Examining the Impact of Urban Connectivity on Urban Innovation Efficiency: An Empirical Study of Yangtze River Delta in China

Abstract

Innovation serves as a vital catalyst for sustainable urban development, with the enhancement of urban innovation efficiency representing a critical strategy to bolster cities’ innovative capacity. Rigorous scientific measurement of urban innovation efficiency and thorough investigation into the key factors influencing it are imperative for advancing urban innovation capacity. Despite this significance, prior research has largely overlooked the impact of urban connections on urban innovation efficiency. Therefore, this paper undertakes the task of measuring the innovation efficiency of 27 cities within China’s Yangtze River Delta (YRD) region using an improved DEA model, while also examining the associated influencing factors. The primary findings are as follows: (1) The comprehensive efficiency of the 27 cities in the YRD remains relatively low, with pure technical efficiency representing a notable constraint, while scale efficiency demonstrates higher overall performance. (2) The cities can be classified into four distinct categories: innovation-leading, innovation-optimizing, innovation-breaking, and innovation-improving cities. (3) The urban innovation efficiency within the YRD exhibits negative spatial spillover effects. (4) And notably, local economic and social characteristics such as human capital and degree of openness play a positive role in enhancing innovation efficiency in YRD cities. Conversely, factors such as economic foundation and government involvement exhibit negative contributions to innovation efficiency enhancement in YRD cities. Additionally, population mobility between cities is identified as a significant contributor to urban innovation efficiency. This study sheds light on the complex dynamics shaping urban innovation efficiency and underscores the importance of leveraging urban connections to bolster innovation capacity in the YRD and beyond.

1. Introduction

In the knowledge economy era, innovation stands out as a pivotal driver of urban economic growth [1]. An increasing number of cities are recognizing the significance of bolstering their urban innovation capacity to enhance core competitiveness, being particularly prominent in large cities [2,3,4]. For instance, in 2023, New York unveiled the PILOT: NYC-A roadmap to make New York the global hub of urban innovation. This initiative is tailored to support technology companies in New York City, fostering their establishment, expansion, and the acceleration of urban innovation [5]. Urban innovation efficiency represents the comprehensive performance concerning the input and output of urban innovation resources, serving as a critical indicator of a city’s science and technology innovation prowess [6,7,8]. Consequently, the scientific and rational measurement of urban innovation efficiency holds profound theoretical significance in optimizing the allocation of regional innovation resources and elevating regional scientific and technological innovation capacity.

In recent decades, an extensive amount of literature has focused on measuring innovation efficiency through the lens of innovation input–output analysis, utilizing methodologies such as stochastic frontier analysis (SFA) and data envelopment analysis (DEA) [8,9]. These studies span various scales, including national, regional, and urban contexts [10,11,12,13,14]. Furthermore, beyond measuring innovation efficiency, researchers have widely examined the determinants of innovation efficiency across dimensions such as local economic conditions, institutional frameworks, and socio-cultural environments [15,16]. Cities are increasingly interconnected, forming regional, national, and global urban networks in an era characterized by globalization, informatization, and networking [17,18,19]. With the advancement of intercity rapid transit systems and the evolution of complex innovation networks, cross-regional innovative city clusters are emerging worldwide [20]. For instance, the Global Innovation Index identifies the world’s top 100 science and technology clusters, with Tokyo–Yokohama ranking as the top-performing cluster, followed by Shenzhen–Hong Kong–Guangzhou, Beijing, Seoul, and San José–San Francisco [21]. Cross-regional collaboration in innovation activities plays a crucial role in exchanging complementary knowledge and facilitating the diffusion of knowledge [22].

Consequently, the trajectory of urban development is influenced not only by local economic and social factors but also by the dynamics of neighboring and interconnected cities, all of which significantly impact urban innovation. Urban innovation efficiency is thus shaped by a combination of local economic and social development conditions, available innovation resources, and the innovation activities of neighboring cities [23,24,25]. However, the role of urban linkages in shaping urban innovation efficiency is largely overlooked in the existing literature. As urban connectivity continues to grow, there is a pressing need for deeper investigation into the mechanisms governing innovation efficiency.

As the largest developing country, China has undergone remarkable economic growth since embarking on its reform and opening-up journey. Throughout this process, both innovation inputs and outputs have surged, propelling China to the forefront of innovative nations. For instance, China’s investment in research and development (R&D) has soared from CNY 5.289 billion in 1978 to CNY 340.88 billion in 2020, accompanied by a corresponding rise in R&D expenditure as a percentage of GDP from 1.46 percent to 2.41 percent. Moreover, the number of patent applications in China has surged from 0.019 million in 1985 to 5.4 million in 2020. Despite these significant strides, there persists a substantial gap between the inputs and outputs of science and technology innovation, indicating that innovation efficiency remains below its optimal level [26]. Hence, there is a critical need to scientifically and systematically measure innovation efficiency and gain insights into the specific mechanisms influencing it in order to enhance it effectively.

The Yangtze River Delta (YRD) region stands out as one of the most developed economic regions in China, boasting significant advantages in science, technology, capital, and market resources, which collectively contribute to its remarkable innovation capabilities. For instance, the YRD is home to an impressive array of innovation resources, including 425 institutions of higher education. Moreover, since the 1990s [27], the YRD has been actively fostering regional integration, a process that gained further momentum when YRD regional integration was elevated to a national strategy in 2018. This concerted effort has led to a surge in cooperation and innovation links among cities, fostering a more robust framework for collaborative innovation [28]. Consequently, this has effectively propelled the enhancement of city innovation efficiency within the region. However, despite these advancements, there remains a significant disparity in the innovation capabilities among different cities within the YRD region, and the impact of inter-city collaborative innovation on urban innovation efficiency remains unclear. Against the backdrop of accelerating YRD integration, the increasingly interconnected links between cities offer a compelling case study for examining the dynamics of urban innovation efficiency. Therefore, this paper selects the YRD as its focal point to measure innovation efficiency and investigate its influencing factors from the perspective of synergistic linkages.

