The Impact of Interregional Collaboration on Multistage R&D Productivity and Their Interregional Gaps in Chinese Provinces

Abstract

Interregional collaboration is a core element of Chinese innovation policy, as it accelerates the knowledge recombination across geographic boundaries and promotes regional R&D performance. This study emphasizes interregional collaboration and investigates its effect on R&D productivity using 2009–2017 panel data for 30 Chinese provinces. Furthermore, it examines the relationship between interregional research collaboration and interregional gaps of R&D productivity based on a multistage perspective. Our findings reveal that although interregional collaboration and R&D productivity in China constantly improved during the study period, there is to some extent a mismatch in their spatial distribution. We find that interregional collaboration is required to support overall R&D productivity. We also emphasize that interregional collaboration contributes more to narrowing the interregional gaps of knowledge productivity (rather than technology transfer productivity).

1. Introduction

Research collaboration is considered a major component of agglomeration economies and plays a key part in analyzing the spatial heterogeneity of innovation [1,2,3,4]. The research cooperation across geographic boundaries could reinforce regional innovation capability by continuously reorganizing knowledge embedded in innovation actors [5,6,7]. Many studies have found evidence for the significant impact of regional research cooperation on economic growth and R&D productivity [8,9]. Based on these views, many countries/regions have carried out innovative policies encouraging regional research collaboration.

Most previous studies have captured research collaboration from a geographic knowledge spillover perspective [10,11]. Studies of research collaboration at the micro level have revealed that the different ways of spillover effects resulting from regional research collaboration are largely localized [12]. It is well known that the codification of knowledge is imperfect and is therefore related to a particular researcher’s experience or is “attached” to persons, and it spreads through personal relationships and face-to-face communication promoted due to spatial proximity. While geographical proximity is often a good channel for tacit knowledge flow, some authors believe that it may be overestimated and that other forms of proximity (relational proximity and so on) and their interplay with spatial features are ignored [13,14,15,16]. Previous studies emphasized the role of collaboration networking among organizations and regions as paths of knowledge flow. Compared to informal networks, which operate within particular regions, leading to localized knowledge spillovers [17], a formal collaboration network across regions is a significant path for knowledge spillover beyond the boundaries of a given locality. This suggests that a regional collaboration network needs to be considered to fully characterize the knowledge spillover effect.

The differential effects of an interregional collaboration network and geographical proximity in knowledge production and diffusion have important implications for the geospatial R&D pattern. Geographically concentrated collaboration creates uneven R&D spatial patterns, widening the gaps between lagging-behind and knowledge-intensive regions [18]. Research collaborations (both localized and non-localized) occur more frequently in knowledge-intensive regions than in lagging-behind regions because the former have access to more resources and services to support information exchange [19].

From this perspective, to reduce the unbalanced R&D spatial pattern, the need arises for a quantitative evaluation of whether regional R&D performance could benefit from interregional collaborations aimed at improving local innovation capabilities by incorporating externally acquired knowledge to make up for the insufficient local knowledge spillovers [20,21]. This will also help determine the extent to which the reduction in “relational” distances produced by interregional collaborations can overcome the divergent effects that may arise from the spillover effects of geographic agglomeration [22,23].

Although there are many studies related to the relationship between R&D productivity and collaboration, much disagreement still remains, from an empirical viewpoint, on the effect of interregional collaboration in improving R&D productivity from a multistage perspective, which involves a series of inputs and outputs, requiring collaboration between R&D actors [24,25]. Thus, the types of collaboration efforts and R&D inputs and outputs differ from stage to stage.

As mentioned above, some research has been conducted on the impact of collaboration on R&D performance, but there are still many areas that need to be explored and deserve further research. First, the multistage perspective has revealed fresh insights about the R&D process, while existing studies view the R&D process as a whole to analyze its relationship with interregional collaboration, and they ignore the influence of interregional collaboration on different R&D sub-stages, which indirectly affects overall R&D productivity. Second, fewer empirical studies consider the effects of interregional collaboration on narrowing the interregional gaps of R&D productivity from a multistage perspective.

