Do Spatial Spillovers of Technology Transfer Networks Impact Urban Innovation Capacity? Evidence from Chinese Cities

Abstract

As the flow of innovation elements breaks through geographical boundaries, patent transfer and the resulting spatial knowledge spillovers have become a crucial pathway for cities to enhance their competitive advantages and foster collaborative innovation. This study crawls technology transfer data through Big Data mining and uses social network analysis to construct an intercity technology transfer network among 286 Chinese cities at the prefecture-level and above between 2000 and 2020. The study explores the influence of technology transfer networks and their spatial spillovers on urban innovation capacity. The results are as follows: (1) Moran’s I results indicate that technology transfer and innovation activities among Chinese cities exhibit significant spatial dependence. (2) The Markov chain analysis reveals that the technology transfer networks among Chinese cities exhibit significant spatial spillovers. (3) Spatial econometric analysis and effect decomposition demonstrate that technology transfer networks exhibit significant spatial dependence and spillover effects. Through the induced spatial knowledge spillovers, technology transfer networks contribute to enhancing the innovation capabilities of neighboring cities.

1. Introduction

Against the backdrop of accelerating restructuring of global innovation paradigms, technology transfer networks are transcending geographical boundaries to reshape regional innovation landscapes [1]. At the macro level, according to the 2024 global intellectual property filing statistics released by the World Intellectual Property Organization (WIPO), China has emerged as the largest filer under the Patent Cooperation Treaty (PCT) framework. However, substantial disparities persist in innovation capabilities across cities, exhibiting an increasingly agglomerative growth pattern, which underscores the pronounced spatial imbalance in innovation activities among Chinese urban centers [2]. At the meso-level, the Yangtze River Delta region in China demonstrated intensive intra-regional technology exchange in 2023, with over 25,000 cross-boundary technology contracts and a total transaction value reaching 186.3 billion RMB, a figure that substantially surpasses those of northwest China. This emerging core–periphery structure has exacerbated the Matthew Effect in regional innovation activities through spatial knowledge spillovers.

This observed divergence reflects the diminishing explanatory power of traditional innovation factors emphasized in conventional studies, while spatial spillover effects generated by technology transfer networks, including cross-regional knowledge recombination, innovation factor reallocation, and collaborative innovation mechanisms, are emerging as critical ways in overcoming the geographical lock-in of innovation. Against the paradoxical backdrop of accelerating global innovation resource flows coexisting with persistent regional innovation barriers, the spatial spillover effects of technology transfer networks have emerged as a new important lens for understanding urban innovation capability differentiation.

The process of technology transfer extends beyond the mere transfer of patent rights and associated knowledge; the dynamic flow of patents can also generate interurban knowledge spillovers [3]. As pivotal actors within regional innovation networks, cities’ embeddedness in these networks not only intensifies intra-urban knowledge creation processes and elevates their node status and regional competitiveness but also enhances the overall innovation capacity of the region through knowledge spillovers, thereby fostering sustainable regional development [4]. Therefore, a comprehensive understanding of the spatial spillover mechanisms through which technology transfer networks influence urban innovation capabilities plays a pivotal role in identifying novel pathways for enhancing urban innovation capacity and developing methodologies for regional collaborative innovation.

From a geographical perspective, economic activities across nations, provinces, and cities exhibit pronounced spatial disparities in their distribution patterns. New Economic Geography provides a theoretical foundation for understanding various agglomeration phenomena in economic activities. With the deepening of regional integration, regional economic and innovation development has become increasingly embedded within complex spatial interconnections [5]. Consequently, spatial factors have emerged as indispensable elements in urban innovation research. Current research on technology transfer networks predominantly focuses on innovation outputs within administrative boundaries [6,7,8], while systematically neglecting both the quantitative identification of knowledge externalities and the spatial spillover effects inherent in such networks. This study innovatively employs spatial Markov chain matrix analysis while constructing a spatial econometric model, systematically revealing the characteristic patterns of spatial spillovers in technology transfer networks and their heterogeneous impacts on urban innovation capabilities. The findings provide both theoretical foundations and practical guidance for optimizing.

This study uses big data mining technology to obtain patent data from China’s Patent Information Search Platform. A spatial database of patent transfers in Chinese cities is established after data cleaning and manual screening. Subsequently, this study employs social network analysis (SNA) to construct technology transfer network metrics, systematically investigating how spatial spillovers from the networks affect innovation capacity in both focal cities and their neighboring urban areas. In the empirical analysis, this study employs Moran’s I to examine the spatial autocorrelation of both technology transfer networks and urban innovation capacity. Concurrently, this study investigates the spatial spillover effects through which technology transfer networks influence urban innovation capacity, utilizing both spatial Markov chain methods and spatial econometric modeling.

The main conclusions of this study are as follows. A significant spatial correlation exists between technology transfer networks and innovation in Chinese cities. Intercity technology transfer not only promotes local cities’ innovation capacity but also benefits cities with similar spatial characteristics through spatial knowledge spillover. This suggests that patent transfer linkages with geographically proximate and economically comparable cities particularly foster urban innovation growth. Heterogeneity analysis reveals that these spillover effects are more pronounced among eastern cities, high-administrative-level cities, and innovative cities.

The remainder of the paper is organized as follows. Section 2 presents the literature review and theoretical analysis. Section 3 describes the method and data. Section 4 shows the result of the empirical analysis and Section 5 concludes.

2. Literature Review and Theoretical Analysis

2.1. Regional Analysis and New Economic Geography Theory

The intellectual origins of spatial economic analysis trace back to 19th-century German classical location theory. Thunen’s Agricultural Location Theory first rigorously demonstrated the spatial factors’ impact on agricultural production costs [9]. After that, Weber put forward Industrial Location Theory, which systematically and comprehensively explains the locational determinants [10]. Christaller presented Central Place Theory [11], and Lösch established Market Location Theory on this basis [12]. Isard was devoted to integrating classical location theory into mainstream economic analytical frameworks, striving to establish spatial issues as a core research domain within economics [13,14]. However, Isard failed to establish a general equilibrium model of regional economies, and this theoretical limitation remained unresolved until Dixit and Stiglitz introduced their seminal monopolistic competition model, which ultimately provided the analytical framework to address this critical gap [15]. Building upon this foundation, Krugman pioneered spatial economics as a distinct discipline [16,17]. His analytical framework for trade pattern analysis became known as the New Trade Theory, while the modeling approach for geographic distribution of economic activities established the field of New Economic Geography. Krugman’s New Economic Geography represents a direct theoretical extension of his New Trade Theory, incorporating Samuelson’s “iceberg transport costs [18]” to construct a two-region general equilibrium economic model [17]. This groundbreaking framework successfully integrated spatial factors into mainstream general equilibrium analysis for the first time.

The seminal work establishing New Economic Geography theory is the core–periphery (CP) model [17]. The CP model elucidates the formation mechanisms of spatial agglomeration and dispersion, explicitly demonstrating how an economic system endogenously evolves industrial core regions and agricultural peripheries through labor mobility in the manufacturing sector. The CP model posits that the spatial agglomeration and dispersion of economic activities result from the interplay of three fundamental effects: the market access effect, the cost-of-living effect, and the market crowding effect. The first two effects generate agglomerative forces that promote spatial concentration, while the third effect creates dispersion forces that counteract industrial clustering, thereby inducing spatial decentralization. The CP model operationalizes the measurement of agglomeration and dispersion forces through transaction costs (parameterized as trade freeness). It demonstrates that when transaction costs are sufficiently high, dispersion forces dominate agglomeration forces. However, since dispersion forces diminish at a faster rate than agglomeration forces as trade costs decrease, a critical threshold emerges where agglomerative forces surpass dispersive pressures. Beyond this tipping point, the spatial concentration of economic activities becomes self-reinforcing through cumulative causation, ultimately leading to complete locational concentration of all firms in a single region.