The research framework of the article is structured as follows: Section 2 comprises the literature review and conceptual framework, providing a comprehensive overview of relevant literature and establishing the theoretical underpinnings for the study. Following this, Section 3 delineates the study area, outlines the data processing procedures, and elucidates the research methodology employed. Subsequently, Section 4 delves into the pattern of innovation efficiency, analyzing the trends and characteristics observed within the context of the study. Moving forward, Section 5 examines the primary factors influencing urban innovation efficiency, offering insights into the multifaceted determinants shaping innovation outcomes. Finally, the article concludes with a synthesis of findings and discussions, drawing implications and potential avenues for future research.

2. Literature Review and Conceptual Framework

2.1. Measurement of Innovation Efficiency

The measurement of urban innovation capacity has long been a central focus of innovation studies [29]. Typically, existing studies have relied on indicators of urban innovation outputs, such as the number of urban patents, published papers, and sales of new products, to assess urban innovation capacity [30,31,32].

However, the relationship between innovation inputs and outputs is intricate; high levels of innovation inputs may not necessarily translate into high innovation outputs, leading to low innovation efficiency. As a relative indicator, innovation efficiency gauges the production efficiency exhibited by a given amount of innovation resource input. Compared to direct output indicators like patents, papers, and sales revenue of new products, innovation efficiency better reflects the innovation capacity and level of a region [33,34]. Consequently, it has garnered increasing attention from scholars in recent years.

Scholars typically measure innovation efficiency by analyzing the ratio between innovation inputs and outputs. Evaluation indicators of innovation output are generally clear-cut and are primarily assessed across two dimensions: scientific and technological output, and economic output. Scientific and technological output encompasses metrics such as the number of patent applications, patents granted, and scientific and technological papers published, while economic output involves indicators like turnover in the technological market and total revenue from the sale of industrial new products [35,36,37].

Additionally, two research strands are associated with innovation inputs. The first emphasizes capital and manpower sources in the innovation process, including metrics like the number of scientific and technological employees and expenditure on R&D funding [38,39]. The second strand focuses on comprehensive indicator systems in the innovation input process. For example, Chen et al. (2021) selected 21 indicators across finance, infrastructure, socio-economics, humanities, and education as input indicators of science and technology innovation [40]. However, an excessive number of indicators can lead to variable covariance and may not always accurately reflect the nature of innovation. Some models even impose limits on the number of input and output indicators; for instance, the DEA model generally stipulates that the sum of input and output indicators should be less than or equal to one-third of the number of evaluation units [41].

Regarding specific measurement methods for innovation efficiency, there are primarily two types: parametric estimation methods and non-parametric estimation methods. Non-parametric estimation methods, primarily based on data envelopment analysis (DEA), are widely used as they do not require knowledge of the specific form of the production frontier and can evaluate innovation efficiency without assuming a specific production function [32]. This study also employs the DEA method for measuring innovation efficiency.

2.2. Determinants of Urban Innovation Efficiency

Urban innovation efficiency is influenced by a myriad of factors, with localization and globalization playing pivotal roles. Localization factors encompass economic development levels, infrastructure quality, industrial agglomeration, and governmental influence, yet the conclusions drawn from studies on these factors often vary. For instance, the impact of local government involvement in R&D and innovation remains uncertain. While governments can provide financial and policy support to innovation entities, fostering a fair competitive market environment that enhances urban innovation efficiency, excessive intervention may stifle the initiative for independent innovation among enterprises. This, in turn, hampers the optimal allocation of innovation resources and diminishes innovation efficiency [42,43].

On the other hand, globalization factors, such as foreign direct investment, can bolster regional innovation efficiency through both indirect spillover effects and their own direct enhancement of innovation capacity. However, they may also trigger a “crowding out effect” on the host country’s innovation by competing for innovation resources [42,44].

Urban innovation efficiency is not solely determined by local economic conditions, technological inputs, and social and cultural environments but is also influenced by neighboring regional innovation activities [23,24,25]. Yet, previous studies have largely overlooked the interactions between different cities. It was highlighted that inter-regional collaborative innovation behaviors, such as patent cooperation, thesis collaboration, personnel and capital mobility, play a crucial role in enhancing innovation efficiency. For example, Yu et al. (2023) discovered that the agglomeration of regional knowledge yields a positive spatial spillover effect on innovation efficiency, whereas the agglomeration of regional technology has a negative spatial spillover effect [23]. Similarly, Sheng et al. (2019) argued for a significantly positive spatial spillover effect between cities on innovation efficiency due to close socioeconomic linkages and the flow of innovation resources [24].

In summary, current research on the factors influencing innovation efficiency predominantly focuses on local attributes, overlooking the interactions between different regions and underemphasizing the role of regional collaborative innovation in local innovation efficiency. Therefore, there is a pressing need for deeper exploration and analysis in this area.

2.3. Conceptual Framework

Building upon the preceding discussions, innovation efficiency can be gauged by analyzing the proportional relationship between innovation inputs and outputs. Regarding innovation inputs, scientific and technological human resources, along with financial resources, constitute the fundamental elements essential for scientific and technological production to occur [33]. Thus, we primarily chose research and experimental development (R&D) personnel and expenditure as variables to measure human and financial resource inputs, respectively. From the perspective of innovation outputs, scientific papers and patents serve as tangible manifestations of research outcomes and are crucial for quantifying the output of scientific and technical innovation [33]. Among these, invention patents encapsulate a more intricate amalgamation of knowledge and exhibit a higher degree of innovativeness compared to utility model patents and design patents. Hence, we opted to utilize the number of invention patent applications and scientific papers as output indicators in this study (see Figure 1).

