities, and their consumption does not generate additional utility differences, so they are not included in the utility function.

Assuming that the migration cost of moving between regions A and B of type $H$ people at time $t$ is $C\left(t\right)$, the lifetime utility function of consumer $j$ at time 0 can be defined as

$$U_j\left(0\right)=V_j\left(0\right)-{\displaystyle \sum _h{e}^{-\gamma t_{h}C\left(t_h\right)}}$$

(3)

where $\gamma >0$ is the subjective discount rate common to all consumers, and:

$$V\left(0\right)={\displaystyle {\int }_0^{\infty }{e}^{-\gamma t}\ln \left[v(t)\right]}dt$$

(4)

Equation (4) represents the total lifetime utility of the migration cost. Where $v\left(t\right)$ is the interest rate on bonds in the aggregate economy at moment $t$, and the interest rates in regions A and B are equal. Let $w_{r_j\left(t\right)}\left(t\right)$ be the wage rate when the consumer lives in region $r_j\left(t\right)$ at moment $t$. Thus, the present value of wage income is

$$W_j\left(0\right)={\displaystyle {\int }_0^{\infty }{e}^{-\overline{v}\left(t\right)t}{w}_{r_j\left(t\right)}\left(t\right)}dt$$

(5)

where $\overline{v}\left(t\right)=\left(1/t\right){\displaystyle {\int }_0^{t}v\left(\tau \right)d\tau }$ is the average interest rate between 0~$t$. Then, according to the study of Barro and Sala-i-Martin [37], the intertemporal budget constraint for consumer $j$ can be written as the present value of expenditures being equal to the wealth owned:

$${\displaystyle {\int }_0^{\infty }{\epsilon }_j\left(t\right)e^{-\overline{v}\left(t\right)t}}dt=a_j+W_j\left(0\right)$$

(6)

where $a_j$ is the value of the consumer’s initial asset.

In summary, the first-order condition on the optimal expenditure path ${\epsilon }_j\left(·\right)$ after maximizing Equation (3) on any location path $r_j\left(·\right)$ from constraint Equation (6) is

$${\dot{\epsilon }}_j\left(t\right)/{\epsilon }_j\left(t\right)=v\left(t\right)-\gamma ,t\ge 0$$

(7)

where ${\dot{\epsilon }}_j\left(t\right)\equiv d{\epsilon }_j\left(t\right)/dt$. If the above equation holds for every consumer, and denote the total economic expenditure at the moment $t$ by $E\left(t\right)$, we have:

$$\dot{E}\left(t\right)/E\left(t\right)=v\left(t\right)-\gamma ,t\ge 0$$

(8)

3.2. Production Department

Suppose that sector T, which produces a traditional product, produces a homogeneous good at a fixed return. This product is produced in both regions A and B, and the wage rate of unskilled workers (L) is equal in both regions, being normalized to 1.

The modern product sector (M) produces differentiated modern products using proprietary technology specific to product $i$. Each unit of production of $i$ requires the investment of one unit of technicians (H). Each unit of product $i$ has no transportation costs within the same region but incurs trade friction costs of $\mathsf{\Upsilon }>1$ when it is moved from one region to another for sale. That is, only $1/\mathsf{\Upsilon }$ units of each unit of product $i$ can reach its destination when it is transferred for sale from region $r\in \left\{A,B\right\}$ to another region $s\in \left\{s\ne r|A,B\right\}$. This assumption follows the iceberg transportation cost theory [38], which states that a certain percentage of products are lost during transportation. Thus, product $i$ is produced in region $r=\left\{A,B\right\}$ and is sold at price $p_r\left(i\right)$. However, the price paid by the consumer changes when the product is transported to region $s\ne r$:

$$p_{rs}\left(i\right)=p_r\left(i\right)\mathsf{\Upsilon }$$

(9)

Assume that the consumer demand function for product $i$ is $q\left(i\right)=\mu \epsilon p{\left(i\right)}^{-\sigma } P^{\sigma -1},i\in \left[0,M\right]$. Where $\mu$ is the product share of the modern product sector (M) in consumer expenditure $\epsilon$. Then, set $E_r$ to be the total expenditure of region $r$ at a given moment and $P_r$ to be the price index of the products of the modern product sector (M) of the region. Combined with Equation (9), it can be seen that the total demand for the production of the product $i$ in the region $r$ is

$$q_r\left(i\right)=\mu E_r{p}_r{\left(i\right)}^{-\sigma }{P_r}^{\sigma -1}+\mu E_s{\left[p_r\left(i\right)\mathsf{\Upsilon }\right]}^{-\sigma }{P_s}^{\sigma -1}\mathsf{\Upsilon }$$

(10)

The corresponding profit is

$${\pi }_r\left(i\right)=\left[p_r\left(i\right)-1\right]q_r\left(i\right)$$

(11)

For simplicity, set $\varphi \equiv {\mathsf{\Upsilon }}^{-\left(\sigma -1\right)}$. Define $\rho$ as the subjective discount rate, which represents consumers’ time preference (i.e., the trade-off between current consumption and future consumption). This parameter is exogenous and its value is determined by social consumption habits [39]. Combining Equations (10) and (11) show that the common equilibrium price $p_r^{*}$ for all types of products, the equilibrium product $q_r^{*}$ for any type of product, and the equilibrium profit ${\pi }_r^{*}$ for the modern product sector (M) in region $r$ during the time window under study are, respectively:

$$p_r^{*}=1/\rho$$

(12)

$$q_r^{*}=\mu \rho \left({\displaystyle \frac{E_r}{M_r+\varphi M_s}}+{\displaystyle \frac{\varphi E_s}{\varphi M_r+M_s}}\right)$$

(13)

$${\pi }_r^{*}=q_r^{\ast }/\left(\sigma -1\right)$$

(14)

From Equation (13), $q_r^{*}$ in a region is directly proportional to total expenditures in each region and inversely proportional to the quantity of heterogeneous products in that individual region. The higher the equilibrium product output of the modern product sector (M) in a region, the higher the equilibrium profit, and the higher the constant elasticity of substitution among final products with heterogeneity, the lower the equilibrium profit.