The CP model provides a rigorous theoretical explanation for the formation mechanisms of spatial economic agglomeration. However, due to its restrictive model assumptions and conclusions that deviate from empirical reality, subsequent scholars have progressively refined and enhanced this framework through various extensions. Regarding the geographical scale specification, contemporary research has extended the original two-region CP model to incorporate three-region and four-region frameworks [19,20]. These theoretical advancements systematically investigate the evolutionary patterns of intra-national economic agglomeration under conditions of economic globalization and trade liberalization. In terms of production factor assumptions, Martin and Rogers made a seminal contribution by introducing capital as a distinct factor of production, thereby developing the Footloose Capital (FC) model [21]. This theoretical advancement effectively addressed the critical limitation of the traditional CP model, which had exclusively considered labor as the sole production factor. Regarding model specification methodology, Ottaviano et al. achieved a breakthrough by substituting the CES utility function and iceberg transport costs with a quasi-linear quadratic utility function and linear transport costs, respectively [22]. This analytical innovation enabled the derivation of closed-form solutions for the CP model, thereby significantly reducing its dependence on computational numerical simulations. With the continuous evolution of the CP model framework, researchers have improved it to make it more realistic [23,24]. Therefore, the theoretical edifice of New Economic Geography (NEG) has undergone substantial enrichment and refinement.

2.2. Knowledge Flow and Spatial Spillover Effects

The dynamic flow of elements generates spatial knowledge spillover, and knowledge infusion and technology linkages from outside a region are key ways to achieve regional innovation [25]. Compared to tacit knowledge that needs to be transmitted through direct face-to-face communication, patents, as a type of explicit knowledge recorded in written words or codes, have the advantage of being able to be transmitted indirectly and on a larger scale [26]. Knowledge spillover is often affected by space and distance, and according to the respective characteristics of explicit and tacit knowledge, the spatial spillover effect of explicit knowledge is often greater than that of tacit knowledge [27,28]. Patents, especially invention patents, contain a large amount of knowledge information and have the potential to be transformed into innovation, promoting the interaction and exchange between different subjects through inter-regional flow, thus favorably driving the spillover of knowledge between cities. Building upon the two-region endogenous growth model developed by Fujita and Thisse [29], the dual mechanisms of knowledge diffusion externalities and agglomeration effects have been theoretically demonstrated to significantly accelerate the pace of innovation. On the one hand, the flow and dissemination of explicit knowledge brought about by patent transfer can reduce the innovation costs of relevant cities, and spatial knowledge spillover is conducive to cities achieving innovation catch-up [4,30]. On the other hand, exchanges between associated cities with similar spatial characteristics can better facilitate the absorption and utilization of transferred innovation resources [31]; thus, knowledge diffusion and spillover can contribute to innovation activities and performance in the region. The spatial knowledge spillover generated by intercity innovation interaction with patents can promote the concentration of innovation resources, and this innovation element positively influences the spatial enhancement of urban innovation capacity in technology transfer networks by increasing returns. Thus, technology transfer networks promote the innovation capacity of neighboring cities by inducing spatial knowledge spillover [32].

The First Law of Geography, as formalized by Tobler [33], posits that all spatial entities demonstrate interconnectedness, with the strength of association exhibiting an inverse relationship to geographical distance. Since the 1990s, the emergence of New Economic Geography (NEG) has spurred growing scholarly attention to examining knowledge spillovers through a spatial lens [34,35]. The deepening processes of globalization and regional integration have fundamentally reshaped scholarly understanding, demonstrating that economic growth and innovation development are never isolated spatial phenomena. Innovation activities consistently exhibit spatial agglomeration patterns [36], whose complex interactions and resultant spillover effects play pivotal roles in regional coordinated development [37]. Regional economic and innovation development has become increasingly embedded within complex spatial interdependencies [5], making the facilitation of factor mobility and its spatial spillover effects a growing focus of scholarly research.

With continuous advancements in data availability and methodological sophistication, scholars have progressively developed diverse modeling frameworks to quantify the spatial spillover effects generated by factor mobility. Building upon established theoretical frameworks, Autant-Bernard and LeSage and Yu et al. have employed advanced spatial econometric modeling to systematically elucidate how interregional flows of knowledge and innovation factors, along with their associated spatial knowledge spillover effects, significantly influence regional innovation performance [38,39,40]. Wu et al. develop a spatial econometric interaction model to investigate the knowledge flow-induced spillover effects during urban agglomeration processes [41]. Conley and Ligon pioneered a groundbreaking statistical framework for analyzing regional spillovers [42], which has subsequently served as the foundation for numerous quantitative investigations into spatial spillover effects in regional economic development [43]. In addition, geographically weighted regression (GWR) models have been increasingly applied to quantify spatial spillover effects [44], though existing applications remain predominantly focused on environmental domains like carbon emissions, with relatively limited utilization for analyzing knowledge-based factors. In summary, the existing literature on spatial spillover effects has primarily employed the frameworks mentioned above, utilizing adjacency matrices, geographical distance matrices, and economic distance matrices to quantify spatial spillovers across economic and innovation activities, industrial distribution, carbon emissions, and related domains.

2.3. Mechanism Analysis and Research Hypothesis

From the perspective of factor mobility, technology transfer networks significantly reduce barriers to the flow of production factors, thereby accelerating the cross-regional circulation of talent, capital, and technological resources. Core cities within the network establish robust linkages with neighboring cities through technology transfer networks, thereby driving the diffusion of high-skilled talent and innovation capital to peripheral regions. This cross-regional factor mobility serves as a dual-channel mechanism that not only supplies neighboring cities with critical innovation resources but also facilitates the transfer of both codified and tacit knowledge through talent circulation and technology diffusion, thereby substantially augmenting the knowledge stock essential for enhancing peripheral innovation capabilities.

The factor mobility within technology transfer networks actively facilitates knowledge spillovers, which constitute a critical transmission channel through which these networks enhance the innovation capabilities of neighboring cities. Knowledge spillovers occur through dual transmission channels: formal mechanisms such as collaborative R&D and technology transfer contracts facilitate the flow of codified knowledge (e.g., documented patents, technical specifications), while informal interactions, including professional exchanges and personnel mobility, promote the diffusion of tacit knowledge (e.g., technical know-how, experiential insights). Consequently, technology transfer networks serve as a critical platform that structurally enables these dual knowledge spillover channels, significantly enhancing the efficiency of technology and knowledge diffusion from core cities to neighboring regions. Furthermore, in accordance with Tobler’s First Law of Geography, knowledge spillovers exhibit distinct spatial thresholds and decay effects, that is, their intensity follows a negative power–law relationship with increasing geographical distance. Therefore, proximate cities derive advantages from core cities’ technology transfer networks due to spatial adjacency effects, thereby enhancing their innovation capacity.