The innovation outputs of a region are influenced not only by various factors such as local economic conditions, scientific and technological inputs, and the policy environment but also by the developmental status of neighboring regions. In the context of the transition from “local space” to “flow space” [45], the establishment of a network-based innovation development model, facilitated by various types of linkages, emerges as a novel paradigm for regional innovation [24]. This model aims to promote the interactive flow of innovation resources and elements, facilitating the exchange of knowledge and technology. Consequently, regional innovation efficiency is determined not only by local economic and social development factors but also by the dynamics of inter-regional collaborative innovation.

Therefore, based on the assessment of innovation efficiency across 27 cities in the Yangtze River Delta in 2018, this study delves deeper into the influencing factors of urban innovation efficiency. It not only examines the impact of local economic and social characteristics—including the level of economic development, human capital, government participation (degree of marketization), and economic openness—on innovation efficiency but also integrates variables reflecting inter-city collaborative innovation (see Figure 1). This comprehensive analysis aims to evaluate the role of different dimensional variables in enhancing innovation efficiency. To guide our empirical study, we propose hypotheses that specify the factors influencing urban innovation efficiency as follows:

Hypothesis 1.

A city’s innovation efficiency increases with higher levels of economic development, richer human capital, greater market openness, and reduced government intervention.

Hypothesis 2.

Strengthened investment linkages with other cities and increased population mobility significantly contribute to enhancing a city’s innovation efficiency.

3. Data and Methods

3.1. Study Area

The Yangtze River Delta (YRD) stands out as one of China’s most economically advanced regions, distinguished by its unparalleled level of openness and robust innovation capacity. Positioned strategically, the YRD plays a pivotal role in China’s modernization efforts and comprehensive opening-up strategy. Facilitating the integrated development of the YRD and bolstering its innovation and competitiveness holds profound significance in spearheading China’s high-quality development and constructing a modernized economic framework.

On 1 December 2019, the Central Committee of the Communist Party of China (CPC) and the State Council unveiled the Outline of the Plan for the Integrated Development of the YRD Region, a comprehensive blueprint guiding the region’s integrated development in the present and future. This document serves as the cornerstone for devising pertinent plans and policies. The outlined policy framework sets the trajectory for the YRD’s innovation landscape in the years to come. Consequently, our study predominantly focuses on the central area outlined in the aforementioned plan, encompassing the following 27 cities: Shanghai, Nanjing, Wuxi, Changzhou, Suzhou, Nantong, Yangzhou, Zhenjiang, Yancheng, Taizhou, Hangzhou, Ningbo, Wenzhou, Huzhou, Jiaxing, Shaoxing, Jinhua, Zhoushan, Taizhou, Hefei, Wuhu, Ma’anshan, Tangling, Anqing, Chuzhou, Chizhou, and Xuancheng (see Figure 2).

3.2. Data Sources

In our assessment of innovation efficiency across YRD cities, we primarily focused on two key variables to gauge human and financial resource inputs: research and experimental development (R&D) personnel, and R&D expenditure, respectively. Additionally, we selected the number of invention patent applications and the volume of scientific and technological papers as output indicators. Data regarding R&D personnel and expenditure were sourced from the China City Statistical Yearbook and local statistical bulletins. Information pertaining to invention patents was obtained from the State Intellectual Property Office, while data on scientific and technological papers were sourced from the Chinese Journal Full-Text Database.

Given the disruptive impact of the COVID-19 epidemic on social mobility and urban connectivity, we made a deliberate effort to mitigate its effects by focusing our investigation on data preceding 2019. Furthermore, recognizing that the influence of innovation inputs on output efficiency typically entails a noticeable lag time [46], we utilized input data from 2017, while predominantly relying on output data from 2018.

In our examination of the factors influencing innovation efficiency in YRD cities, GDP per capita, year-end deposit and loan balances of financial institutions, the number of university students, the proportion of science and technology expenditures in local financial expenditures, and the amount of actual utilized foreign investment are sourced from corresponding years of the China Urban Statistical Yearbook and Local Statistical Yearbook. However, data concerning listed enterprises are sourced from the annual report database of listed enterprises of Wind, whereas information regarding population flow is derived from Baidu migration data.

3.3. Data Envelopment Analysis

In this paper, we employ Data Envelopment Analysis (DEA) to evaluate urban innovation efficiency. DEA, introduced by Charnes, Cooper, and Rhodes in 1978, is a non-parametric technique for assessing technical efficiency through relative comparisons among evaluated entities [47]. This method offers several advantages over alternative assessment approaches, including its straightforward structure, elimination of the need to predetermine comparability and indicator weights, provision of insights into identifying inefficient aspects, and suitability for evaluating the relative efficiency of national or regional innovation inputs and outputs [48].

The DEA model based on Constant Returns to Scale (CRS) can be expressed as follows:

$$\left\{\begin{array}{c}\min (\mathsf{\theta }-\mathsf{\epsilon }({\displaystyle \sum _{k=1}^K}{s}^{-}+{\displaystyle \sum _{l=1}^L}{s}^{+}))\\ \mathrm{s}.\mathrm{t}.{\displaystyle \sum _{\mathrm{m}=1}^{\mathrm{M}}}{\mathrm{X}}_{\mathrm{mk}}{\lambda }_{\mathrm{m}}+s^{-}=\theta {\mathrm{X}}_{\mathrm{k}}^{\mathrm{m}} \mathrm{k}=\mathrm{1,2},\cdots ,\mathrm{K}\\ {\displaystyle \sum _{\mathrm{m}=1}^M}{y}_{\mathit{ml}}{\lambda }_{\mathrm{m}}-s^{+}=y_l^m l=1, 2, \cdots , L\\ {\lambda }_{\mathrm{m}}\ge 0 m=1, 2, \cdots , M\end{array}\right.$$

In the formula, θ (0 < θ ≤ 1) signifies the comprehensive index of input–output efficiency, referred to as the comprehensive efficiency index. When evaluating the input–output efficiency of innovation resources across M cities, assuming an evaluation indicator system comprising K input indicators and L output indicators, where x_mk (x_mk > 0) denotes the volume of the k^th type of resource input in the m^th city, and y_ml (y_ml > 0) represents the volume of the l^th type of output in the m^th city. For the m^th city (m = 1, 2, …, M), ε denotes a non-archimedean infinitesimal quantity. λ_m (λ_m ≥ 0) serves as a weighting variable determining returns to scale for urban innovation resources. s⁻ (s⁻ ≥ 0) denotes a slack variable indicating the reduction in inputs required for R&D resources to achieve DEA effectiveness, while s⁺ (s⁺ ≥ 0) represents a residual variable indicating the additional output needed for innovation resources to attain DEA effectiveness.