3.3. R&D Department

Based on the R&D growth theory [35], the productivity of technicians (H) grows with the accumulation of their own intellectual capital (experience and work methods). The productivity of each technician (H) in the region is also given by $K_r$ if the intellectual capital of the region r is $K_r$. The total number of technicians (H) in the region is normalized to 1, and the total number of technicians (H) in the region r is normalized to 1. The total number of technicians (H) in region r is normalized to 1. Therefore, the number of patents developed per unit of time in region r when the share of technicians (H) in that region is ${\lambda }_r$ is

$$n_r=K_r{\lambda }_r$$

(15)

Let the amount of personal knowledge possessed by technician (H) $j$ be $h\left(j\right)$ and the total amount of intellectual capital available to region $r$ be

$$K_r={\left[{\displaystyle {\int }_0^{{\lambda }_r}h{\left(j\right)}^{\beta }dj+\eta {\displaystyle {\int }_0^{1-{\lambda }_r}h{\left(j\right)}^{\beta }dj}}\right]}^{1/\beta },0<\beta <1$$

(16)

where $\beta$ measures the degree of complementarity between technicians (H) in R&D and innovation, and $\eta \left(0\le \eta \le 1\right)$ denotes the intensity of technological spillovers between the two regions.

Finally, assuming that j’s personal knowledge $h\left(j\right)$ is proportional to the number of existing patents $M$ in the economy as a whole: $h\left(j\right)=\alpha M$, normalizing a to 1, and combining with Equation (16), we get

$$K_r=M{\left[{\lambda }_r+\eta \left(1-{\lambda }_r\right)\right]}^{1/\beta },0<\beta <1$$

(17)

Substituting (17) into (15), we get

$$n_r=M{\left[{\lambda }_r+\eta \left(1-{\lambda }_r\right)\right]}^{1/\beta }{\lambda }_r$$

(18)

It is assumed that patents have an infinite duration, so that the firm producing a particular product will always be a monopoly. In summary, the equation of motion for the number of categories (or number of patents) in the economy is obtained:

$$\begin{array}{l}\dot{M}=n_A+n_B\\ =M\left\{\lambda {\left[\lambda +\eta \left(1-\lambda \right)\right]}^{1/\beta }+\left(1-\lambda \right){\left(1-\lambda +\eta \lambda \right)}^{1/\beta }\right\}\end{array}$$

where $\lambda \equiv {\lambda }_A$ and $1-\lambda \equiv {\lambda }_B$. For simplicity, set

$$k_A\left(\lambda \right)\equiv {\left[\lambda +\eta \left(1-\lambda \right)\right]}^{1/\beta };k_B\left(\lambda \right)\equiv {\left(1-\lambda +\eta \lambda \right)}^{1/\beta }$$

(19)

and

$$g\left(\lambda \right)\equiv \lambda k_A\left(\lambda \right)+\left(1-\lambda \right)k_B\left(\lambda \right)$$

(20)

Thus, the above equation of motion becomes

$$\dot{M}=g\left(\lambda \right)M$$

(21)

where $g\left(\lambda \right)$ is the growth rate of the number of patents/categories in the economy as a whole when the distribution of technicians (H) is $\lambda$. It is easy to obtain that $g\left(\lambda \right)$ is symmetric about 1/2 such that $g\left(0\right)=g\left(1\right)=1$. The partial derivative of $g\left(\lambda \right)$ with respect to the intensity of technology spillovers $\eta$ between the two regions is obtained:

$${\displaystyle \frac{\mathsf{\partial }g\left(\lambda \right)}{\mathsf{\partial }\eta }}={\displaystyle \frac{\lambda \left(1-\lambda \right)}{\beta }}\left\{{\left[k_A\left(\lambda \right)\right]}^{1-{\beta }^{-1}}+{\left[k_B\left(\lambda \right)\right]}^{1-{\beta }^{-1}}\right\}>0$$

(22)

This implies spatial spillovers of technology between city clusters that can contribute to R&D growth rates.

To analyze the equilibrium wage $w_r$ of technicians (H) in this sector: combining Equation (18), the intellectual capital $K_r$ acquired by each research and development(R)-based firm in region $r$ can be taken as given, so that the marginal productivity of the labor of the technicians (H) is also $K_r$ and the unit cost of a new patent is $w_r/M{k}_r\left(\lambda \right)$. Firms are free to enter the research and development (R), and the zero-profit condition is ${\Pi }_r=w_r/M{k}_r\left(\lambda \right)$, where ${\Pi }_r$ denotes the market price of a particular patent in the market price of a patent developed in region $r$.

$$w_r^{\ast }={\Pi }_{r}M{k}_r\left(\lambda \right)$$

(23)

The profit for each type of personnel can be defined:

$$\begin{array}{l}{\epsilon }_j=\gamma \left[a_j+W_j\left(0\right)\right]\\ =\left\{\begin{array}{l}1,j\in L\\ \gamma \left[a_H+W_j\left(0\right)\right],j\in H\end{array}\right.\end{array}$$

(24)

The initial endowment of technicians is

$$a_H=M_A\left(0\right){\Pi }_A\left(0\right)+M_B\left(0\right){\Pi }_B\left(0\right)$$

(25)

3.4. Market Equilibrium

Since firms in each modern product sector (M) in the economy as a whole are free to choose locations in both regions to produce any new product. Therefore, given any moment, the profits of firms in each region must be the same when the market reaches equilibrium. Combining Equation (14), we have $q_A^{\ast }=q_B^{\ast }$. Again, from Equation (13) and $E_A+E_B=E^{\ast }$ and $M_A+M_B=M$, we have:

$$M_A={\displaystyle \frac{E_A-\varphi E_B}{\left(1-\varphi \right)E^{\ast }}}M,M_B={\displaystyle \frac{E_B-\varphi E_A}{\left(1-\varphi \right)E^{\ast }}}M$$

(26)

When $M_A>0, M_B>0$, there is $\varphi <E_A/E_B<1/\varphi$, from Equations (26) and (13), we have:

$$P_r=\left(1/\rho \right){\left[\left(1+\varphi \right)\left(E_r/E^{\ast }\right)M\right]}^{-1/\left(\sigma -1\right)}$$

(27)

$$q_A^{\ast }=q_B^{\ast }=\mu \rho E^{\ast }/M$$

(28)

Similarly, the equilibrium results can be obtained when $M_A=M, M_B=0$, $E_A/E_B\ge 1/\varphi$, $M_A=0, M_B=M$ and $E_A/E_B\le 1/\varphi$.