In this context, based on the concept of the innovation value chain [26], a conceptual framework is constructed to divide the R&D process into sub-stages: knowledge production and technology transfer. This allows us to more accurately identify the role of interregional collaboration at each R&D stage. As such, the purpose of this study is to analyze empirically whether interregional collaboration fosters multistage R&D productivity, and what effects interregional collaboration has on narrowing the interregional gaps of multistage R&D productivity in China.

This study employed the network slacks-based measure (SBM) model to calculate regional R&D productivity at each stage and overall for 30 Chinese provinces. The time dimension of the study was selected from 2009 to 2017 due to data acquisition limitations and changes in the statistical caliber of some indicators after 2017. A panel econometric model was then established to study the impact of interregional collaboration on R&D productivity. In addition, we empirically examined the relationship between interregional collaboration and their interregional gaps of multistage R&D productivity from a multistage R&D perspective. Conducting econometric modeling of multistage R&D helps distinguish influencing factors that promote or limit interregional cooperation at each stage.

This study has two main contributions. First, it reveals that interregional collaboration shows a positive impact on R&D productivity at each stage. Second, the role of interregional collaboration in narrowing interregional gaps operates at distinct parts of the R&D process. Specifically, interregional collaboration only narrows the interregional gaps of knowledge productivity (rather than technology transfer productivity). These results show that the impact of interregional collaboration varies at each stage, allowing us to examine a richer set of possible contingencies and offering significant policy implications.

2. Literature Review and Hypotheses Development

2.1. Previous Literature

Many scholars have conducted in-depth research on the role of interregional cooperation in R&D performance. It has been revealed that spatial heterogeneity of R&D performance is often explained by knowledge spillovers. These spillovers constitute an advantage in that R&D actors in particular areas have a dominant position in acquiring complementary knowledge that is spillover from other areas, intentionally or unintentionally. Knowledge spillover needs to be investigated according to the distinct effects of geographical agglomeration and interregional connections from a spatial perspective, in the context of physical distance and relational distance [27]. In the debate on how knowledge spills over, Bathelt et al. [28] argued that the so-called “local buzz” and “global pipeline” are complementary. From this viewpoint, knowledge spillovers are not only limited to geographically close agglomerations; long distance knowledge flow can also occur through interregional collaborations. However, Singh [29] argued for the substitutability of geographical proximity by close network ties (past collaboration networks) by comparing the effects of geographical spillover and interregional relational spillover. This makes it theoretically possible that regions that are well embedded in interregional collaboration can be highly productive in R&D, even if their geographical knowledge spillover effect is weak.

Interregional collaboration, which is a type of relational knowledge spillover, occurs frequently over longer distances in geographical space. It aims to acquire external knowledge sources or specific technologies unavailable locally. In general, interregional collaboration is tied to specific purposes and thus is often characterized by formal interaction [30,31]. This is especially true for basic research-based industries and universities, where interregional collaboration is viewed as the key to innovation [32]. Interregional collaboration is able to create enduring social relationships among R&D actors over any distance, potentially leading to future spillovers because R&D actors, influenced by path dependence, are likely to continue exchanging knowledge informally [17].

The ability of interregional collaboration to enhance R&D performance has already been considered in many studies in the literature. Most of them focus on the positive effect of interregional collaboration on knowledge productivity. For example, Varga, Pontikakis and Chorafakis [9] found that an interregional collaboration network is a major influencing factor of knowledge productivity. Di Cagno et al. [33] showed that after controlling for local spatial spillovers, the impact of research collaboration on regional knowledge production is still significantly positive. More recently, examining co-patenting between 284 European regions, De Noni et al. [34] showed that effective and balanced collaboration in the regional base of knowledge is demanded to facilitate local knowledge production.