When an optimal solution θ_m = 1 is achieved, it signifies that the innovation resources of the m^th city are operating on the optimal production frontier, and the city’s innovation outputs are efficient relative to the inputs. Conversely, θ_m < 1 indicates inefficiency in the utilization of innovation resources, with values closer to 1 indicating closer proximity to effective input–output efficiency, and vice versa [48].

Introducing constraint conditions and transforming the model into a DEA model of Variable Returns to Scale (VRS), the overall efficiency can be decomposed into the product of pure technical efficiency and scale efficiency, expressed as θ_m = θ_TE × θ_SE. Here, θ_m represents the overall efficiency index of innovation resources for the mth city; θ_TE denotes the pure technical efficiency (TE) index, with 0 < θ_TE ≤ 1 and θ_TE ≥ θ_m; θ_SE signifies the scale efficiency (SE) index, with 0 < θ_SE ≤ 1 and θ_SE ≥ θ_m. Similarly, higher values of θ_TE and θ_SE approaching 1 indicate higher levels of pure technical and scale efficiency of input–output innovation resources. When θ_TE = 1 or θ_SE = 1, the city’s innovation resources are optimal in terms of pure technical or scale efficiency [48].

3.4. Spatial Regression Models

Considering the spatial correlations inherent in urban innovations, it becomes imperative to incorporate spatial effects when investigating the determinants of urban innovation efficiency through regression models. Spatial lag models (SLM) and spatial error models (SEM) are commonly employed to address the spatial interactions among variables. In our study, we utilize both models to elucidate the factors influencing the innovation efficiency of YRD cities.

The spatial lag model (SLM) accounts for the spatial autocorrelation of the dependent variable, thereby capturing potential diffusion or agglomeration effects in neighboring areas. Its formula is expressed as

y = ρWy + Xβ + ϵ

where y represents the dependent variable, X denotes the independent variable, W denotes the spatial weight matrix, Wy signifies the spatial lagged dependent variable, β represents the coefficient to be estimated, ρ denotes the spatial error coefficient, and ε represents the random error following a normal distribution.

On the other hand, the spatial error model (SEM) considers the spatial interactions present in the error term. It is mathematically represented as

y = Xβ + ε

ε = λWε + μ

where y denotes the dependent variable, X denotes the independent variable, W represents the spatial weight matrix, β signifies the coefficient to be estimated, λ denotes the spatial error coefficient, and ε and μ represent the random errors following normal distributions, respectively.

The spatial weight matrix W is constructed based on the common boundary or vertices adjacency rule (Queen), where W = 1 if two cities share a common boundary or adjacent vertices, and W = 0 otherwise.

4. Innovation Efficiency Patterns in YRD Cities

The efficiency of science and technology innovation serves as a crucial manifestation of a region’s science and technology innovation capacity, offering comprehensive insights into the effective allocation, rational utilization, and management of regional science and technology innovation resources [25]. The original output results from DEA analysis, as analyzed using MaxDEA 8 software, encompass three efficiency metrics: comprehensive efficiency, pure technical efficiency, and scale efficiency (see

Table 1. Innovation Efficiency of 27 Cities in the YRD.

Cities	Comprehensive Efficiency	Pure Technical Efficiency	Scale Efficiency
Shanghai	0.432	1.000	0.432
Nanjing	1.000	1.000	1.000
Wuxi	0.280	0.282	0.994
Changzhou	0.369	0.374	0.987
Suzhou	0.431	1.000	0.431
Nantong	0.334	0.338	0.987
Yangzhou	0.424	0.432	0.980
Zhenjiang	0.414	0.416	0.997
Yancheng	0.409	0.416	0.984
Taizhou	0.388	0.397	0.978
Hangzhou	0.449	0.630	0.713
Ningbo	0.358	0.358	0.999
Wenzhou	0.379	0.431	0.878
Huzhou	0.773	0.774	0.999
Jiaxing	0.432	0.441	0.979
Shaoxing	0.252	0.253	0.997
Jinhua	0.368	0.394	0.934
Zhoushan	0.506	0.611	0.828
Taizhou	0.302	0.313	0.963
Hefei	0.529	0.786	0.673
Wuhu	1.000	1.000	1.000
Maanshan	0.493	0.518	0.953
Tongling	0.285	0.318	0.898
Anqing	1.000	1.000	1.000
Chuzhou	0.765	0.771	0.993
Chizhou	0.969	1.000	0.969
Xuancheng	0.455	0.504	0.902
Average Value	0.511	0.584	0.905

).

Comprehensive efficiency reflects the innovation production efficiency of the decision-making unit (DMU) based on a specific scale of innovation input factors. A value of 1 indicates that the input–output of the DMU is deemed effective. Pure technical efficiency pertains to the efficiency of innovation production with a predetermined level of inputs, such as management and technology. Similarly, a value of 1 signifies efficient utilization of the decision-making unit’s input resources. Scale technical efficiency, on the other hand, denotes the level of innovation production efficiency achieved through scale efficiency in the region [46].