The equilibrium profits for all firms in the modern product sector (M) in all three of these cases are

$${\pi }^{\ast }\equiv \max \left\{{\pi }_A^{\ast },{\pi }_B^{\ast }\right\}={\displaystyle \frac{\mu E^{\ast }}{\sigma M}}$$

(29)

3.5. Spatial Innovation Spillovers from R&D Growth Rates on a Steady-State Path to Economic Growth

For any given case of $\lambda \in \left[0,1\right]$, the steady-state growth path of the regional economy is analyzed as follows. Based on Equation (21), the number of patents (the number of modern product sector-type enterprises) at moment $t$ is as follows:

$$M\left(t\right)=M_0{e}^{g\left(\lambda \right)t}$$

(30)

where $M_0$ is the number of initial product types. Combined with Equation (29), the value of the firm’s assets at moment $t$ is

$$\begin{array}{l}{\Pi }_t\equiv {\displaystyle {\int }_t^{\infty }{e}^{-\gamma \left(\tau -t\right)}{\pi }^{\ast }\left(\tau \right)d\tau }\\ ={\displaystyle {\int }_t^{\infty }{e}^{-\gamma \left(\tau -t\right)}\frac{\mu E}{\sigma M\left(\tau \right)}d\tau }\end{array}$$

(31)

In summary, the asset value of all firms in the modern product sector (M) sector at moment $t$ is

$$M\left(t\right)\Pi ={\displaystyle \frac{\mu E^{\ast }}{\sigma }}{\displaystyle {\int }_t^{\infty }{e}^{-\gamma \left(\tau -t\right)}\frac{M\left(t\right)}{M\left(\tau \right)}d\tau }$$

where $M\left(t\right)/M\left(\tau \right)=\exp \left[-g\left(\lambda \right)\left(\tau -t\right)\right]$, so the above equation can be written as

$$M\left(t\right)\Pi ={\displaystyle \frac{\mu E^{\ast }}{\sigma \left[\gamma +g\left(\lambda \right)\right]}}\equiv a^{\ast }\left(\lambda \right)$$

(32)

Obviously, since Equation (32) does not vary over time, substituting ${\Pi }_{r}M$ in Equation (23) into $a^{\ast }\left(\lambda \right)$ leads to the equilibrium wage rate for technicians (H) in each region as

$$w_A\left(\lambda \right)=a^{\ast }\left(\lambda \right)k_A\left(\lambda \right)$$

(33)

$$w_B\left(\lambda \right)=a^{\ast }\left(\lambda \right)k_B\left(\lambda \right)$$

(34)

For Equation (25), there are $a_H=a\ast \left(\lambda \right)$ and $W_j(0)=w_r\left(\lambda \right)/\gamma$ for each technician (H) living in region $r$. And Equation (24) implies that at any given time, the total expenditure for all personnel in region $r$ is

$$E_r\left(\lambda \right)={\displaystyle \frac{L}{2}}+{\lambda }_r{a}^{\ast }\left(\lambda \right)\left[\gamma +k_r\left(\lambda \right)\right]$$

(35)

Therefore, the total return to the economy as a whole on the equilibrium path is

$$\begin{array}{l}E=E_A\left(\lambda \right)+E_B\left(\lambda \right)\\ =L+\lambda a^{\ast }\left(\lambda \right)\left[\gamma +k_A\left(\lambda \right)\right]+\left(1-\lambda \right)a^{\ast }\left(\lambda \right)\left[\gamma +k_B\left(\lambda \right)\right]\end{array}$$

(36)

Moreover,

$${\displaystyle \frac{E_A\left(\lambda \right)}{E_B\left(\lambda \right)}}={\displaystyle \frac{L/2+\lambda a^{\ast }\left(\lambda \right)\left[\gamma +k_A\left(\lambda \right)\right]}{L/2+\left(1-\lambda \right)a^{\ast }\left(\lambda \right)\left[\gamma +k_B\left(\lambda \right)\right]}}$$

(37)

Substituting Equation (19) into Equation (36) leads to the effect of spatial S&T innovation spillovers on total returns is

$${\displaystyle \frac{\mathsf{\partial }E}{\mathsf{\partial }\eta }}=\lambda \left(1-\lambda \right)a^{\ast }\left(\lambda \right){\displaystyle \frac{1}{\beta }}\left[{\left(1-\lambda +\eta \lambda \right)}^{1-\beta /\beta }+{\left(\lambda +\eta -\eta \lambda \right)}^{1-\beta /\beta }\right]$$

(38)

${\displaystyle \frac{\mathsf{\partial }E}{\mathsf{\partial }\eta }}>0$, that is, space S&T innovation spillovers favor the growth of the economy.

From Equation (20), the R&D growth rate can be written as

$$\begin{array}{l}g\left(\lambda \right)\equiv \lambda k_A\left(\lambda \right)+\left(1-\lambda \right)k_B\left(\lambda \right)\\ =g_A\left(\lambda \right)+g_B\left(\lambda \right)\end{array}$$

(39)

Combining Equations (19) and (39), the effect of R&D growth rate on spatial S&T innovation spillovers can be obtained as

$${\displaystyle \frac{\mathsf{\partial }{\eta }_A}{\mathsf{\partial }{g}_A}}={\displaystyle \frac{\beta }{\lambda \left(1-\lambda \right)}}{g}_A^{\beta -1}> 0, {\displaystyle \frac{\mathsf{\partial }{\eta }_B}{\mathsf{\partial }{g}_B}}={\displaystyle \frac{\beta }{\lambda \left(1-\lambda \right)}}{g}_B^{\beta -1}>0$$

Which is

$${\displaystyle \frac{\mathsf{\partial }\eta }{\mathsf{\partial }g}}={\displaystyle \frac{\beta }{\lambda \left(1-\lambda \right)}}{g}^{\beta -1}>0$$

(40)

Based on Equations (38) and (40), and according to the chain rule, the marginal contribution of the growth rate of R&D innovation $g\left(\lambda \right)$, to the total return $E$ is found to be

$${\displaystyle \frac{\mathsf{\partial }E}{\mathsf{\partial }g}}={\displaystyle \frac{\mathsf{\partial }E}{\mathsf{\partial }\eta }}{\displaystyle \frac{\mathsf{\partial }\eta }{\mathsf{\partial }g}}=a^{\ast }\left(\lambda \right)\left[{\left(1-\lambda +\eta \lambda \right)}^{1-\beta /\beta }+{\left(\lambda +\eta -\eta \lambda \right)}^{1-\beta /\beta }\right]g^{\beta -1}>0$$

(41)

From the above theoretical model, it can be seen that an increase in the R&D growth rate of each region in the city cluster will accelerate the spatial spillover of S&T innovation among regions, which in turn will promote the economic growth of the city cluster.

4. Data and Methods

4.1. Data and Sample

This study focuses on cities in the BTH and YRD city clusters in China, with 2012–2020 as the observation period. The main data were obtained from the Zhihuiya database, China National Intellectual Property Administration (CNIPA), and the statistical yearbooks of the provinces and cities. If a city had several missing values for a statistical year, the data were supplemented using interpolation. Continuous variables have no extreme values and need not be truncated.