Nevertheless, other scholars are less optimistic in this regard, indicating that interregional collaboration is not always beneficial to knowledge production. For example, as the number of collaborations increases, some low-value collaboration projects may be maintained, while their costs may rise [35]. Further, intensive or “excessive” research collaboration among regions and R&D actors may result in overly dense collaboration networks, including inappropriate and redundant relations [36]. Establishing and maintaining such links is not free, which means that redundant relations can lead to waste of resources, undermining innovation activities [37]. Additionally, the establishment and maintenance of collaboration agreements involve great effort but do not guarantee success. Moreover, free riding is a well-known problem that usually causes collaboration failure [38]. Therefore, whether interregional collaboration is beneficial depends on the complementarity of knowledge bases and on a common aim among collective actors [39].

Furthermore, the above-mentioned research, aimed at gauging the effects of interregional collaboration by viewing each region as a research unit, has neglected the influence of cooperative relationships on narrowing the R&D performance gap that may separate them. In other words, interregional collaboration among regions could form a pair of relationships. Few studies have investigated how such relationship pairs affect the interregional gaps of R&D productivity. For example, Gao and Zhai (2021) considered the capability of the collaboration of social–economic indicators and regional innovation mobility to narrow the innovation gap [40]. Hong et al. (2019) found that academia–industry collaboration can narrow innovation differences among regions and can promote interregional innovation convergence [41]. Moreover, even less research has comparatively analyzed the importance of interregional collaboration from the multistage R&D perspective. Taking into account five fields of the innovation process, Fan et al. (2020) analyzed the relationship between cooperative innovation and innovation efficiency in Chinese cities [42]. The matters mentioned above are considered in this study, with the aim of producing novel evidence in this field.

2.2. Conceptual Framework and Hypotheses Development

2.2.1. Conceptual Framework for R&D Productivity

Here, the conceptual framework for R&D productivity was developed from the theory of innovation value chain, emphasizing the interdependence of inputs (such as R&D investments), intermediates (such as new patent authorization), and outputs (such as revenue from technology transfer) [26]. It constructs a two-stage R&D process where innovators can produce knowledge and technology, so as to transform them into benefits [43]. Figure 1 outlines the key two-stage conceptual framework and the aims related to knowledge productivity and technology transfer productivity. Note that these two-stages are relational since they are connected by intermediates. This means that intermediates have a dual role, that is, the output in the stage of knowledge production and the input in the stage of technology transfer. Effective innovation policies need to take these two sub-stages into account.

2.2.2. Hypotheses Development

Interregional collaboration is becoming a critical element in improving R&D productivity; it involves exploring and developing a range of highly specialized and spatially decentralized knowledge [44]. Interregional collaboration enables R&D actors to foster knowledge spillovers and to collectively reduce the costs of acquiring external knowledge. This approach is common in both universities and industry, where the underlying R&D process comprising knowledge production and technology transfer cannot always be separated [45,46].

Based on the above-mentioned previous studies, there are some findings supporting the correlation of local agglomeration and research collaboration for regional R&D performance. Knowledge spillover through geographical agglomeration is expected to provide a form of collective capital for local R&D actors, promoting and enhancing embeddedness for the exchange of tacit knowledge across organizational boundaries within regions [47]. However, the spatial location of specific knowledge agglomeration is usually not the same. If R&D actors located close to each other were to interact only within the region and exclusively combine knowledge locally, it may induce inferior local technological trajectories and result in “path lock” [48]. For this reason, regions search for distant external knowledge sources to help develop path-breaking inventions through interregional collaboration.

Interregional collaborative relationships embedded in non-local innovation systems may foster access to complementary, and avoid innovators being locked into disadvantaged, innovation paths and may diversify external knowledge acquisition [49]. Furthermore, the nature of interregional knowledge flow and the resulting benefits may vary depending on the channels of collaboration and R&D sub-stages [50].