From the perspective of technology diffusion, technology transfer networks serve as catalytic channels that systematically enhance neighboring cities’ innovation capabilities through spatially mediated knowledge flows. Technology diffusion constitutes a core function of technology transfer networks, while collaborative innovation represents its advanced manifestation and systemic extension. First, core cities in technology transfer networks can provide foundational support for the commercial application of patented technologies in neighboring cities through patent licensing and authorization, thereby promoting localized adaptation and secondary innovation of technologies. This enhances their technological capabilities and innovative capacity, fostering new competitive advantages in innovation. Second, the mobility of personnel during technology transfer can significantly enhance neighboring cities’ absorption and transformation of technologies through the accompanying knowledge diffusion, thereby improving innovation efficiency.

Building on this foundation, technology diffusion facilitates collaborative innovation among neighboring cities through intercity technology transfer, thereby strengthening the overall innovation capacity of the region. Collaborative innovation refers to an integrated innovation organizational model involving major cross-cutting coordination among different innovation entities to achieve significant technological advancements [45]. Its core lies in knowledge sharing and technological complementarity. Knowledge sharing forms the foundation of collaborative innovation, while technological complementarity serves as its driving force. The technology transfer network provides both the platform and mechanisms for such regional innovation synergy, enabling core cities and their neighboring areas to engage in more efficient technological cooperation. The mechanism of the impact of technology transfer networks on the innovation capacity of local and neighboring cities is shown in Figure 1.

In summary, through dual pathways of factor mobility with knowledge spillovers and technology diffusion with collaborative innovation, technology transfer networks not only enhance the innovation capacity of local cities but also significantly boost that of neighboring cities. Technology transfer networks accelerate the flow of production factors and knowledge spillovers, reducing barriers to the mobility of innovation elements. Through both formal and informal channels, these networks facilitate the dissemination of both explicit and tacit knowledge, thereby providing neighboring cities with critical resources and knowledge support essential for innovation. In addition, technology transfer networks enhance technology diffusion, facilitate knowledge sharing and technology complementarity, and promote collaborative innovation through industry–university–research collaboration, joint R&D and commercialization, as well as frontier technology co-development within regional innovation clusters. This effectively elevates the technology and innovation efficiency of neighboring cities. Based on this, the following hypotheses is proposed:

Hypothesis 1.

Technology transfer networks enhance the innovation capacity of neighboring cities through spatial knowledge spillovers.

3. Model, Variables, and Data

3.1. Model Specification

This study employs spatial econometric methods to investigate the spatial effects of technology transfer networks’ spillovers on the innovation capacity of neighboring cities. Based on the principles for optimal model selection proposed by Anselin [46], four statistics, LM lag, LM error, RLM lag, and RLM error, are first calculated using the Lagrange multiplier method. Both LM lag and LM error statistics passed significance tests at the 1% level. However, RLM lag failed the 10% significance level test and RLM error passed the 1% significance level test, indicating that SAR and SEM may coexist, favoring Spatial Durbin Model (SDM) [39]. In light of this, a SDM is established as follows:

$$In{v}_{it}={\theta }_0+\rho W\ast In{v}_{it}+{\theta }_1{X}_{it}+{\theta }_{2}Contro{l}_{it}+{\mu }_{1}W\ast X_{it}+{\mu }_{2}W\ast Contro{l}_{it}+{\alpha }_i+{\delta }_t+{\epsilon }_{it}$$

(1)

where $In{v}_{it}$ is the explained variable urban innovation capacity; $X_{it}$ denotes the explanatory variable technology transfer network; $Contro{l}_{it}$ is the control variables; ${\alpha }_i$ is the individual fixed effect; ${\delta }_t$ is the time fixed effect; ${\epsilon }_{it}$ is the error term; ${\theta }_0$, ${\theta }_1$, ${\theta }_2$, $\rho$, ${\mu }_1$, and ${\mu }_2$ are coefficients to be estimated; and $W$ is the spatial matrix. To comprehensively measure the spatial spillover effects of technology transfer networks, this study constructs a spatial weight matrix ($W_1$) based on geographical distance characteristics. Additionally, to ensure robustness, spatial adjacency ($W_2$) and spatial economic distance matrices ($W_3$) are established, respectively.

SDM simultaneously incorporates spatially lagged explanatory variables and spatially lagged dependent variables, enabling it to capture both local effects and spatial spillover effects. However, the SDM also has several limitations. First, the results of SDM depends on the choice of spatial weight matrix (geographic, economic and so on), which may not fully capture complex linkages between cities. Second, although the use of spatial econometric methods can detect spillovers, it has difficulty in distinguishing the mechanisms of spillover. Third, SDM incorporates spatially lagged explanatory variables and spatially lagged dependent variables simultaneously; the explanation of the regression coefficient is more complex than the ordinary methods.

3.2. Variables

3.2.1. Explained Variable: Urban Innovation Capacity

Innovation output is a visual representation of regional knowledge output, dissemination capacity, and overall strength of science and technology. Patents are also an important outcome of innovation output and are the most commonly used data in innovation empirical studies [7,47,48]. Among the three main patent types, invention patents have the highest technological content and value compared to design and utility patent, whereas patent grants, which are officially examined and tested, have greater recognition and innovativeness than patent applications. Therefore, the logarithm of invention patents granted ($Inv$) is used as a proxy variable for urban innovation capacity in the benchmark model, and the number of invention patents per 10,000 people ($lnW$) is used as an alternative variable.

3.2.2. Explanatory Variable: Technology Transfer Networks

According to social network analysis theory, network centrality measures the extent to which nodes are near the center of the overall network. However, structural holes describe their role as intermediaries, which refers to the gaps created between individuals in a network with complementary information sources owing to the absence of social connections [49].

Network centrality is classified into four types: degree centrality, closeness, betweenness, and eigenvector centrality. Degree centrality is one of the most intuitive ways to measure the central position of cities in technology transfer networks. The logarithm of degree centrality ($Deg$) is selected to measure cities’ network centrality, and the logarithm of eigenvector centrality ($Egdeg$) is used as an alternative indicator for the analysis.

Burt proposed four main metrics for measuring structural holes: effective size, efficiency, constraint, and hierarchy [49]. The structural hole constraint index is the most widely used. Betweenness measures the intermediary role of nodes in a network; therefore, previous studies have also utilized it as a measure of structural holes [50]. The logarithm of the difference between 1 and the structural hole constraint index is calculated as the richness of the structural holes occupied by the nodes in the network ($Hole$), and the logarithm of betweenness is chosen ($Btw$) as a substitute for further analysis.

(1) Degree centrality. Following Freeman, a relative indicator $C_{RD}(i)$ is used to measure degree centrality [51]. It determines the extent to which node city is located at the core of the intercity technology transfer network. It is calculated by $C_{RD}(i)={\displaystyle \frac{{\displaystyle {\sum }_{j=1}^N{a}_{ij}}}{n-1}}$ (where $a_{ij}$ is the patent transfer adjacency matrix of cities and ${\displaystyle {\sum }_{j=1}^N{a}_{ij}}$ denotes the degree of node city i in the network (i.e., the sum of the existing associations between nodes $i$ and $j$). If a technology transfer relationship exists between nodes $i$ and $j$, $a_{ij}$ takes the value of 1; otherwise, it takes the value of 0). A larger degree indicates that the node city has established a patent transfer relationship with many other nodes and is closer to the center of the technology transfer networks. The spatial and temporal evolutions of the degree centrality are shown in Figure 2.