4.1. Comprehensive Efficiency

Regarding comprehensive efficiency, the average score across the 27 cities in the YRD for the year 2018 stood at a modest 0.511, indicating an overall lower level of efficiency. Notably, only three cities—Nanjing in Jiangsu Province, and Wuhu, and Anqing in Anhui Province—achieved a perfect score of 1.000, signaling optimal efficiency levels. Additionally, Chizhou and Chuzhou in Anhui Province, along with Huzhou in Zhejiang Province, demonstrated a commendable comprehensive efficiency exceeding 0.700. Conversely, cities in Zhejiang, most cities in Jiangsu, and even Shanghai exhibited relatively lower comprehensive efficiency scores.

For instance, the comprehensive efficiency of Wuxi and Shaoxing hovered below 0.300, specifically at 0.280 and 0.252, respectively, falling short of the optimal efficiency benchmark by 30%. Shanghai, despite its prominence, also registered a relatively modest comprehensive efficiency score of 0.432, ranking 12th among the 27 cities (see Figure 3).

4.2. Pure Technical Efficiency

In 2018, the average pure technical efficiency across the 27 cities stood at 0.584. Notably, Nanjing, Wuhu, Anqing, Chizhou, Shanghai, and Suzhou demonstrated exemplary pure technical efficiency, achieving a perfect score of 1.000 in both innovation resource input and output. Following closely behind are cities such as Hefei, Huzhou, and Chuzhou, which attained pure technical efficiency levels ranging between 70% and 90% of the optimal value. Meanwhile, cities like Hangzhou, Zhoushan, and Maanshan operated at levels between 50% and 70% of the optimal value of pure technical efficiency.

Furthermore, twelve cities exhibited pure technical efficiency falling within the range of 30% to 50% of the optimal value, collectively representing 44.4% of all cities. Wuxi and Shaoxing recorded the lowest pure technical efficiency, standing at 0.282 and 0.253, respectively, both falling below 30% of the optimal value (see Figure 3). Interestingly, despite Nanjing, Shanghai, and Suzhou showcasing high pure technical efficiency, their comprehensive efficiency did not reach optimum levels, primarily due to scale inefficiency. This suggests that while these cities effectively utilize their input resources at the current technological level, the lack of efficiency in scale utilization impedes them from achieving optimal comprehensive efficiency. Hence, future efforts should focus on maximizing scale efficiency to unlock further breakthroughs in innovation efficiency.

4.3. Scale Efficiency

In 2018, the average scale efficiency of innovation inputs and outputs across the 27 cities stood at 0.905, surpassing the average values of both comprehensive and pure technical efficiency. However, only three cities—Nanjing, Wuhu, and Anqing—achieved a perfect score of 1.000, indicating that the scale efficiency of other cities still had room for optimization.

Notably, the scale efficiency of seventeen cities fell within the range of 90% to 100% of the optimal value, encompassing 63% of all cities. Additionally, three cities—Tongling, Wenzhou, and Zhoushan—attained the optimal value of scale efficiency between 80% and 90%. Hangzhou and Hefei, with scale efficiency values ranging between 60% and 70%, represent two cities within this bracket.

Interestingly, Shanghai and Suzhou recorded the lowest scale efficiencies, standing at 0.432 and 0.431, respectively, ranking penultimate and first among the cities. Despite their significant investments in innovation, these cities, along with Hangzhou and Hefei, have not effectively translated their efforts into improved innovation efficiency. Therefore, optimizing the scale structure becomes a critical area for improvement.

Model calculations indicate that for further enhancements in innovation efficiency, nine cities—Shanghai, Hangzhou, Hefei, Suzhou, Wenzhou, Jinhua, Taizhou, Jiaxing, and Ningbo—should focus on streamlining their scale and enhancing the quality of R&D investment, rather than solely focusing on increasing scale.

4.4. Types of Innovation Input–Output

The trajectory of urban innovation development primarily hinges on both innovation inputs and innovation efficiency. The magnitude of inputs serves as a barometer for the abundance of urban science and technology innovation resources, while innovation efficiency reflects the effective allocation and utilization of these resources. Generally, cities boasting high inputs and high efficiency are inclined to witness more robust science and technology innovation development [31].

Following the methodology employed by Liu et al. (2018) [31], the 27 cities are stratified based on the scale of innovation investment and the level of innovation efficiency to unveil the underlying patterns of science and technology innovation development. Leveraging the Quantile classification method, the R&D investment scale and innovation efficiency of these cities in 2018 are categorized into high, medium, or low tiers. The R&D investment scale is delineated into three levels: high investment (CNY >13.5 billion), medium investment (CNY 6.5 billion to CNY 13.5 billion), and low investment (CNY <6.5 billion). Similarly, innovation efficiency is segmented into three efficiency levels: high efficiency (>70%), medium efficiency (40% to 70%), and low efficiency (<40%). By considering the input scale and efficiency level of each city, nine distinct types of input-efficiency patterns of scientific and technological innovation are identified, as illustrated in

Table 2. Categorization of 27 Cities in the YRD by City Innovation Inputs and Comprehensive Innovation Efficiency.

Innovation Inputs		Comprehensive Efficiency
		High Efficiency	Medium Efficiency	Low Efficiency
Input Scale	High Input	Nanjing	Hefei, Hangzhou, Shanghai, Suzhou, Yangzhou	Changzhou, Ningbo, Wuxi, Nantong
	Medium Input	Wuhu, Huzhou	Jiaxing, Zhenjiang, Yancheng	Taizhou, Wenzhou, Taizhou, Shaoxing
	Low Input	Chuzhou, Anqing, Chizhou	Zhoushan, Maanshan, Xuancheng	Jinhua, Tongling

. Building upon Liu’s (2018) classification method [31], these types are further comprehensively delineated (see Figure 4).