Regarding collaboration between regions, imbalances in R&D level and resource allocation have promoted more collaboration between less developed and more developed regions. Interregional joint R&D endeavors in diverse academic fields are dedicated to exchanging or pooling knowledge and technology, greatly increasing the opportunity for R&D actors to recognize, explore, and capture breakthrough inventions by participating in other actors’ specialized R&D activities and absorbing advanced knowledge for future technologies [51]. Such interregional R&D linkages are considered to be channels of knowledge flow, where innovators in different regional surroundings facilitate the knowledge transfer [52]. In this way, interregional collaborations increase the space of possibilities and boost the reorganization of different knowledge in the chain R&D process [53].

Therefore, by developing collaborative pipelines to benefit from remote knowledge sources, regional R&D actors can stimulate knowledge flows and increase regional R&D productivity [54]. Based on these insights, interregional collaboration can positively impact R&D productivity at each stage. Hence, we put forward the following pair of hypotheses:

Hypothesis 1.

There is a significant positive effect of interregional collaboration on knowledge productivity.

Hypothesis 2.

There is a significant positive effect of interregional collaboration on technology transfer productivity.

Several studies have examined the effect of interregional collaboration on narrowing interregional R&D differences in the context of a multistage R&D process. Interregional cooperation is a possible solution to “spatial lock-in”, which makes the exploration, dissemination and utilization of external knowledge more efficient and effective [55]. The capacity of a region to enhance R&D performance through interregional linkages may depend on the marginal benefit of knowledge spillover. The diminishing marginal effect of knowledge spillover shows that it is easier to attain a large improvement in R&D performance in less efficient regions.

Based on these considerations, knowledge spillovers are usually related to the innovative capacity of the knowledge source and the scope of the local knowledge base [56]. Regions with high R&D productivity are usually characterized by strong local R&D support services, innovation ecosystems, and agglomerations of R&D actors. This facilitates and stimulates interregional knowledge flows or exchanges with cooperative regions to accelerate their knowledge and technology production or transfer processes [57].

Interregional collaboration and knowledge spillover between knowledge-intensive and lagging-behind regions usually have unequal benefits in terms of R&D productivity. Generally, regions lagging behind in R&D productivity usually have imperfect infrastructures and weakly developed knowledge transfer and production networks [58]. In other words, these regions spill less knowledge over to regions with high R&D productivity compared to knowledge exposed to them. Conversely, high R&D productivity regions with strong knowledge spillover capacity are able to benefit more to their cooperation partners through interregional research cooperation [57]. Therefore, regions with lagging-behind R&D productivity will benefit more from the interregional collaborations compared to the regions with high R&D productivity. This phenomenon (i.e., that the benefits of knowledge spillover differ between regions) should result in a convergence of R&D productivity among regions. As such, we formulate the following pair of hypotheses:

Hypothesis 3.

There is a significant positive effect of interregional collaboration on narrowing the interregional gaps of knowledge productivity.

Hypothesis 4.

There is a significant positive effect of interregional collaboration on narrowing the interregional gaps of technology transfer productivity.

3. Methods

3.1. Network Slacks-Based Measure (SBM)

We used network SBM to define the multistage productivity of a decision-making unit (DMU).We employed the following objective function to measure overall regional R&D productivities corresponding to the network SBM by

$$\min {\rho }_0^{*}=\frac{{\displaystyle {\sum }_{k=1}^K{w}^k\left[1-\frac{1}{m_k}\left({\displaystyle {\sum }_{i=1}^{m_k}\frac{s_{io}^{k-}}{x_{io}^k}}\right)\right]}}{{\displaystyle {\sum }_{k=1}^K{w}^k\left[1+\frac{1}{r_k}\left({\displaystyle {\sum }_{i=1}^{r_k}\frac{s_{ro}^{k+}}{y_{ro}^k}}\right)\right]}}$$