4.2. Model Construction

According to the first law of geography, cities do not exist isolated, but are interconnected. And neighboring cities are even more closely linked to each other. Based on this, the S&T innovation and high-quality development of a city is not only affected by local factors, but also by the influence of neighboring cities. Specifically, the S&T innovation of a central city within a cluster not only generates local impacts but also drives technology diffusion through spillover effects, thereby fostering industrial upgrading and regional economic growth in adjacent areas. Therefore, this study chooses the spatial econometric model that considers the spillover of S&T innovation. If $\lambda =0$, the model becomes the Spatial Durbin Model (SDM); if $\lambda =\delta =0$, the model becomes the Spatial Autoregressive Model (SAR); if $\rho =\delta =0$, the model becomes the Spatial Error Model (SEM).

$$Y_{it}=\rho {W_i}^{\prime }{Y}_t+\ln {X_{it}}^{\prime }\beta +{W_i}^{\prime }{x}_t\delta +\ln C{V_{it}}^{\prime }\gamma +{\epsilon }_{it}$$

$${\epsilon }_{it}=\lambda {W_i}^{\prime }{\epsilon }_t+v_{it}$$

where $W_i$ is the row $i$ of the spatial weight matrix, $W_{ij}$ is the spatial distance between two regions. $i$ and $j$ represent region $i$ and region $j$, respectively. If there are $n$ regions in total, $W$ is an $n\times n$ symmetric square matrix in which the elements on the main diagonal are 0. This study adopts the adjacency matrix in the baseline regression, i.e., if region $i$ is bordered by region $j$, then $W_{ij}=1\left(i\ne j\right)$; otherwise, $W_{ij}=0$. In the robustness test, the city cluster matrix is used, i.e., if region $i$ and region $j$ belong to the same city cluster, then $W_{ij}=1\left(i\ne j\right)$; otherwise, =0.

$Y_{it}$ is the explanatory variable, and this study uses the city’s high-quality development score excluding the innovation dimension. It is replaced with the score calculated by global principal component analysis in the robustness test. $X_{it}$ represents the core explanatory variable, i.e., the S&T innovation capacity of the region. In the benchmark regression, this study uses the number of invention patents authorized. Moreover, this study uses ${CV}_{it}$ as a series of control variables, respectively, and to avoid endogeneity problems caused by omitted variables, this study controls GDP per capita, degree of marketization, city development resilience, transportation convenience, regional development gap and foreign trade situation.

4.3. Definitions of High-Quality Development

To obtain a precise measure of high-quality economic development, this study refers to existing studies [18,40,41] to develop 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 advanced	Ratio of output value of secondary and tertiary industries
	Transportation convenience	Miles of highway
	Greening of industry	Comprehensive utilization rate of general industrial solid waste
Regional coordinated	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 author.

). 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, modernized industrial system, regional coordinated development, opening up, scientific and technological innovation, and green development. The development of this indicator is consistent with Dai et al.’s [30].

High-quality development indicator was measured using principal component analysis and equalization methods [32]. The specific measurement process is shown in Appendix A.

4.4. Definitions of Collaborative Innovation

To clarify whether collaborative innovation can enhance the spillover effect of S&T innovation on high-quality development, this study introduces collaborative innovation as a moderating variable in the model. The specific approach is to introduce collaborative innovation and its cross-multiplier term with S&T innovation capability into the benchmark regression model.

Specifically, Figure 2 shows the three steps for measuring collaborative innovation in this study: First, this study is based on the Zhihuiya database and China National Intellectual Property Administration (CNIPA) that reviews valid Chinese invention patents with patent application dates from January 2012 to December 2020 and having two or more collaborators. Second, after using the Crawler method to match firm locations with addresses from Gaode Map and Aiqicha’s enterprise data, this study finds that these collaborative patents involve a total of 46,912 innovation subjects and 337 prefectural-level municipalities (including 4 municipalities directly under the central government and 333 pre-feature-level cities, regions or autonomous states, leagues, and units under provincial jurisdiction). Finally, matching the cities according to the development plans of the YRD and the BTH city clusters, this study obtains the number of cooperative patents of the two city clusters.

4.5. Description of Variables

Table 2. Description of key variables.

Variable Type	Variable Symbols	Variable Definition
Explained Variable	$Y_{it}$	Degree of high-quality development of the city
Explanatory variable	$X_{it}$	S&T innovation capacity of the city, number of invention patents authorized.
Mechanism variable	$CooInn$	Collaborative innovation, number of patent collaborations with other prefecture-level cities

shows all key variables used in this study.

5. Conclusions

5.1. Results of High-Quality Development

Figure 3 shows the average development level of the two city clusters from 2012 to 2020. In terms of the average level of high-quality development, the YRD city cluster has been better than the BTH city cluster. Specifically, the high-quality development of the YRD is more stable, with only a 0.01-point difference between 2012 and 2020, while the BTH city cluster has a slight downward trend in fluctuation, with a 0.08-point decrease in 2020 compared to 2012.

Table 3. Dimension scores for high-quality development of the BTH city cluster.

	Marketization	Modernized Industrial System	Regional Coordinated	Opening Up	Scientific and Technological Innovation	Green Development
2012	4.03	3.15	1.98	0.19	0.98	6.50
2013	4.03	3.17	1.98	0.19	0.98	6.49
2014	4.00	3.18	1.96	0.18	0.95	6.48
2015	3.98	3.18	1.95	0.18	0.91	6.48
2016	4.02	3.19	1.98	0.19	0.97	6.51
2017	3.96	3.19	1.93	0.17	0.87	6.48
2018	3.93	3.19	1.92	0.17	0.81	6.48
2019	3.91	3.20	1.91	0.16	0.76	6.48
2020	3.88	3.22	1.89	0.15	0.70	6.49

and

Table 4. Dimension scores for high-quality development of the YRD city cluster.

	Marketization	Modernized Industrial System	Regional Coordinated	Opening Up	Scientific and Technological Innovation	Green Development
2012	4.24	3.74	2.22	0.43	0.88	6.04
2013	4.25	3.73	2.26	0.50	0.94	6.04
2014	4.25	3.73	2.25	0.49	0.93	6.04
2015	4.25	3.73	2.24	0.48	0.92	6.04
2016	4.21	3.68	2.22	0.31	0.91	6.12
2017	4.25	3.73	2.24	0.47	0.92	6.04
2018	4.24	3.74	2.23	0.46	0.91	6.04
2019	4.24	3.74	2.23	0.45	0.90	6.04
2020	4.24	3.74	2.22	0.44	0.89	6.04

show the dimension scores of the two city clusters. Among the many dimensions, the BTH city cluster performs less well than the YRD city cluster in terms of the degree of marketization, the construction of a modern industrial system, the coordinated development of the region, and opening up to the outside world, and only the green development is higher than that of the YRD on average. In terms of S&T innovation, the two are basically equal, with the YRD city cluster in general showing a steady upward trend and the BTH city cluster showing a slight downward trend.