(2) Eigenvector centrality. The network centrality of a node is closely related to, and is even a linear function of, the centrality of its neighboring nodes [52]. Therefore, the eigenvector centrality of a node is related to both the number and importance of neighboring nodes and is calculated by $C_{ED}(i)=c{\displaystyle {\sum }_{j=1}^N{a}_{ij}x}$, where $c$ is a constant and $x$ is the eigenvalue of the adjacency matrix. A higher eigenvector centrality of a node city indicates that the city can not only enhance its innovation capability by improving its own importance in the network but also actively establishes transfer links with the central city.

(3) Structural holes. Intermediaries in structural holes tend to occupy important positions, which increases their control over resources. The structural hole constraint describes a node’s role as an intermediary in a network. The higher the constraint index, the less the structural holes in the network, which is calculated based on Burt by $C_{SH}(i)={{\displaystyle {\sum }_{j\in \Gamma (i)}\left(p_{ij}+{\displaystyle {\sum }_q{p}_{iq}{p}_{qj}}\right)}}^2$ ($\Gamma (i)$ is the set of neighboring nodes of node $i$, $p_{ij}$ denotes the proportion of the total energy invested by node $i$ to maintain the relationship with node $j$, and $p_{iq}$ and $p_{qi}$ are the proportion of the total energy invested by nodes $i$ and $j$ to maintain the relationship with their common neighbor $q$, respectively. In addition, $p_{ij}=a_{ij}/{\displaystyle {\sum }_{j\in \Gamma (i)}{a}_{ij}}$. If a technology transfer relationship exists between nodes $i$ and $j$, $a_{ij}$ takes the value of 1; otherwise, it takes the value of 0. $p_{iq}$ and $p_{qi}$ are calculated similarly. According to the above equation, the smaller the value of $C_{SH}(i)$, the lower the number of structural holes) [49]. Because the maximum value of the structural hole constraint index is 1, drawing on existing studies, the difference between 1 and this index is used as a measure of the richness of structural holes ($Hole$). Nodes with richer structural holes can have better control of the network in their intermediary position. The spatial and temporal evolutions of structural holes are shown in Figure 3.

(4) Betweenness. Betweenness is defined as the proportion of shortest paths through node $i$ for all node pairs. Betweenness, as proposed by Freeman [51], is borrowed as the structural hole proxy to measure the degree of intermediary control over resources [51]. It is calculated by $C_B(i)={\displaystyle \sum _{j=1;k=1;j\ne k\ne i}^N\frac{N_{jk}(i)}{N_{jk}}}$ ($N_{jk}$ is the number of shortest paths between cities $j$ and $k$, and $N_{jk}(i)$ is the number of shortest paths between cities $j$ and $k$ through city $i$).

3.2.3. Control Variables

Referring to existing research [53], this study includes several control variables to enhance the robustness of the findings. A city’s economic development level is measured by calculating its gross regional product per capita ($Gdpp$). The ratio of the gross product of the tertiary sector to that of the secondary sector ($Ind$) is used to characterize a city’s industrial sophistication. The level of openness is expressed as a share of the GDP by the amount of real foreign investment ($Fdi$). The share of science and education expenditure in urban fiscal expenditure ($Sci$) is used to measure the government’s attention to and innovation investment in science and education. The share of the total deposits and loans of financial institutions in the GDP of cities ($Finac$) reflects the size and development of regional financial markets. Urban spatial structure may affect its innovation [54]; thus, urban population density ($Ubpd$) is added as a control variable. Wernsdorf et al. found that network infrastructure facilitates the expansion of innovation boundaries and capability by increasing information accessibility [55]. Therefore, the number of Internet-accessible households per capita ($Infra$) is considered to assess the degree of development of urban Internet infrastructure.

3.3. Data Sources

The transfer of patents is the most direct form to measure technology transfer, according to previous studies. Owing to the large volume of patent data and restriction of access rights, this study uses data mining technology to obtain patent data from a “Patent Information Search Platform” (http://search.cnipr.com, accessed on 1 June 2022). After data cleaning and manual screening using Python 3.11 and Excel 2019 (i.e., removing transfers between domestic cities and foreign countries), a spatial database of patent transfers in Chinese cities is established. Data on 1,270,826 Chinese patent transfers are included, ranging between 1985 and 2020. The address attributes of the patents before and after the transfer are extracted from the patent legal status information, and their corresponding cities are extracted from the addresses. For data without a city clearly marked in the address, address matching is performed using the API of Gaode Map Service to fetch valid city information; if matching fails, the data are discarded. Ultimately, data on 1,262,316 valid transfer patents are obtained (706,759 city self-transfers and 555,557 intercity transfers).

After a preliminary analysis of the intercity technology transfer network, cities lacking sufficient transfer data are eliminated, and the study’s time period is set as 2001–2020, owing to the small amount of patent transfer data between 1985 and 2000. Ultimately, 286 cities at the prefecture level and above in China are identified as the research subject. Other data for the empirical analysis are obtained from the Chinese Research Data Services (CNRDS) platform, China City Statistical Yearbook (2001–2020), and official website of the Ministry of Science and Technology of the People’s Republic of China.

Table 1. Descriptive statistics.

Variables	Symbols	Definition and Measurements	Mean	SD	Min	Max
Explained variables	Inv	Number of invention patents granted (log)	3.821	2.035	0	11.050
	InW	Number of invention patents granted per 10,000 people (log)	0.048	0.228	0	6.325
Explanatory variables	Deg	Degree centrality	0.079	0.124	0	0.632
	Egdeg	Eigenvector centrality	0.042	0.042	0	0.215
	Hole	Richness of structural holes	0.713	0.326	0	0.981
	Btw	Betweenness	0.052	0.142	0	1
Control variables	Gdpp	GDP per capita (log)	10.150	0.875	7.415	13.060
	Ind	Ratio of output of tertiary sector to secondary sector (log)	−0.189	0.466	−2.361	2.249
	Fdi	Share of foreign real investment in GDP (log)	−6.419	1.423	−14.85	−0.965
	Sci	Share of expenditure on science and education in GDP (log)	−1.724	0.278	−4.535	−0.977
	Finac	Share of total deposits and loans of financial institutions in GDP (log)	0.752	0.493	−0.677	3.644
	Ubpd	Population per square kilometer (log)	5.716	0.909	1.548	7.904
	Infra	Number of Internet access households per capita	−2.583	1.242	−9.714	1.298

shows the results of descriptive statistics.

4. Empirical Analysis

4.1. Spatial Correlation Analysis

Prior to conducting spatial regression analysis, this study employs the global Moran’s I index to measure the spatial characteristics of the technology transfer networks and urban innovation capacity, thereby testing their spatial correlation.

Table 2. Test of spatial correlation.