(1)

$$s.t.\{\begin{array}{l}{\displaystyle {\sum }_{k=1}^K{w}^k}=1,w^k\ge 0\left(\forall k\right)\\ x_0^k=X^k{\lambda }^k+s_0^{k-}\begin{array}{cc}& \left(k=1,\mathrm{K},K\right)\end{array}\\ y_0^k=Y^k{\lambda }^k-s_0^{k+}\begin{array}{cc}& \left(k=1,\mathrm{K},K\right)\end{array}\\ S_0^{k+},S_0^{k-},{\lambda }^k\ge 0,(\forall k)\\ z_0^{(k,h)}=Z^{(k,h)}{\lambda }^h\begin{array}{cc}& (\forall (k,h))\end{array}\\ z_0^{(k,h)}=Z^{(k,h)}{\lambda }^k\begin{array}{cc}& (\forall (k,h))\end{array}\end{array}$$

where m_k and r_k represent the number of inputs and outputs, respectively, at stage k. $X_{i0}^k$ and $Y_{r0}^k$ represent the input and output vectors to DMU_i at division k, respectively; $s_{i0}^{k-*}$ and $s_{r0}^{k+*}$ are the respective optimal input and output slacks; w^k is the weight of sector k; z₀^{(k h)} is the input and output linkage to DMU₀; λ^k ∈ ${\mathrm{R}}_n^{+}$ is the intensity vector of stage k. We define the divisional productivity score of division k by

$${\rho }_k=\frac{{\displaystyle {\sum }_{k=1}^{K}1-\frac{1}{m_k}\left({\displaystyle {\sum }_{i=1}^{m_k}\frac{s_{io}^{k-*}}{x_{io}^k}}\right)}}{{\displaystyle {\sum }_{k=1}^{K}1+\frac{1}{r_k}\left({\displaystyle {\sum }_{i=1}^{r_k}\frac{s_{ro}^{k+*}}{y_{ro}^k}}\right)}}\begin{array}{cc}& \left(k=1,\mathrm{K},K\right)\end{array}$$

(2)

If ${\rho }_0^{*}$= 1, then the whole R&D process is productive, indicating the highest productivity level. If ρ_k = 1, the relevant sub-stage is productive.

3.2. The Model

Based on the knowledge production function, the model enables us to construct the influencing factors of R&D and identify their relative impact on R&D productivity at the regional scales [59]. According to Griliches [60], regional R&D activities depend on innovatory efforts and a set of regional characteristics. R&D outputs are not only the outcomes of formal R&D investment, but they also come from knowledge spillovers caused by interregional collaboration [61]. Some knowledge spillovers are localized, whereas other spillovers occur over larger distances. Therefore, both local innovatory effort and interregional research networking can strengthen regional R&D performance.

Regional R&D productivity can be a revealing summary measure of R&D performance. Based on the above conceptual framework, this study believes that R&D is a two-stage process of the upstream knowledge production stage and the downstream technology transfer stage, where the role of inter-regional collaboration is different in each stage. In other words, interregional collaboration is distinguished to measure its impact on regional R&D productivity and their interregional gaps at each different stage. To empirically test the hypothesized relationships, we built models that include four equations for two-stage chain R&D productivity, representing knowledge productivity and technology transfer productivity, and began by estimating the following econometric specifications:

$$\mathit{KNOW}\_{\mathit{PY}}_{\mathit{it}}={\beta }_{1}De\_{\mathit{Col}}_{\mathit{it}-1}+{{\displaystyle \sum }}_i{\phi }_{i}Cont{r}_{it-1}+{\epsilon }_{\mathit{it}}$$

(3)

$$\mathit{TECH}\_{\mathit{PY}}_{\mathit{it}}={\beta }_{2}De\_{\mathit{Col}}_{\mathit{it}-1}+{{\displaystyle \sum }}_i{\phi }_{i}Cont{r}_{it-1}+{\epsilon }_{\mathit{it}}$$