Using the years 2012, 2016, and 2020 as examples,

Table 5. Top 10 cities for high-quality development.

Year 2012		Year 2016		Year 2020
City	Degree of High-Quality Development	City	Degree of High-Quality Development	City	Degree of High-Quality Development
Beijing	3.81	Beijing	4.27	Beijing	4.41
Shanghai	3.73	Shanghai	3.89	Shanghai	3.92
Suzhou	3.44	Suzhou	3.63	Suzhou	3.57
Tianjin	3.34	Tianjin	3.40	Hangzhou	3.57
Hangzhou	3.25	Nanjing	3.34	Nanjing	3.50
Nanjing	3.17	Hangzhou	3.29	Tianjin	3.43
Wuxi	3.04	Wuxi	3.20	Hefei	3.21
Shijiazhuang	2.97	Wuhu	3.16	Jiaxing	3.14
Changzhou	2.96	Changzhou	3.13	Shijiazhuang	3.14
Yangzhou	2.92	Zhenjiang	3.09	Wuhu	3.13

shows the top ten cities in terms of the degree of high-quality development in each year. Overall, the entry threshold of the top ten has increased from 2.92 in 2012 to 3.13 in 2020, an increase of 0.21 points, amounting to a 7.2% increase. Unlike the overall development trend, the average score of the top ten shows a continuous improvement, from 3.26 in 2012 to 3.50 in 2020. Among the top ten cities, those in the YRD city cluster occupy more seats. And the top three cities that remain stable, are Beijing, Shanghai and Suzhou.

Figure 4 shows the development of the top ten cities of the two city clusters in each dimension. The YRD cities are on the list significantly more often than the BTH city cluster. The drivers of high-quality development in cities are diversified and differentiated. S&T innovation and the degree of marketization in Beijing have remained at the top of the list. Additionally, S&T innovation has become an important driving force for high-quality development in Beijing. The regional coordinated development and opening up of Shanghai is ranked first, which is a strong boost to the high-quality development of Shanghai. Suzhou is often ranked first in terms of its opening up. The other cities have a relatively balanced development pattern with a high degree of green development.

According to the theoretical prediction in Section 2, an equilibrium spatial structure will appear when equilibrium is approached. To verify this prediction, this study evaluates the degree of proximity to equilibrium between the actual structures of the YRD and BTH city clusters through equilibrium deviation testing. Based on the equilibrium conditions required by the theoretical model (Equation (20)), the spatial distribution of technical personnel must satisfy the optimal configuration state (${\lambda }^{\ast }=0.5$). The relative deviation between the actual distribution of technical personnel and the theoretical optimal value is calculated as follows:

$$\mathrm{deviation}=\left|{\displaystyle \frac{{\lambda }_{\mathrm{actual}}-{\lambda }^{\ast }}{{\lambda }^{\ast }}}\right|$$

The test results show that there is a significant difference between the two city clusters. The Yangtze River Delta city cluster has a multi-center structure ($\lambda =0.52$), with a deviation of only 7.9% ($\delta =\mid 0.52-0.5\mid /0.5$) between the actual distribution and the theoretical optimal value, indicating that its technical personnel allocation is very close to equilibrium. The Beijing-Tianjin-Hebei city cluster maintains a single-core radiation model ($\lambda =0.87$), with a deviation of 134% ($\delta =\mid 0.87-0.5\mid /0.5$) between the actual distribution and the theoretical optimal value, indicating that its technical personnel allocation seriously deviates from the equilibrium. The test reveals the underlying mechanism of the differences in the collaborative innovation networks of the two major city clusters: the nearly balanced distribution of the Yangtze River Delta city cluster supports a multi-center network structure (The left figures of Figure 5, Figure 6 and Figure 7), promoting the efficient flow of innovation factors between node cities such as Shanghai, Nanjing, and Hangzhou; the serious deviation of the Beijing-Tianjin-Hebei city cluster reflects the characteristics of Beijing’s monopolar agglomeration (The right figures of Figure 5, Figure 6 and Figure 7), making it difficult to achieve the complementary effects $k_A(\lambda )+k_B(\lambda )$ in the theoretical model, which theoretically corroborates the empirical findings of negative spatial spillover in Section 5.4.

5.2. Results of Collaborative Innovation

Table 6. Network density.

	YRD City Cluster			BTH City Cluster
Year	2012	2016	2020	2012	2016	2020
Network density	0.1966	0.3105	0.3875	0.2967	0.3626	0.4286

shows the network density values of the two city clusters after binarization. It is found that the network density of both city clusters shows an increasing trend, which indicates that the node cities within the city clusters are more closely connected with each other and the degree of collaborative innovation is stronger. Comparing the two city clusters, the network density of the BTH city cluster is generally higher than that of the YRD city cluster during the observation period, which may be related to the number of cities within the city cluster. Moreover, the increase in density in the YRD city cluster is significantly higher than the increase in the BTH city cluster.

Figure 5, Figure 6 and Figure 7 show the network structure maps of the two city clusters in 2012, 2016 and 2020. The larger the city nodes are, the stronger their centrality is. Based on the analysis of point degree centrality, the S&T innovation network of the BTH city cluster presents a cooperative network with Beijing as the central position and Tianjin and Shijiazhuang as the secondary central positions. In 2012, there was a weakly connected city with only a single line of connectivity, which is Anyang.

There are more innovation centers in the YRD city cluster. Its S&T innovation network has gradually evolved from the initial pattern with Shanghai and Hangzhou as the core and Nanjing as the sub-core to a pattern with Shanghai, Nanjing and Hangzhou as the core and Suzhou, Wuxi and Hefei as the sub-core. In 2012, there were two isolated cities in the YRD city cluster, namely Wuhu and Zhoushan. Since then, there have been no more “isolated cities” in the YRD. Moreover, Tongling, Anqing, and Chuzhou in 2012, and Xuancheng and Tongling in 2016 are all cities with only a single line of connection to the city cluster. By 2020, however, all cities had established multiple links to the city cluster innovation network.