	Deg		Hole		Inv
Year	Moran’s I	Z Value	Moran’s I	Z Value	Moran’s I	Z Value
2001	0.001	0.634	−0.009	−0.720	0.348	2.556 **
2002	0.004	1.174	−0.003	0.0530	0.448	3.277 ***
2003	0.008	1.863 *	0.012	1.902 *	0.429	3.139 **
2004	0.016	3.276 ***	0.024	3.468 ***	0.417	3.054 **
2005	0.022	4.364 ***	0.033	4.601 ***	0.451	3.304 ***
2006	0.015	3.280 ***	0.038	5.314 ***	0.437	3.196 ***
2007	0.028	5.186 ***	0.051	6.966 ***	0.413	3.024 **
2008	0.032	5.758 ***	0.066	8.918 ***	0.403	2.950 **
2009	0.048	8.007 ***	0.078	10.33 ***	0.414	3.032 **
2010	0.051	8.512 ***	0.089	11.67 ***	0.414	3.035 **
2011	0.053	8.771 ***	0.093	12.00 ***	0.438	3.208 ***
2012	0.059	9.706 ***	0.080	10.38 ***	0.448	3.283 ***
2013	0.071	11.37 ***	0.090	11.56 ***	0.448	3.277 ***
2014	0.082	12.91 ***	0.115	14.47 ***	0.456	3.338 ***
2015	0.093	14.43 ***	0.107	13.55 ***	0.439	3.213 ***
2016	0.121	18.43 ***	0.087	11.18 ***	0.437	3.199 ***
2017	0.148	22.40 ***	0.054	7.613 ***	0.440	3.222 ***
2018	0.157	23.60 ***	0.093	12.09 ***	0.439	3.213 ***
2019	0.157	23.60 ***	0.064	8.944 ***	0.423	3.095 **
2020	0.163	24.39 ***	0.084	10.94 ***	0.411	3.013 **

Note: *, **, and *** represent a significance level of 10%, 5%, and 1%, respectively.

presents the temporal evolution of Moran’s I indices for both the technology transfer networks and urban innovation capacity over the study period. Under the spatial geographic distance matrix, urban innovation capacity exhibits statistically significant spatial autocorrelation throughout the study period. In contrast, the z value of Moran’s I of technology transfer networks’ core metrics is insignificant in the period 2001–2002, attributable to sparse transfer data. However, the z value of other periods shows a robust significance. Therefore, the spatial distribution of both the technology transfer networks and urban innovation capacity across cities exhibits non-random characteristics, which indicates that a strong spatial dependence and agglomeration phenomenon exist; the influence of spatial effects must be considered when making estimations.

4.2. Analysis of Spatial Spillover Effects Based on Markov Chains

A Markov chain is a stochastic process that models the transition of a system between discrete states. This method discretizes the degree centrality and structural hole metrics of node cities within the technology transfer networks into $k$ distinct types, then calculates the probability distribution of each type and its temporal evolution. This dynamic process is approximated as a Markov process, enabling the analysis of state transitions within the network. At period $t$, the probability distribution of technology transfer network intensity types can be represented by a $1\times k$ state probability vector $P_t=[P_{1,t},P_{2,t},\dots ,P_{k,t}]$. The temporal dynamics of these states are governed by a Markov transition probability matrix M of dimension $k\times k$, where each element $m_{ij}$ quantifies the probability that a city in type $i$ at period $t$ transitions to type $j$ at time $t+1$, with its estimation formula as follows:

$$m_{ij}={\displaystyle \frac{n_{ij}}{n_i}}$$

(2)

where $n_{ij}$ is the total number of observed transitions from state $i$ (at period $t$) to state $j$ (at period $t+1$) across all consecutive time periods in the study. $n_i$ is the total count of cities observed in state i across all time periods.

The spatial Markov chain method incorporates neighborhood conditions into the traditional Markov chain framework, establishing spatial relationships between cities and their surrounding neighbors. It further determines the neighborhood type for each city category through the spatial lag factor (i.e., the product $WX$ of the observed value $X$ and the spatial weight matrix $W$) [56]. According to the First Law of Geography, all things are interrelated. In a regional context, geographically adjacent areas are not independent of each other but rather exist in a state of mutual interaction. The spatial Markov chain incorporates spatial lag factors by computing the transition probability of cities shifting from type $i$ at period $t$ to type $j$ at period $t+1$ under the condition that the spatial lag type is $k$, thereby addressing the neglect of spatial interactions in conventional Markov chain methods.

4.2.1. Markov Transition Probability Analysis

Table 3. Markov transition probability matrix.

	State	N	1	2	3	4
Deg	1	338	0.768	0.171	0.059	0.002
	2	797	0.108	0.652	0.222	0.018
	3	1662	0.045	0.110	0.614	0.231
	4	2637	0.000	0.003	0.167	0.830
	state	N	1	2	3	4
Hole	1	565	0.869	0.113	0.013	0.005
	2	1071	0.098	0.682	0.117	0.103
	3	2399	0.009	0.099	0.765	0.127
	4	1399	0.000	0.080	0.099	0.821

presents the Markov transition probability matrix for China’s inter-city technology transfer networks. The conventional Markov probability matrix reveals that the diagonal probabilities are consistently higher than the off-diagonal probabilities. For degree centrality, the minimum and maximum diagonal probability is 61.4% and 83%, respectively. For structural hole metric, the value is 68.2% and 86.9%, which indicates that, during the study period, the technology transfer networks exhibited state persistence probabilities ranging from 61.4% (minimum) to 86.9% (maximum), revealing strong stability in inter-city technology transfer across China. The probabilities of maintaining original network intensity significantly exceeded those of upward or downward transitions for all regional types.

Furthermore, the diagonal probabilities reveal asymmetric stability patterns: intermediate-intensity types exhibit notably lower persistence (65.2% for degree centrality, 68.2% for structural holes) compared to both low-intensity (76.8% degree centrality, 86.9% structural holes) and high-intensity types (83% degree centrality, 82.1% structural holes). Compared with the analysis of off-diagonal probabilities, both intermediate–low (24% for degree centrality, 22% for structural holes) and intermediate–high types (23.1% for degree centrality, 12.7% for structural holes) exhibit higher probabilities of upward transitions than their downward transition counterparts (10.8% of degree centrality and 9.8% of structural holes for intermediate–low; 15.5% and 10.8% for intermediate–high). This demonstrates a net upward mobility trend among intermediate intensity nodes in the technology transfer networks.

However, the year-to-year evolution analysis reveals pronounced stability at network intensity extremes: cities maintain low-intensity types with high probability (76.8% for degree centrality, 86.9% for structural holes) and high-intensity types similarly persist (83% and 82.1%, respectively). Conversely, both upward transitions from low-intensity states and downward transitions from high-intensity states exhibit comparatively low probabilities, indicating systemic rigidity at the network periphery and core. These findings demonstrate the presence of Matthew effects in inter-city technology transfer networks. Cities occupying central positions in the network (high degree centrality) or bridging structural holes exhibit self-reinforcing advantages, progressively enhancing their capacity to attract and retain innovation resources. Furthermore, the relatively low probabilities observed in both off-diagonal and adjacent transition cells indicate that enhancing a city’s degree centrality and securing structural hole positions within the technology transfer networks constitute a gradual path-dependent process, with limited potential for leapfrog development in the short term.

4.2.2. Spatial Markov Transition Probability Analysis

The conventional Markov chain approach, while capable of analyzing transition probabilities between distinct states of technology transfer networks intensity, fails to account for spatial interactions by treating regions as isolated entities. As inter-city technology transfer is inherently constrained by regional context, neighboring relationships and regional background collectively exert significant influence on state transition dynamics. Furthermore, this study employs spatial Markov chain analysis to rigorously evaluate how neighborhood typologies influence the transition probabilities of cities’ technology transfer networks intensity. By augmenting traditional Markov transition matrices with neighborhood-specific conditions, this study derives spatially stratified transition probability matrices, capturing the nuanced interdependencies between cities and their regional contexts (

Table 4. Spatial Markov transition probability matrix.