(4)

where KNOW_PY and TECH_PY are knowledge productivity and technology transfer productivity, respectively. De_Col is the degree of interregional collaboration. Subscripts i and t denote individual region and period, respectively. We employed KNOW_PY and TECH_PY as dependent variables in Equations (3) and (4) to indicate R&D productivity at different stages, and we analyzed and compared the differences in the impact of interregional collaboration on regional R&D productivity. KNOW_PY and TECH_PY are calculated by the network SBM model described in Section 3.1. Contr_ijt-1 is the control variable including economic development level (Eco), degree of openness (Open), governmental R&D support (Gov), internet penetration rate (Int), geographical distance (Dis), and human capital availability (Hum).

Second, following the hypotheses concerning the impact of interregional collaboration on narrowing the interregional gaps of R&D productivity, we substitute interregional gap proxies in the same model framework, giving the following equations:

$$\mathit{Gap}\_\mathit{KNOW}\_{\mathit{PY}}_{\mathit{ijt}}={\mathit{\beta }}_3\mathit{Co}\_{\mathit{Col}}_{\mathit{ijt}-1}+{{\displaystyle \sum }}_n{\phi }_{n}Gap\_Cont{r}_{ijt-1}+{\epsilon }_{\mathit{ijt}}$$

(5)

$$\mathit{Gap}\_\mathit{TECH}\_{\mathit{PY}}_{\mathit{ijt}}={\beta }_4\mathit{Co}\_{\mathit{Col}}_{\mathit{ijt}-1}+{{\displaystyle \sum }}_n{\phi }_{n}Gap\_Cont{r}_{ijt-1}+{\epsilon }_{\mathit{ijt}}$$

(6)

where Gap_KNOW_PY_ijt and Gap_TECH_PY_ijt are the knowledge and technology-transfer productivity gaps between regions i and j, respectively. Co_Col_ijt-1 is the degree of interregional collaboration between regions i and j. Apart from the Gap_Dis_ij representing the geographical distance between regions i and j, Gap_Contr_ijt-1 is the gap of control variables between regions i and j. All independent and control variables were processed with a lag of one year to minimize problems of endogeneity and reverse causality bias [62].

In terms of independent variables, De_Col stands for the degree of interregional collaboration, which is measured using social network analysis, widely used in relevant past research [63]. The degree of interregional collaboration is determined by the number of direct cooperative links between a node in the collaboration network and other nodes. The number of direct collaboration connections of a node reflects the intensity of knowledge spillovers from different sources in the collaboration network [64]. Through the collaboration network, nodes can absorb external innovation resources and exert their influence externally; their strength influences node performance.

De_Col constructed here is a collection of collaboration relationships based on interregional coauthored patent applications. We used the weighted-degree centrality of a network to measure the degree of interregional collaboration. The weighted-degree centrality of region i in the collaboration network represents the total number of innovation collaborations between region i and other regions:

$$De\_Co{l}_i={{\displaystyle \sum }}_{j\in N_i}{w}_{ij}$$

(7)

where De_Col is the degree of interregional network connection. N_i represents the set of all regions directly connected to region i. w_ij represents the total number of coauthored patent applications between regions i and j. Co_Col_ijt-1, as another independent variable, represents the number of interregional coauthored patent applications between regions i and j.

Similar to the typical case in provincial-scale analysis, the model controls for some factors that may be related to regional R&D productivity. Economic development generally increases the quantity of R&D personnel and equipment, thereby facilitating the innovation infrastructure and environment of the region [65]. We employed per capita GDP to measure economic development level. The openness degree (Open) is captured by the ratio of foreign direct investment to GDP. This indicator is expected to affect R&D as FDI leads to greater competition for innovation, thereby increasing the drive to innovate and the efforts to acquire external knowledge [66].