Innovation-leading cities: This category encompasses eight cities of three distinct types: high input-high efficiency, exemplified by Nanjing; high input-medium efficiency, represented by Hefei, Hangzhou, Shanghai, Suzhou, and Yangzhou; and medium input-high efficiency, characterized by Wuhu and Huzhou. These cities boast a robust foundation for innovation, coupled with high levels of economic and social development and abundant scientific and educational resources. Consequently, they possess the potential to emerge as leading innovation hubs within the YRD. Moving forward, the emphasis should be on advancing the frontiers of science and technology and addressing major national needs to bolster the establishment of innovation centers and the cultivation of high-end industries. For cities categorized as high input-medium efficiency, optimizing the structure of innovation inputs and enhancing the quality of innovation resource input is imperative.

Innovation-optimized cities: This category comprises eleven cities, classified into three types: high input-low efficiency (Changzhou, Ningbo, Wuxi, and Nantong), medium input-medium efficiency (Jiaxing, Zhenjiang, and Yancheng), and medium input-low efficiency (Taizhou, Wenzhou, and Shaoxing). These cities possess certain advantages in their innovation base, characterized by relatively high levels of innovation inputs, yet their innovation outputs remain comparatively low. To address this, a concerted effort should be directed toward optimizing the input structure, improving the quality of innovation resource input, and enhancing overall innovation efficiency.

Innovation-breakthrough cities: This category features three cities—Chuzhou, Anqing, and Chizhou—all located in Anhui Province, characterized by low input-high efficiency dynamics. Despite their relatively low input levels, these cities exhibit efficient innovation outputs. Going forward, these cities could leverage local high-tech enterprises to bolster investments in innovation resources.

Innovation-enhanced cities: This category includes five cities, categorized into two types: low input-medium efficiency (Zhoushan, Maanshan, and Xuancheng) and low input-low efficiency (Jinhua and Tongling). These cities exhibit relatively backward levels of economic and social development, suggesting a need for improvement in their innovation foundation. To enhance their innovation capacities, future efforts should focus on strengthening investments in innovative resources in alignment with their specific contexts.

5. Determinants of Innovation Efficiency in YRD Cities

5.1. Variables Selection

This section adopts a two-dimensional approach, drawing variables that influence urban innovation efficiency in the YRD from local socioeconomic characteristics and urban connections. Seven variables are selected to construct the analytical framework of factors influencing urban innovation efficiency in the YRD (see

Table 3. Definition and Expectations of Explanatory Variables.

Variables		Variable Definition	Expected Impact
Local socio-economic characteristics	Economic base	Gross domestic product per capita (CNY)	Positive
	Financial support	Balance of deposits and loans from financial institutions at the end of the year (CNY 10,000)	Positive
	Human capital	The number of university college students enrolled per ten thousand people (individuals)	Positive
	Government participation	The proportion of science and technology expenditure in local government financial expenditure (%)	Negative
	Openness	Proportion of actual utilization of foreign capital to regional GDP (%)	Positive
Inter-city connection characteristics	Investment connection	Network-weighted centrality based on the headquarter–branch investment network of A-share-listed firms	Positive
	Population connection	Network-weighted centrality based on Baidu migration data	Positive

). Among these, the local socioeconomic characteristics encompass five variables, including two pertaining to the economic base and financial support, one relating to human capital in the demographic dimension, and two variables concerning government participation and openness in the institutional dimension. The regional network connection characteristics comprise investment and population connections.

GDP per capita serves as an indicator of the city’s economic development level. Financial support, a critical environmental factor influencing regional innovation efficiency, exhibits an intrinsic connection with urban innovation efficiency, primarily through the financial support-input redundancy-regional innovation efficiency mechanism [49]. The balance of financial deposits and loans at year-end is selected as a proxy for financial support, wherein a higher index suggests cities are more likely to access sufficient funds to encourage local technology enterprises to engage in scientific and technological innovation activities. Consequently, there arises a demand for additional scientific and technological personnel and funding, which reduces input redundancy and enhances innovation efficiency in the city.

Human capital, represented by the number of university students per ten thousand people, plays a crucial role in regional innovation activities. Government influence on regional innovation activities primarily stems from government fiscal expenditure behavior [50]. The proportion of science and technology expenditure in government financial expenditure relative to local financial expenditure is selected to gauge the degree of government participation in regional innovation activities [51]. Cities with higher levels of openness are predisposed to introducing and utilizing advanced technological innovation achievements, thereby improving local innovation efficiency. The proportion of foreign capital utilization to regional GDP serves as an indicator of the degree of openness.

Intercity investment connections, fostered through cross-city investments by firms, facilitate the interactive flow of innovative resource factors, knowledge, and technology spillover and diffusion. Regional investment connection networks promote the flow and integration of innovation resources among different network nodes, thereby enhancing regional innovation efficiency. Network-weighted centrality based on the headquarter–branch investment network of A-share-listed firms is selected to signify intercity connections. Additionally, the dynamic evolution of population mobility’s scale and distribution pattern influences the redistribution of talent and innovation resources among cities, ultimately affecting innovation output and efficiency. Network-weighted centrality based on Baidu migration data serves as an indicator of population mobility.

To address heteroscedasticity and reduce variable fluctuation, the extreme variance normalization method is applied to the explanatory variables before model estimation. To apply this method, begin by identifying the maximum (Xmax) and minimum (Xmin) values of the indicator and calculate the range (R = Xmax − Xmin). Then, for each data point (X) of the variable, compute X′ = (X − Xmin)/(Xmax − Xmin). This normalization ensures that each observation in the variable falls within the range 0 ≤ X′ ≤ 1, transforming all values into positive indicators and aligning them consistently. Table 3 outlines the definition and expected impact of explanatory variables, with descriptive statistics of standardized data provided in

Table 4. Descriptive Statistics of Explanatory Variables.