	Neighbor Type	State	N	1	2	3	4
Deg	1	1	26	0.872	0.058	0.070	0.000
		2	25	0.055	0.902	0.036	0.007
		3	55	0.080	0.200	0.704	0.016
		4	66	0.000	0.000	0.500	0.500
	2	1	29	0.786	0.196	0.018	0.000
		2	252	0.299	0.592	0.108	0.001
		3	603	0.020	0.250	0.667	0.063
		4	1002	0.000	0.004	0.172	0.828
	3	1	214	0.770	0.176	0.055	0.000
		2	347	0.108	0.565	0.325	0.002
		3	694	0.003	0.099	0.781	0.116
		4	654	0.000	0.000	0.033	0.967
	4	1	69	0.891	0.107	0.002	0.000
		2	173	0.014	0.638	0.305	0.043
		3	310	0.000	0.025	0.578	0.396
		4	915	0.000	0.000	0.016	0.984
	neighbor type	state	N	1	2	3	4
Hole	1	1	289	0.988	0.012	0.000	0.000
		2	150	0.091	0.909	0.000	0.000
		3	154	0.000	0.250	0.750	0.000
		4	93	0.000	0.012	0.105	0.883
	2	1	129	0.982	0.018	0.000	0.000
		2	224	0.169	0.708	0.120	0.002
		3	344	0.095	0.101	0.804	0.000
		4	480	0.000	0.008	0.071	0.921
	3	1	140	0.814	0.071	0.114	0.000
		2	637	0.064	0.804	0.131	0.001
		3	1594	0.000	0.037	0.839	0.124
		4	692	0.000	0.000	0.149	0.851
	4	1	7	0.700	0.183	0.117	0.000
		2	60	0.143	0.429	0.413	0.016
		3	307	0.000	0.023	0.800	0.177
		4	134	0.000	0.001	0.108	0.891

). As evidenced in Table 4, the transition probabilities between distinct intensity types vary significantly across regional contexts and systematically deviate from the elements of the conventional Markov chain matrix. This unequivocally demonstrates that the regional background exerts a substantial influence on state transitions within urban technology transfer networks.

The influence of neighborhood types on urban state transitions is heterogeneous and context-dependent. Cities adjacent to low- or intermediate–low intensity technology transfer networks exhibiting significantly reduced probabilities of upward mobility in both degree centrality and structural hole metrics demonstrate that low- and intermediate–low intensity neighborhood contexts exert negative spillover effects, constraining cities’ capacity to advance within the technology transfer hierarchy. By contrast, cities adjacent to high or intermediate–high intensity technology transfer networks exhibit significantly greater probabilities of upward transitions than downward shifts in both degree centrality and structural hole measures, clearly indicating positive spillover effects from these advanced regional contexts.

The analysis robustly confirms the classical adage “proximity to vermilion makes one red, near ink turns one black” in the context of technology transfer networks: cities adjacent to high-intensity innovation hubs demonstrate progressive enhancement of their network positions, while those bordering low-intensity regions face persistent barriers to upward mobility. The analysis demonstrates a discernible convergence tendency among cities with comparable technology transfer network intensities, revealing the presence of a club convergence effect within China’s inter-city technology transfer networks. However, the predominant pattern reveals synchronized directional transitions among neighboring regions, with co-upward mobility occurring most frequently, underscoring the critical role of spatial spillovers in inter-city technology transfer.

The preceding analysis demonstrates that technology transfer networks exhibit spatial spillover effects contingent on regional contexts. To statistically validate these effects, we conduct a hypothesis test. The null hypothesis is that the intensity types of technology transfer networks across cities are mutually independent, and transition probabilities are invariant to spatial lag types. The specific test statistics are as follows:

$$Q=-2\log \left\{{{\displaystyle \prod _{l=1}^k{\displaystyle \prod _{i=1}^k{\displaystyle \prod _{j=1}^k\left[\frac{m_{ij}}{m_{ij}(l)}\right]}}}}^{n_{ij}(l)}\right\}$$

(3)

where $k$ represents the number of technology transfer network intensity categories. $m_{ij}$ denotes the conventional Markov transition probability, while $m_{ij}(l)$ and $n_{ij}(l)$, respectively, represent the spatial Markov transition probability and corresponding city count under spatial lag type $l$. The test statistic $Q$ asymptotically follows a chi-square distribution with degrees of freedom equal to $k{(k-1)}^2$. The unadjusted degree of freedom is calculated as $4\times {(4-1)}^2=36$. According to Equation (3), the $Q$ statistic for degree centrality is 80.592, which exceeds the critical value ${\chi }^2(40)=66.766$ at the significance level $\alpha =0.005$; similarly, the $Q$ statistic for structural holes is 63.476, surpassing the threshold ${\chi }^2(40)=59.342$ at the $\alpha =0.025$ level. Therefore, the null hypothesis that the technology transfer network intensity types among different cities are mutually independent during the study period is rejected.

4.3. Spatial Effect Decomposition

Due to the inclusion of spatial lag terms, the estimated coefficients in standard spatial econometric regressions—apart from the spatial term of the dependent variable—cannot accurately capture the true marginal effects of explanatory variables on the dependent variable. Moreover, the statistical significance of these coefficients does not reliably indicate whether the explanatory variables genuinely influence the dependent variable [39,57]. LeSage and Pace proposed a methodological framework utilizing average direct effects and average indirect effects to rigorously analyze the influence of explanatory variables on the explained variable in spatial econometric models [39]. To address the inherent coefficient bias issue, this study employs an SDM to decompose the impact of technology transfer networks on urban innovation capacity, empirically examining these relationships through the lens of direct and indirect effects.

Table 5. Spatial effect decomposition.

		(1) Inv	(2) Inv	(3) Inv	(4) Inv	(5) Inv	(6) Inv
Direct Effect	Deg	0.337 ***	0.281 ***	0.146 ***
		(0.035)	(0.032)	(0.027)
	Hole				0.017 ***	0.020 ***	0.101 ***
					(0.007)	(0.004)	(0.022)
Indirect Effect	Deg	0.660 ***	0.120 **	0.419 ***
		(0.047)	(0.060)	(0.151)
	Hole				0.071 ***	0.167 ***	0.693 ***
					(0.017)	(0.060)	(0.211)
Total Effect	Deg	0.997 ***	0.401 ***	0.565 ***
		(0.051)	(0.075)	(0.148)
	Hole				0.088 ***	0.187 **	0.794 ***
					(0.012)	(0.060)	(0.214)
	rho	0.637 ***	2.713 ***	0.889 ***	0.126 ***	1.294 ***	0.300 ***
		(0.018)	(0.610)	(0.019)	(0.040)	(0.172)	(0.067)
	Year	Y	Y	Y	Y	Y	Y
	City	Y	Y	Y	Y	Y	Y
	R2	0.401	0.752	0.491	0.277	0.252	0.185
	N	5720	5720	5720	5720	5720	5720
	Matrix	W1	W2	W3	W1	W2	W3

Note: **, *** represent significance level of 5% and 1%, respectively. The cluster-robust standard errors are given in parentheses.

shows the total effect of technology transfer networks on urban innovation capacity under the two-way fixed effects SDM and the decomposition of the direct and indirect effects. The coefficients of the direct effects of degree centrality and structural holes are both significantly positive at the 1% level, indicating that technology transfer networks significantly enhance urban innovation capability. Technology transfer drives the flow of a large amount of information resources between regions; cities use the explicit knowledge contained in patents and the implicit knowledge transmitted by interactive exchanges to promote the use of this innovation resource, thereby promoting their own innovation capacity.