In light of the evidence on government innovation support, we also controlled for Gov (intensity of government support). We anticipated that Gov would positively impact regional R&D productivity [67]. Gov is measured as the ratio of scientific and technological innovation expenditure to general financial expenditure. Personnel plays a crucial role because embedded innovators’ experience and skills not only directly support their ability to generate new knowledge, but also affect their ability to acquire external knowledge coming from interregional collaboration. Personnel is calculated based on the number of full-time R&D personnel.

Internet penetration (Int) as another control variable, measured by the proportion of the population with the Internet to the total population, is used to characterize the information technology infrastructure. Additionally, there is considerable evidence that spatial distance is an important indicator that affects the productivity with which knowledge spillovers are received. We use geographical distance to all provinces to measure Dis. We also take into account regional human capital, which is expected to affect local R&D activities. The ability of one region to utilize internal and external knowledge and technology for R&D relies on individual skills and prior experience as reflected in a well-educated workforce [68]. Hum is measured by the number of people with college degrees and above per 10,000 residents.

3.3. Data

The dataset covers 30 Chinese provinces from 2009–2017. Most data were obtained from the National Bureau of Statistics. The data for the co-authored patent applications were obtained from the patent search system of the State Intellectual Property Office. R&D output has exploded in China since 2009, driven by massive R&D spending. As such, we began analyzing China’s R&D productivity from 2009 onward. This time frame may partly explain this trend of explosive growth in R&D output. To cleanse patent collaboration data, first, the patents jointly filed by two or more innovators were screened out. Since it is difficult to identify the address of individuals applying for patents, such patents were excluded. Second, for the data on patent applications coauthored by more than two innovators, the collaboration relationship between innovators was calculated in a pairwise manner. Finally, the addresses of the innovators were assigned to the province where they are located, and the data on coauthored patent applications between the provinces were obtained. The selection of variables was based on data availability, and the data sources are shown in

Table 1. Variable selection and data sources.

Indicator Type	Variable
Inputs of stage one	R&D expenditures in basic and applied research a
	Number of R&D personnel in basic and applied research a
Intermediates (Outputs of stage one)	Number of publications of SCI and SSCI b
	Number of granted patents a
Inputs of stage two	R&D expenditures in experimental development research a
	Number of R&D personnel in experimental development research a
Outputs of stage two	Revenue from technology transfer a
	Sales revenue from new product a

Note: ^a represents data from China’s National Bureau of Statistics; ^b represents data from Web of Science.

.

4. Results and Discussion

4.1. Spatial Patterns of R&D Productivity and Interregional Collaboration in China

This study uses the network SBM model to estimate the overall R&D productivity (RD_PY), knowledge productivity, and technology productivity of 30 provinces in China. According to the mean and standard deviation (SD) of the classification statistics, RD_PY is classified into four grades: very low, low, medium, and high (Figure 2).

Generally, RD_PY in the early part of the period studied was at a relatively low level, which reflects important issues in China’s R&D productivity and performance. Without huge changes in the use of funds and a transformation in national research culture and institutions, large investments might not have produced more innovation [69]. However, by comparing the scores in 2009 and 2017, we found that the number of provinces with high RD_PY increased from 3 in 2009 to 13 in 2017, showing a significant upward trend.

KNOW_PY and TECH_PY show significant spatial heterogeneity at provincial scales. Specifically, a large gap exists between both east China and west China in spatial distribution of KNOW_PY as shown in Figure 3, which reveals a decreasing east–west spatial trend. In coastal and central provinces, such as Jiangsu, Tianjin, Shandong and Zhejiang, their KNOW_PY is better than TECH_PY. By comparison, high TECH_PY provinces (such as Gansu, Guangxi, Sichuan, and Xinjiang) are located in western China. Identifying how low KNOW_PY or TECH_PY in different regions impacts RD_PY is significant because regional-specific innovation policies might be needed to respond to low productivity in each sub-stage. For instance, the policy should emphasize enhancing the stage with the poorest performance.