Variables		Mean	Median	Standard Deviation	Variance
Urban socio-economic characteristics	Economic base	0.4706	0.4590	0.2849	0.0812
	Financial support	0.1275	0.0717	0.2009	0.0403
	Human capital	0.2293	0.1780	0.2188	0.0479
	Government participation	0.2949	0.2785	0.1924	0.0370
	Openness	0.2429	0.1757	0.2407	0.0579
Inter-city connection characteristics	Investment connection	0.1656	0.0918	0.2157	0.0465
	Population connection	0.2628	0.1589	0.2554	0.0652

.

5.2. Determinants of Urban Innovation Efficiency

The regression results regarding the influencing factors of urban innovation efficiency in the YRD are presented in

Table 5. Regression Results of the Determinants of Innovation Efficiency in YRD Cities.

Variables		OLS	SLM	SEM
Local socio-economic characteristics	Economic base	−0.4549 ** (0.1995)	−0.4743 *** (0.1672)	−0.2975 *** (0.1132)
	Financial support	−0.1049 (0.8632)	0.1044 (0.7121)	0.4830 (0.6716)
	Human capital	0.3989 (0.2835)	0.3928 * (0.2310)	0.3531 ** (0.1683)
	Government participation	−0.1718 (0.3005)	−0.1813 (0.2480)	−0.5640 ** (0.2242)
	Openness	0.1578 (0.2228)	0.2337 (0.1842)	0.4336 *** (0.1544)
Urban connection characteristics	Investment connection	−0.4429 (0.8887)	−0.8076 (0.7483)	−1.2140 (0.6429)
	Population connection	0.6376 (0.4821)	0.7803 * (0.3984)	0.8659 *** (0.2811)
	Constant	0.5651 *** (0.0937)	0.6738 *** (0.1269)	0.5314 *** (0.0563)
	ρ	/	−0.2429	/
	λ	/	/	−0.8861 ***
	R2	0.4780	0.5074	0.6345
	LogL	9.8736	10.4851	12.3519
	AIC	−3.7471	−2.9701	−8.7038
	SC	6.6196	8.6924	1.6629

Note: *, ** and *** are statistically significant at 10%, 5% and 1%, respectively.

. Evaluating from the perspective of R² values, the spatial error model demonstrates the highest coefficient at 0.6345, indicating a potentially strong fit for the model. Further comparison involving the log-likelihood function value (LogL), the Akaike information criterion (AIC), and the Schwartz criterion (SC) corroborates this finding. Notably, the spatial error model exhibits the highest LogL value alongside the lowest AIC and SC values. Following the criterion proposed by Anselin (1988) [52], it can be deduced that the spatial error model stands as the most appropriate model for this analysis, offering the best goodness of fit. Consequently, our primary focus is directed towards the regression outcomes derived from the spatial error model.

5.2.1. Urban Socio-Economic Characteristics

In YRD cities, urban socio-economic characteristics are pivotal in shaping innovation efficiency. Below, we delineate the specific impacts.

To begin, the regression coefficient of the economic base on innovation efficiency in YRD cities unveils a notable negative association at a confidence level of 1%. Holding other variables constant, a 1% increase in the economic base results in a 0.2975% decline in urban innovation efficiency. Contrary to expectations, heightened levels of urban economic development do not consistently translate into improved innovation efficiency. This observation can be interpreted in two ways.

On one hand, cities with a robust economic base often possess the capacity to invest in innovation. However, many YRD cities with significant innovation investments lack corresponding advancements in innovation management capabilities and supportive infrastructure. Consequently, in regions with advanced economic development, efforts to enhance innovation management capacity and construct innovation ecosystems lag behind the influx of innovation resources, resulting in a haphazard innovation development paradigm and diminished efficiency.

On the other hand, some cities with strong economic fundamentals fail to capitalize on the scale effect of their investments in science and technology innovation. Despite high levels of innovation resource investment, the distribution remains dispersed or congested, hindering efforts to bolster innovation efficiency.

Moving on, the regression coefficient of the financial development scale on regional innovation efficiency appears positive but insignificant. This suggests that cities still require a conducive financial development environment to foster science and technology innovation and enhance the capacity of financial services to support the real economy and drive innovation-led development.

Furthermore, the regression coefficient for human capital is 0.3531, significant at a 5% level. This indicates that each 1% increase in human capital contributes 0.3531% to enhancing the city’s innovation efficiency. This finding resonates with prior national and international studies, underscoring the pivotal role of human capital, measured here as the number of university students per 10,000 people, in fostering regional innovation.

Moreover, the effect of government involvement on innovation efficiency in YRD cities is significantly negative (−0.564). This suggests that government financial inputs do not significantly contribute to technological innovation efficiency and may even have a counterproductive effect. The inefficient allocation of local government financial resources towards science and technology expenditures hinders the construction of regional innovation systems, adversely affecting urban innovation efficiency.

Lastly, the regression coefficient for openness is 0.4336, significant at the 1% level. This finding supports the “global pipeline-local buzzing” theoretical hypothesis by Bathelt (2004) [53]. Increased openness attracts cross-border capital, often accompanied by advanced knowledge and technology, fostering an eclectic mix of knowledge production systems and improving innovation efficiency in YRD cities [54].

5.2.2. Urban Connections

The interconnectivity among cities within the YRD has shown a notable increase over time. A prime illustration of this trend can be observed in the realm of patent cooperation among these cities. Since the year 2000, there has been a discernible enrichment in innovation collaboration among YRD cities, gradually forming an intricate innovation network (see Figure 5). Initially, in 2000, the count of patent collaborations among the 27 cities in the YRD stood at a mere 20, occurring across 11 cities. However, by 2019, the landscape had transformed significantly. The number of patent collaborations among the 27 cities within the YRD surged to 5988, with every single city actively participating in the cooperative framework. Notably, Shanghai emerged as the preeminent node, engaging in patent collaborations with 26 cities and contributing 2044 patents, constituting 34.1% of the total collaborations. To ascertain the impact of enhanced city linkages on innovation efficiency, we chose investment and personnel linkages as variables for examination.