5.3. Regression Results of the Spatial Durbin Model

Figure 8 shows the results of the spatial correlation test using the spatial Moran’s I index for the explanatory variables between statistic years. The results of the analysis show that Moran’s index is significantly positive; that is, the degree of high-quality development has a significant spatial correlation. Therefore, the utilization of the OLS model cannot reflect the objective facts and a spatial econometric model should be selected. Further, according to the Hausmann test results and experience, the spatial panel econometric model is selected as fixed effects. According to the judgment rule proposed by Anselin et al. [42], the Wald test and LR test are chosen to test the fitting effect of the spatial econometric model. The calculation results show that the spatial Durbin model does not degenerate into the spatial lag model and the spatial error model. In other words, both spatial transmission mechanisms included in the SDM model can significantly affect the degree of high-quality development. Based on the above, to analyze the spatial spillover effect more accurately, this study chooses the SDM model.

Table 7. Decomposition of spatial effects.

	(1)	(2)	(3)	(4)	(5)
Direct effect	0.1559 ***	0.1593 ***	0.4126 ***	0.1527 *	0.1574 *
	(0.013)	(0.013)	(0.034)	(0.012)	(0.013)
Indirect effect	0.0479 ***	0.0687 ***	0.2541 ***	0.0583 *	0.0352 *
	(0.018)	(0.026)	(0.052)	(0.015)	(0.013)
Total effect	0.2038 ***	0.2279 ***	0.6666 ***	0.2110 *	0.1926 *
	(0.02)	(0.026)	(0.045)	(0.022)	(0.020)

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

presents the regression results. The first column shows the results of the baseline regression, the second column shows the results of the regression in which the spatial weight matrix is replaced by the city cluster matrix, and the third column shows the results of the regression in which high-quality development as well as the spatial weight matrix obtained by replacing high-quality development as the principal component analysis at the same time. The fourth and fifth columns show the regression results of replacing the spatial distance matrix with the economic distance matrix ($W_{ij}=1/\mid {\mathrm{GDP}}_i-{\mathrm{GDP}}_j\mid$) and the geographic distance matrix ($W_{ij}=1/d_{ij}$), respectively. From the regression results, it can be seen that the direct effect is significantly positive at the 1% level (0.1559 ***), indicating that city S&T innovation has a significant contribution to the high-quality development of the city. This is consistent with the findings of Huang et al. at the firm level, which confirms the facilitating effect of digital innovation on the high-quality development of firms [43]. This further confirms the generalization of innovation as a core driver of high-quality development from another perspective, and that innovation is a key factor in promoting high-quality development, both at the macro-level of cities and at the micro-level of enterprises.

The indirect effect is also positive at the 1% level of significance (0.0479 ***), and its degree of influence is about one-third of that of the direct effect. This indicates that the improvement of S&T innovation capacity in neighboring cities has a positive impact on high-quality development in this city, but this impact is smaller than the impact of the local effect. This is also consistent with the reality, as local S&T innovation has a more direct and significant impact on local economic development.

Overall, S&T innovation in all cities in the BTH and YRD city clusters has a certain positive promotion effect on local economic development. This promotion effect mainly comes from local S&T innovation, while S&T innovation in neighboring cities has relatively little impact on local economic development.

Table 8. The moderating role of collaborative innovation.

Variable	Adjacency Matrix			City Cluster Matrix
	Direct Effect	Indirect Effect	Total Effect	Direct Effect	Indirect Effect	Total Effect
X	0.1622 ***	0.0118	0.1740 ***	0.1605 ***	0.0193	0.1798 ***
	(0.010)	(0.013)	(0.013)	(0.010)	(0.016)	(0.014)
	0.0611 ***	−0.0097 **	0.0514 **	0.0719 ***	−0.0267 **	0.0452 **
	(0.023)	(0.005)	(0.023)	(0.023)	(0.011)	(0.018)
$CooInn$ × X	−0.0046 **	0.0001	−0.0044 **	−0.0054 **	0.0014	−0.0040 **
	(0.002)	(0.000)	(0.002)	(0.002)	(0.001)	(0.002)

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

shows the results of the decomposition of spatial effects after considering collaborative innovation. The results show that the direct effect of collaborative innovation is significantly positive at the 1% level (0.0611 ***), which means that local collaborative innovation has a significant positive driving effect on local high-quality development. The indirect effect is significantly negative at the 5% level (−0.0097 **), which means that local co-innovation does not drive high-quality development in neighboring cities. This indicates that the spillover effect of innovation is not yet sufficient for subjects not involved in collaborative innovation. This is also consistent with the conclusion that geographic distance does not have a significant effect on the patent output of industry-university-research cooperation in existing studies [44].

For the cross-multiplier term between co-innovation and S&T INNOVATION, the direct and total effects are significantly negative at the 5% level (−0.0046 **, −0.0044 **). This means that collaborative innovation does not strengthen the driving effect of S&T innovation on high-quality development as expected, but instead shows a certain inhibitory effect. This may result from two types of mechanisms. The first is that excessive cooperation leads to the dispersion of R&D resources [6], weakening local core innovation capabilities and producing a resource crowding-out effect. The second is that peripheral cities rely on the innovation of central cities, thereby inhibiting local independent innovation [45], which is consistent with the situation of the single-core network structure in the Beijing-Tianjin-Hebei region. In this case, local S&T innovation may become relatively closed and lack diversity and autonomy, thus weakening the driving effect on high-quality development. The indirect effect is positive, but statistically insignificant, indicating that there is a small positive effect of collaborative innovation on promoting local S&T innovation impacting peripheral high-quality development. This may be due to the fact that although collaborative innovation can promote local S&T innovation, it is unable to have a significant impact on high-quality development in the neighborhood due to the territoriality of the innovation. This is consistent with the findings of Wei and Chen [6,44].

5.4. Heterogeneity Analysis

Table 9. Heterogeneity of BTH and YRD city clusters.

	BTH City Cluster	YRD City Cluster
Direct effect	0.2318 ***	0.1588 ***
	(0.008)	(0.012)
Indirect effect	−0.0499 ***	0.0085
	(0.006)	(0.020)
Total effect	0.1819 ***	0.1673 ***
	(0.010)	(0.020)

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

shows the comparison between the BTH city cluster and the YRD city cluster. The first column shows the regression results for the BTH city cluster and the second column shows the regression results for the YRD city cluster.

For both direct and total effects, both city clusters are significantly positive (0.2318 ***; 0.1588 ***), which indicates that in both city clusters S&T innovation has a significant contribution to high-quality development both locally and in the city cluster. It is noteworthy that for the indirect effect, the BTH city cluster is significantly negative (−0.0499 ***), while the YRD city cluster is positive (0.0085). This indicates that within the BTH City Cluster, the impact of the improvement of the S&T innovation capacity of the neighboring cities on the high-quality development of this city is negative and has not yet produced a positive spillover effect. This finding is consistent with the viewpoint of An et al. that Beijing’s core radiation-driven capacity needs to be further improved [46]. In the YRD city cluster, on the other hand, S&T innovation shows a positive spillover effect on high-quality development. This finding has similarities with the findings on the impact of central cities on the development of city clusters. The heterogeneity arises because of the differences in the spillover paths of S&T innovation in cities and city clusters of different sizes [47].