Regarding the indirect effects, the coefficients of network centrality and structural hole indicators are significantly positive. This indicates that technology transfer in this city not only significantly improves its own innovation capability but also greatly improves that of cities with similar spatial characteristics through spatial spillover effects. Spatial knowledge spillover can help reduce the innovation costs of related cities, while the exchange between related cities with similar spatial characteristics can promote the sharing and rational allocation of innovation resources, thereby enhancing urban innovation capacity. In addition, the spatial knowledge spillover brought by technology transfer to other cities’ innovation capacity mostly accounts for 60% and above of the total growth effect under different spatial weight matrices, further indicating that the spatial spillover effect of the technology transfer network can help enhance the innovation capacity of cities with similar spatial characteristics.

4.4. Robustness Tests

4.4.1. Replacing the Spatial Matrix

Given the potential limitations in the geographic-distance spatial weight matrix used in baseline regressions, which may inadequately capture economic or institutional linkages, this study conducts robustness tests by substituting it with a spatial contiguity matrix $W_2$ (Queen adjacency) and spatial economic distance matrix $W_3$ (inverse of GDP per capita differences). As shown in Columns (2), (3), (5), and (6) of Table 5, the spatial lag term of urban innovation capacity remains statistically significant at the 1% level. Furthermore, in the effect decomposition analysis, the coefficients for both degree centrality and structural holes retain their positive signs and pass the 1% significance test. These robustness check results are fundamentally consistent with the baseline findings reported earlier. Therefore, the baseline analysis and effects decomposition demonstrate strong robustness, indicating that, across alternative spatial weight matrix specifications, technology transfer networks consistently promote the enhancement of urban innovation capacity.

The analysis of indirect effects reveals consistently positive spatial spillover impacts from the explanatory variables, which account for a substantial proportion of the total effects. This robustly confirms that cities strengthening their central positions and intermediate roles in technology transfer networks not only enhance their own innovation capacity but also induce transformative changes in related factors through spatial spillovers, thereby benefiting geographically proximate cities with similar spatial characteristics in improving their innovation capabilities.

4.4.2. Replacing the Measurements of Variables

To enhance the robustness of the findings, this study conducts additional validation by reconstructing the spatial Durbin model with alternative variable specifications. Specifically, the explanatory variables are replaced with eigenvector centrality and betweenness centrality to capture distinct network roles. And the explained variable is substituted with invention patents per 10,000 population for refined innovation measurement. The regression results are shown in

Table 6. Robustness tests of spatial effect decomposition.

		(1) Inv	(2) Inv		(3) Inw	(4) Inw
Direct Effect	Egdeg	1.073 ***		Deg	12.751 ***
		(0.059)			(2.210)
	Btw		1.079 ***	Hole		0.061 ***
			(0.103)			(0.011)
Indirect Effect	Egdeg	0.128		Deg	8.059 **
		(0.146)			(4.063)
	Btw		0.038 *	Hole		0.036 *
			(0.021)			(0.019)
Total Effect	Egdeg	1.201 ***		Deg	20.810 ***
		(0.166)			(3.952)
	Btw		1.117 ***	Hole		0.097 ***
			(0.237)			(0.018)
	Year	Y	Y		Y	Y
	City	Y	Y		Y	Y
	R2	0.749	0.150		0.105	0.193
	N	5720	5720		5720	5720
	Matrix	W1	W1		W1	W1

Note: *, **, *** represent significance level of 10%, 5% and 1%, respectively. The cluster-robust standard errors are given in parentheses.

. The analysis robustly confirms that technology transfer networks exert significantly positive direct effects on urban innovation, reinforcing that enhancing a city’s centrality position and intermediate role within technology transfer networks actively promotes its innovation performance.

When eigenvector centrality is substituted for degree centrality in the analysis, the indirect effect coefficient remains positive but statistically insignificant. The eigenvector centrality captures a node’s ability to enhance its network prominence by establishing connections with other highly central nodes. When a city node links to influential hubs within the technology transfer networks, multiple confounding factors may intervene in this process, which may lead to the ambiguity of the spatial spillover path, thereby hiding the spatial spillover effects. However, the indirect effects in all other regression specifications consistently pass statistical significance tests at least at the 10% confidence level, further validating that technology transfer networks generate spatial knowledge spillovers benefiting geographically proximate cities. The directionality of both direct and indirect effect coefficients of technology transfer networks on urban innovation remains fundamentally consistent across all model specifications, demonstrating the robustness and reliability of the findings regarding spatial spillover mechanisms.

4.5. Heterogeneity Analysis of Spatial Regression

To examine the heterogeneous spatial spillover effects of technology transfer networks across different types of cities, this study incorporates interaction terms between dummy variables and core explanatory variables into the spatial econometric regression model.

Due to the heterogeneity of geographical space across regions, there are significant differences in the developmental contexts of different cities. The eastern coastal areas of China occupy a pivotal position in the country’s economic development. Over the long term, these regions have enjoyed more favorable economic foundations, policy support, and innovation environments, leading to distinct patterns of technology transfer compared to other areas. Columns (1) and (2) in

Table 7. Heterogeneity analysis.

		(1) Inv		(2) Inv		(3) Inv		(4) Inv		(5) Inv		(6) Inv
Direct Effect	Deg	2.571 ***	Hole	11.859 ***	Deg	2.509 ***	Hole	1.067 ***	Deg	2.599 ***	Hole	1.141 ***
		(0.443)		(1.968)		(0.439)		(0.169)		(0.439)		(0.181)
	Deg × East	−0.342	Hole × East	−0.535	Deg × Level	0.105	Hole × Level	0.014	Deg × nno	0.128	Hole × Inno	−0.122
		(0.313)		(0.327)		(0.257)		(0.028)		(0.155)		(0.299)
Indirect Effect	Deg	9.034 ***	Hole	23.766 **	Deg	11.867 ***	Hole	4.324 ***	Deg	11.128 ***	Hole	2.755 **
		(1.961)		(11.724)		(2.257)		(1.430)		(2.033)		(1.267)
	Deg × East	4.992 ***	Hole × East	5.952 ***	Deg × Level	9.902 ***	Hole × Level	1.116 ***	Deg × Inno	4.657 ***	Hole × Inno	9.745 ***
		(0.994)		(1.028)		(3.524)		(0.394)		(1.006)		(2.977)
Total Effect	Deg	11.605 ***	Hole	35.625 ***	Deg	14.376 ***	Hole	5.390 ***	Deg	13.728 ***	Hole	3.895 ***
		(2.067)		(12.243)		(2.381)		(1.492)		(2.131)		(1.324)
	Deg × East	4.651 ***	Hole × East	5.417 ***	Deg × Level	10.006 ***	Hole × Level	1.130 ***	Deg × Inno	4.785 ***	Hole × Inno	9.623 ***
		(0.856)		(0.905)		(3.681)		(0.412)		(1.030)		(3.086)
	rho	0.486 ***		0.529 ***		0.551 ***		0.596 ***		0.515 ***		0.593 ***
		(0.034)		(0.034)		(0.033)		(0.033)		(0.033)		(0.033)
	Year	Y		Y		Y		Y		Y		Y
	City	Y		Y		Y		Y		Y		Y
	R2	0.674		0.643		0.679		0.653		0.704		0.673
	N	5720		5720		5720		5720		5720		5720

Note: **, *** represent significance level of 5% and 1%, respectively. The cluster-robust standard errors are given in parentheses.

present the regression coefficients for the heterogeneity analysis of eastern cities. The estimation results indicate that the direct effect coefficient of the technology transfer network in eastern cities is statistically significant at the 1% level, whereas the coefficients of the interaction term and the core explanatory variable are not significant. This may be attributed to the fact that eastern cities’ advantages in technology transfer are likely manifested more through inter-regional interactions (i.e., spillover effects) rather than localized technological accumulation or innovation diffusion. Furthermore, as the core region of technology transfer, eastern cities have achieved relatively mature technological innovation. Their primary influence on other cities manifests as diffusion effects, while the local direct effects may be comparatively weaker. The regression results demonstrate that the spatial spillover effects of technology transfer networks in eastern cities are statistically significant, accounting for over 60% of the total effects. This further substantiates the pivotal role of eastern cities within the technology transfer network.