While the impact of regional investment network connections may appear insignificant, the characteristics of regional population network connections stand out as crucial factors in enhancing the innovation efficiency of YRD cities.

Specifically, the level of city investment connections does not exert a significant influence on the innovation efficiency of cities. Nevertheless, it is crucial to underscore the importance of enhancing the role of intercity investment networks in optimizing the allocation of innovation resources.

Conversely, the regression coefficient for population mobility demonstrates a significant positive effect at the 1% level (0.8659). Reasonable population flow among YRD cities fosters the spatial allocation of innovation resources and facilitates effective knowledge spillover, thereby positively impacting innovation efficiency.

In summary, despite only the population mobility variable showing a positive impact, it still lends partial support to the research hypothesis of this paper. This hypothesis suggests that inter-city linkages contribute to the enhancement of urban innovation efficiency. While other variables may not demonstrate significant effects, the positive influence of population mobility underscores the importance of inter-city connections in fostering innovation efficiency within YRD cities.

5.2.3. Spatial Spillover Effects

The spatial error term in the model indicates negative spatial spillover effects (−0.8861), suggesting that an increase in innovation efficiency in one city does not effectively lead to an increase in neighboring cities’ efficiency. This underscores the need to address the lack of effective synergistic development of innovation efficiency among YRD cities, emphasizing the importance of regional science and technology innovation development.

These findings provide valuable insights into the factors shaping innovation efficiency in YRD cities, highlighting areas for policy intervention and strategic focus to enhance regional innovation ecosystems and drive sustainable development. Further testing and discussion are necessary to validate the stability of these conclusions.

6. Conclusions and Discussion

Urban innovation efficiency serves as a comprehensive indicator reflecting the relationship between urban innovation resource input and output, thus offering crucial insights into urban science and technology innovation capability. Against the backdrop of the deep integration of the Yangtze River Delta (YRD), it becomes paramount to scientifically assess and analyze the innovation efficiency of cities in the region. This endeavor aims to optimize the allocation of regional innovation resources and synergistically enhance the innovation capacity and efficiency of YRD cities. Accordingly, this study utilized an improved DEA model to measure the innovation efficiency of 27 cities in the YRD and scrutinized the factors influencing this efficiency. The main conclusions are as follows:

Firstly, the overall comprehensive efficiency of the 27 cities in the YRD remains low, with only three cities—Nanjing, Wuhu, and Anqing—attaining an optimal comprehensive efficiency score of 1.000. Notably, Shanghai, as the largest city, exhibits innovation efficiency ranking only 12th among the 27 cities, falling short of expectations.

Secondly, pure technical efficiency emerges as a notable weakness among the 27 cities in the YRD, with most cities falling within the 30–50% range of optimal efficiency. In contrast, scale efficiency tends to outperform the average values of comprehensive and pure technical efficiency. However, Shanghai and Suzhou display the lowest scale efficiency among the cities.

Thirdly, the cities in the YRD can be classified into four types based on the scale of innovation inputs and efficiency levels, namely, innovation-leading cities, innovation-optimized cities, innovation-breakthrough cities, and innovation-enhanced cities.

Fourthly, urban socio-economic characteristics and inter-city connections exert significant impacts on urban innovation efficiency in the YRD. Human capital and openness positively contribute to improving innovation efficiency, whereas variables like economic base and government involvement pose certain obstacles to enhancing innovation efficiency. The mobility of populations between cities emerges as a critical determinant in enhancing innovation efficiency and enabling the effective spatial distribution of innovation resources, thereby facilitating knowledge spillovers. This phenomenon lends credence to the hypothesis that strong inter-city connections play a pivotal role in augmenting urban innovation efficiency.

Lastly, the study reveals a negative spatial spillover effect in YRD cities’ innovation efficiency, indicating a lack of effective synergistic development. Addressing this challenge and enhancing the innovation efficiency of YRD cities constitute vital imperatives in the integration process of the YRD.

Moreover, we advocate considering both internal and external factors to bolster innovation efficiency in YRD cities. Internally, there is a pressing need to bolster the city’s intrinsic innovation capabilities. This can be achieved by intensifying efforts to attract and nurture high-caliber scientific and technological talent, enhancing the city’s integration with global markets, optimizing the allocation of government innovation funds, and maximizing their efficacy. Externally, fostering collaborative innovation networks among cities is paramount. Strengthening these networks involves establishing robust collaborative innovation platforms, diversifying the channels for collaborative innovation, and refining the institutional mechanisms governing collaborative endeavors.

In summary, we developed an analytical framework to assess urban innovation efficiency and systematically explored the influence of both local and regional synergistic factors using spatial econometric models. Our findings demonstrate that regional innovation efficiency is shaped not only by local conditions but also by regional synergies. This contribution fills a gap in previous research, which predominantly focused on local factors while overlooking regional dynamics, thereby advancing the theoretical underpinnings of innovation efficiency.

Moreover, as intercity rapid transportation systems advance and complex innovation networks evolve, cross-regional innovative city clusters have emerged. Examples include regions such as the San Francisco Bay Area in the United States, the Ponewah City Cluster, and the Tokyo Bay Area in Japan. Our empirical study centered on China’s Yangtze River Delta city cluster lays the groundwork for promoting the formation of innovative city clusters. Additionally, our findings contribute to the development of policies that support innovation within these clusters.

However, our current study offers only a partial view of regional collaborations due to the limited number of variables measuring regional linkages. Future research could broaden this scope by incorporating more indicators and diverse datasets to provide a more comprehensive understanding of regional innovation networks. Furthermore, longitudinal studies examining the evolving impact of collaborative urban innovation on city innovation efficiency would yield valuable insights over time.