There are three limitations to the data and methodology used in this study. In terms of data, cooperative patents do not cover non-patent collaboration such as technology licensing. In the future, technology contract registration data could be integrated. In terms of methodology, the spatial Durbin model fails to capture dynamic cumulative effects. It is recommended that the PVAR model be used in future studies. In terms of sampling, emerging clusters such as the Guangdong-Hong Kong-Macao Greater Bay Area are not included, and the universality of the findings needs to be further verified.

6. Discussion

Knowledge diffusion generates spillover effects between cities. S&T innovation mainly relies on the diffusion of explicit knowledge and tacit knowledge, the former can be learned and reapplied by research subjects through record carriers, while the latter needs to be realized through human capital flows. According to the theoretical model (Equation (38)) and the push-pull theory, the innovation spillover effect is jointly determined by push $\left(PUSH\right)$, pull $\left(PULL\right)$, and resistance $\left(F\right)$: $\mathrm{Externality}={PUSH}_c+{PULL}_{-c}-F_{c_r-c}$. According to the theoretical model (Equation (38)) and the push-pull theory, the innovation spillover effect is jointly determined by push $\left(PUSH\right)$, pull $\left(PULL\right)$, and resistance $\left(F\right)$: where push refers to the level of investment and output in scientific and technological innovation in a city, pull refers to the capacity of other cities to absorb scientific and technological innovation, and resistance $\left(F\right)$ refers to the smoothness of elements that hinder the flow of knowledge and its reapplication. Only when the innovation externality is greater than 0 can a city’s scientific and technological innovation have a positive spillover effect [45]. Focusing on the Yangtze River Delta and Beijing-Tianjin-Hebei city clusters, push, pull, and resistance are measured based on human capital and other innovation inputs, scientific and technological innovation outputs, innovation gaps, and the smooth flow of factors in the indicator system.

Investment in S&T innovation in this study is measured by the ratio of full-time teachers in general higher education institutions, the ratio of people employed in scientific research and technical services, and the share of local financial expenditure on S&T in local financial expenditure. Beijing ranks first with a score of 3.83, which is 4.7 times higher than the lowest score. Although the difference in the ratio score is not large, the difference in the specific amount is huge. Taking the number of full-time teachers in the city’s higher education institutions as an example, within the BTH city cluster, Beijing has 70,645, while Handan has only 4471; within the YRD city cluster, Nanjing has 55,134, followed by Shanghai with 47,668, while Xuancheng, the city with the least, has only 342.

From the number of invention patents authorized and the city innovation index published by Kou et al. [48], S&T innovation shows a huge gap, and the degree of innovation output gap within BTH is significantly larger than the degree of gap within the YRD. Within the BTH city cluster, S&T innovation shows a precipitous fall. Beijing is far ahead, with the number of invention patents authorized and its innovation index in 2020, for example, more than 10 times that of second-place Tianjin and nearly 200 times that of last-place Anyang. The wide gap in S&T innovation is one of the key reasons why the surrounding areas are unable to take up Beijing’s S&T innovation overflow. Within the YRD city cluster, Shanghai is at the top of the list in terms of the number of invention patents authorized, which is 1.4 times that of Hangzhou in the second place, although there is a certain gap, the magnitude is not large compared with Beijing, Tianjin and Hebei. In terms of the innovation index, the gap between Shanghai and the top few cities in the cluster is also significantly smaller than that in the BTH city cluster.

In terms of transportation, the average road mileage of the BTH city cluster is 1.47 times that of the YRD city cluster, while the YRD has an even better shipping network, and the two form both good transportation channels. However, the degree of marketization of the two city clusters shows a clear gap, with the average marketization of the YRD city cluster nearly four times that of the BTH city cluster. Some cities within the YRD city cluster have formed an open market-oriented exchange environment, which has 8 cities with high scores. On the other hand, there are only 2 cities with high scores in the BTH city cluster, indicating that there is still a large gap between the degree of marketization of the neighboring cities and that of Beijing, which to a certain extent hinders the collaboration innovation and development of BTH.

Compared with international cases, the multi-center structure of the Yangtze River Delta city cluster is similar to that of the Rhine-Ruhr city cluster [19], while the single-core model of the Beijing-Tianjin-Hebei city cluster is similar to that of the Seoul metropolitan area in its early stages. After Seoul adopted the “Innovation Diffusion Corridor” policy in 2010, it increased its innovation spillover effect by 37%, which provides a reference for the development of the Beijing-Tianjin-Hebei city cluster.

7. Conclusions and Further Research

This study mainly obtains the following conclusions:

First, from the perspective of the degree of high-quality development, the performance of high-quality development in the YRD city cluster is significantly better than that of the BTH city cluster. This is reflected in the following three aspects: (1) The average score of high-quality development and the average scores of most dimensions in the YRD city cluster are significantly higher than those in the BTH city cluster. (2) More cities within the YRD city cluster have top quality development scores. (3) The degree of high-quality development in the BTH city cluster decreased rather than increased over the study period, while the degree of high-quality development in the YRD city cluster was more stable.

Second, from the perspective of the network structure of collaborative innovation, the node cities within the two city clusters are increasingly connected and the degree of collaborative innovation is gradually increasing, but there is some heterogeneity: (1) The network density of the BTH city cluster is higher than that of the YRD city cluster during the observation period. And the density increase in the YRD city cluster is significantly higher than that of the BTH city cluster. (2) The S&T innovation network of the BTH city cluster always shows a cooperative network with Beijing as the core and Tianjin and Shijiazhuang as the sub-core. On the other hand, the S&T innovation network of the YRD city cluster has gradually evolved from the perspective of Shanghai and Hangzhou as the core and Nanjing as the sub-core to a pattern with Shanghai, Nanjing and Hangzhou as the core and Suzhou, Wuxi and Hefei as the sub-core. (3) The network structure of the YRD city cluster is relatively more stable. There are no more isolated cities in the YRD city cluster after 2012. And in 2020, all cities have established multi-line connections with the city cluster innovation network.