As a fundamental governance institution, administrative zoning enables effective regional administration through hierarchically structured urban systems. Higher-ranked administrative cities generally benefit from preferential resource allocation, policy advantages, and advanced infrastructure. Their administrative hierarchy enhances the capacity to coordinate resources, making them pivotal hubs in technology transfer networks and magnets for innovation-related assets. Moreover, cities with higher administrative status typically possess greater autonomy in policy implementation, industrial planning, and innovation system development, thereby enabling them to play a more dominant role in regional innovation networks. China’s urban administrative hierarchy comprises municipalities, sub-provincial cities, cities with independent planning status, provincial capitals, and regular prefecture-level cities. For analytical purposes, all non-regular prefecture-level cities are defined as high-level administrative cities ($Level$) to investigate their unique spillover effects in technology transfer networks.

As shown in Columns (3) and (4) of Table 7, the direct effect of high-level cities’ technology transfer networks remains significant, whereas neither the interaction term nor the core explanatory variable achieves statistical significance. This phenomenon might stem from the fact that high-tier administrative cities have likely developed robust technology transfer foundations and network externalities, causing their direct effects to approach saturation and thus exhibit diminished local diffusion impacts. Furthermore, as leading drivers of China’s economic development, high-administrative-level cities prioritize inter-regional collaboration and technology transfer, targeting broader markets rather than being confined to local markets. Consequently, the impact of their technology transfer networks manifests predominantly through spatial spillover effects. This explains why the spatial spillover effects of technology transfer networks in high-administrative-level cities are particularly pronounced, accounting for over 90% of the total effects.

Characterized by strong innovative capabilities, mature innovation ecosystems, and cutting-edge research facilities, innovative cities harness their agglomerated science and technology resources, high-end clusters, and dense high-tech firms to persistently advance and spread technologies. Columns (5) and (6) in Table 7 present the heterogeneity tests for spatial spillover effects in innovative cities. Similarly, the direct effect coefficient of innovative cities remains statistically significant at the 1% level, whereas neither the interaction term nor the core explanatory variable shows significant coefficients. This phenomenon may arise because innovative cities serve not only as sources of technological innovation but also as hubs for technology diffusion and knowledge dissemination. As central nodes in technological innovation and transfer, these cities predominantly channel technology transmission and innovation diffusion toward external regions, consequently resulting in relatively weaker local direct effects. However, the indirect effects of innovative cities’ technology transfer networks are statistically significant at the 1% level and constitute most total effects. Leveraging their strong innovation capacity and abundant technological resources, innovative cities persistently extend their influence outward through cross-regional collaboration, knowledge spillovers, and industrial chain synergies.

5. Conclusions

A growing body of research has begun focusing on the impact of regional innovation networks, particularly technology transfer networks, on node cities. This study contributes to this expanding literature by demonstrating, at the urban level, how spatial spillover effects from technology transfer networks influence innovation capabilities in both focal cities and their neighboring cities. First, this study utilizes a unique intercity patent transfer database to construct China’s technology transfer networks at the prefecture level and above for the period 2001–2020. Second, employing patent authorizing data from the CNRDS database to measure urban innovation capacity, a panel dataset comprising 286 Chinese prefecture-level and above cities (2000–2020) is constructed to empirically examine the research questions. Third, four network centrality metrics, including degree centrality, eigenvector centrality, structural hole constraint, and betweenness centrality, are employed to quantify the structural position characteristics of node cities within the technology transfer networks. Building on this framework, this study investigates whether technology transfer can enhance the innovation capacity of cities with similar spatial characteristics through induced spatial knowledge spillover effects. The main findings of this study are as follows:

A significant spatial correlation exists between technology transfer networks and innovation in Chinese cities. Intercity technology transfer not only promotes local cities’ innovation capacity but also benefits cities with similar spatial characteristics through spatial knowledge spillover. (1) Moran’s I tests reveal that the spatial distributions of both the technology transfer networks and urban innovation capacity across China’s prefecture-level cities are non-random, exhibiting strong spatial dependence, distinct clustering patterns, and statistically significant positive spatial autocorrelation. (2) Markov chain analysis demonstrates significant convergence tendencies among cities with similar technology transfer network intensities, accompanied by pronounced spatial spillover effects. Regional contexts characterized by low or intermediate–low technology transfer network intensity exert a negative influence on urban state transitions. Conversely, cities embedded in high or intermediate–high intensity networks exhibit higher probabilities of upward shifts in both degree centrality and structural holes compared to downward transitions, indicating a positive regional spillover effect on urban state evolution. (3) SDM regression results demonstrate that intercity technology transfer not only enhances local innovation activities but also generates spatial knowledge spillovers that benefit cities with similar spatial characteristics. This suggests that patent transfer linkages with geographically proximate and economically comparable cities particularly foster urban innovation growth. Heterogeneity analysis reveals that these spillover effects are more pronounced among eastern cities, high-administrative-level cities, and innovative cities.

These findings demonstrate that as regional innovation increasingly transcends geographical boundaries, technology transfer networks exhibit significant spatial interdependence with urban innovation. The networks and their induced knowledge spillovers not only enhance a city’s endogenous innovation capacity but also play a pivotal role in advancing innovation at both municipal and regional levels. Therefore, in policy practice, differentiated innovation development strategies should be formulated according to cities’ structural characteristics within the technology transfer networks. A dual-driver approach, combining endogenous capacity building with regionally coordinated development, should be adopted to strengthen strategic scientific capabilities, optimize innovation resource allocation, and cultivate new growth engines.

More specifically, cities should prioritize inter-regional coordination and collaboration by dismantling local barriers to facilitate the flow and sharing of innovation resources. On the one hand, when formulating policies for patent transfer to promote regional innovation development, cities should not only consider their own development conditions but also coordinate with neighboring regions with relevant links and regions with similar economic development levels, strengthen exchanges and cooperation, and effectively utilize their resources through spatial knowledge spillover to promote innovation development in the city and the overall innovation capacity of the regional. On the other hand, to better facilitate regionally coordinated innovation development, it is imperative to enhance the alignment and harmonization of cross-regional policies, thereby achieving more efficient sharing of regional innovation resources and improving the effectiveness of patent transfers. This can be accomplished through targeted incentives, such as differentiated tax policies and funding support tailored to regional contexts, to promote balanced flows of innovation resources and amplify the impact of technology transfer across broader geographical scales.

This study has some limitations. First, although several spatial weight matrices are applied for robustness checks, these spatial weight matrices might not fully capture complex economic and institutional linkages between cities. Future research could explore more sophisticated ways to define spatial relationships. Second, apart from the dependence of spatial weight matrices, spatial econometric methods have some limitations. For example, although the use of spatial econometric methods can detect spillovers, it has difficulty distinguishing the mechanisms of spillover, which need to be explored to identify the mechanisms of spatial spillovers in the future. Third, although invention patents reflect a city’s innovation output to a certain extent, they do not reflect all aspects of urban innovation capacity. Other aspects about innovation can be considered in future research.