Thirdly, from the perspective of spatial Durbin analysis: (1) the S&T innovation of all cities in the BTH and YRD city cluster has a certain positive contribution to high-quality development, but it mainly comes from the local S&T innovation; the S&T innovation of the neighboring cities also has a certain positive impact on the high-quality development of the city, but this indirect effect is far less than the direct effect. (2) From the perspective of the spillover effect of collaborative innovation, collaborative innovation has a significant driving effect on local high-quality development, but its spillover effect is not yet obvious; and collaborative innovation has not yet strengthened the spillover effect of S&T innovation on high-quality development. (3) Comparing the BTH city cluster and the YRD city cluster, S&T innovation in the two city clusters has a significant role in promoting the high-quality development of both the local area and the city cluster. However, the BTH city cluster shows a significant negative indirect effect, while the YRD city cluster shows a positive indirect effect.

Fourth, from the perspective of the conduction path of S&T innovation, the spillover effect is influenced by three factors: push, pull and resistance. The study finds that the BTH and YRD city clusters are clearly differentiated internally, and the degree of marketization shows obvious differences. In the BTH city cluster, Beijing is far ahead in the level of input and output of S&T innovation, but the degree of marketization and S&T innovation receiving capacity of neighboring cities have not yet been able to match, resulting in a low degree of factor fluency in the circulation and reapplication of knowledge, and the spillover effect of innovation has not been brought into full play. Within the YRD city cluster, Shanghai is also at the forefront of S&T innovation, but it has formed a close cooperation network with other cities and has a relatively high degree of marketization, which is conducive to the dissemination and undertaking of S&T innovation.

Based on the empirical analysis conclusions of this study on the relationship between technological innovation spillovers, collaborative innovation networks, and high-quality development in the Yangtze River Delta and Beijing-Tianjin-Hebei metropolitan areas, especially the findings of significant regional heterogeneity, this study proposes the following policy recommendations, ranked by urgency:

The primary task is to address the negative spillover challenges faced by the Beijing-Tianjin-Hebei urban agglomeration, with the core focus on removing administrative barriers that hinder the flow of innovative elements. Empirical results clearly indicate that the Beijing-Tianjin-Hebei region exhibits significant negative spatial spillover effects, which are closely linked to its single-core radiation model, the weak innovation absorption capacity of peripheral cities, and low institutional coordination across regions. Therefore, the urgent priority for the coordinated development of the Beijing-Tianjin-Hebei region is to establish a robust cross-regional coordination mechanism. Specifically, it is necessary to mandate the establishment of a unified science and technology resource-sharing platform covering Beijing, Tianjin, and Hebei, requiring national key laboratories, large-scale scientific research instruments, and other core innovation resources to be open and shared among all cities within the region, and to establish a cross-administrative region mutual recognition system for innovation qualification certification. Additionally, a pilot program should be implemented to introduce a cross-regional settlement system for innovation vouchers in the Beijing-Tianjin-Hebei region, prioritizing support for small and medium-sized enterprises in Hebei and Tianjin to conveniently purchase technical services from universities and research institutions in Beijing, thereby effectively reducing technology transaction costs and activating knowledge spillover channels. These measures aim to directly address the core issue of “negative spillover caused by the single-core radiation model”, enhancing the marketization level and innovation absorption capacity of peripheral cities.

The Yangtze River Delta urban agglomeration should shift its focus to strengthening the radiating and driving role of secondary innovation centers and optimizing the multi-center network structure. Although the Yangtze River Delta exhibits a positive spatial spillover trend, it has not yet passed the significance test. Social network analysis shows that the betweenness centrality of secondary centers (such as Nanjing and Hefei) still lags significantly behind that of the core city Shanghai, and the hierarchical radiating potential of its multi-center structure has not yet been fully realized. Therefore, the Yangtze River Delta needs to build on its existing good collaboration and take it a step further. A key measure is for the governments of Shanghai, Jiangsu, Zhejiang, and Anhui to jointly establish a special “industrial chain collaborative innovation fund”, focusing on supporting cross-provincial industrial chain key core technology joint research and development projects led by secondary center cities such as Nanjing (integrated circuits, etc.) and Hefei (quantum technology, etc.), to strengthen the hub role of secondary centers in the innovation network. Concurrently, a three-tier technology transfer network comprising “core (Shanghai)—secondary centers (Nanjing, Hangzhou, Hefei)—node cities” should be established. Policy incentive mechanisms should be explored to encourage high-tech enterprises to prioritize the low-cost transfer and licensing of non-core patents or technology usage rights to enterprises in peripheral cities such as Zhoushan, Xuancheng, and Chizhou, thereby accelerating the hierarchical diffusion of innovation outcomes within the cluster. These measures aim to optimize the multi-center network structure, significantly enhance the radiation efficiency of secondary core cities like Nanjing and Hefei, address the issue of insufficient positive spillover effects, and enable the top-ranked secondary core cities in Table 4 to better drive the development of the entire region.

As a universal basic measure applicable to all city clusters, the “innovation voucher” system should be fully implemented and optimized to accurately support small and medium-sized enterprises in improving their R&D capabilities and technology adoption levels. Research has found that peripheral cities generally have low marketization levels and weak innovation foundations, and that collaborative innovation has not significantly enhanced the spillover effects of scientific and technological innovation on high-quality development as expected, with possible problems such as resource dispersion or dependence on innovation. As an inclusive policy tool, innovation vouchers need to be designed to be more targeted. The issuance of innovation vouchers should prioritize technology buyers (especially small and medium-sized enterprises in peripheral cities) rather than simply subsidizing R&D suppliers, to directly incentivize technology adoption and application, addressing the challenges of “supply without adoption” or “high adoption costs.” At the same time, the effectiveness of innovation vouchers should be linked to multidimensional indicators of high-quality development, requiring subsidized enterprises to commit to and actually improve their performance in areas such as green development (e.g., carbon emission intensity per unit of patent output) and regional coordination (e.g., the proportion of raw materials or services procured across cities) while upgrading their technological level, to ensure that innovation investment is truly transformed into comprehensive efficiency improvements in line with the connotation of high-quality development. This foundational measure aims to systematically enhance the marketization level, technological absorption capacity, and innovative vitality of all cities, particularly peripheral and low-scoring cities, addressing the current shortcomings of collaborative innovation models in reinforcing spillover effects.

This study has the following limitations: (1) The sample is limited to two major city clusters, and future research should expand to other city clusters such as the Guangdong-Hong Kong-Macao Greater Bay Area and the Chengdu-Chongqing Metropolitan Area to validate the generalizability of the conclusions; (2) Collaborative innovation is quantified solely through the number of cooperative patents, failing to encompass non-patent forms such as technology transfer and industry-academia-research alliances; (3) The spatial econometric model identifies spillover effects but lacks sufficient analysis of micro-level transmission mechanisms (e.g., talent mobility and technology diffusion channels). It is recommended that future research combine enterprise microdata and technology transaction data to deepen the analysis of these mechanisms.