In order to recognize the spatiotemporal relationships between interregional collaboration and regional R&D productivity, we visualized the spatial structure of interprovincial collaboration (Co_Col) and RD_PY. In Figure 4, the lines denote interregional collaboration between two regions, and their width is proportional to the number of Co_Col. The nodes represent the provinces, and their size is proportional to their RD_PY score. Regarding interregional collaboration, Co_Col was calculated from 2008–2016 using Equation (7). Overall, the average degree of interregional collaboration across the country increased year by year. The number of Co_Col (from 16,994 to 158,860) and the number of connection paths (from 283 to 400) rapidly expanded over the study period, indicating that the extent and scope of network knowledge spillovers strengthened.

Regarding spatial distribution, there are certain spatiotemporal mismatches between R&D productivity and interregional collaboration. Although interregional collaboration took place more frequently in the eastern provinces such as Beijing, Shanghai, and Guangdong, which have established an eastern triangle core network of Co_Col, this does not necessarily result in high-value R&D productivity in these cooperative regions. For example, the regions with the largest increase (almost 0.3) in R&D productivity are mainly located in Zhejiang, Hubei, and Qinghai, while regions with the largest increase (almost 5000) in interregional collaborations are mainly located in Beijing, Jiangsu, and Guangdong. This phenomenon reflects that increases in regional R&D productivity do not occur in the regions where interregional collaborations increase.

4.2. Econometric Analysis

This study uses panel regression to evaluate the hypothesis test proposed above. The variables are expressed as logarithms or ratios to reduce the sensitivity of estimates to outliers and to facilitate interpretation of estimated coefficients [70]. The Hausmann specification test was conducted to choose between fixed effect and random effect models [71]. The significance test statistics suggested that fixed effects are better for controlling for unobserved heterogeneity in our panel Models 1 and 2.

Models 1 and 3 represent the impact of control variables on KNOW_PY and TECH_PY, respectively. Models 2 and 4 introduce De_Col to test the first two hypotheses (H1a and H1b) in the study. Positive and statistically significant effects of De_Col on KNOW_PY and TECH_PY were detected in both models, confirming that interregional collaboration has a significant relationship with R&D productivity in both the knowledge production and technology transfer stages, supporting H1 and H2. The estimation results show that De_Col contributes more to KNOW_PY (β₁ = 0.0796, p < 0.05) than to TECH_PY (β₂ = 0.0444, p < 0.05). Specifically, when De_Col increases by 1%, KNOW_PY increases by 0.0796%, which is about 1.5 times the impact it has on TECH_PY (

Table 2. Econometric results: the impact of De_Col on knowledge productivity and technology transfer productivity.

Independent Variables	KNOW_PY (1)		KNOW_PY (2)		TECH_PY (3)		TECH_PY (4)
	Coefficient	S.E	Coefficient	S.E	Coefficient	S.E	Coefficient	S.E
Eco	0.0160	0.0448	−0.0072	0.0451	0.0928 **	0.0380	0.0989 **	0.0389
Open	0.2420 **	0.1121	0.2433 **	0.0114	−0.1074	0.0950	−0.0909	0.0957
Gov	0.0320	0.0419	0.0356	0.0415	0.0963 ***	0.0355	0.0991 ***	0.0359
Hum	−0.1092	0.2332	−0.1188	0.2306	0.0280	0.1979	0.0925	0.1983
Int	0.0154 **	0.0026	0.0085 **	0.0039	0.0074 **	0.0022	0.0080 **	0.0034
Dis	−0.0155 ***	0.3437	−0.0150 ***	0.3493	−0.0912	0.2886	0.0001	0.2885
De_Col			0.0796 **	0.0330			0.0444 **	0.0186
Constant	0.0705 ***	0.0207	0.0669 ***	0.0207	−0.0113	0.0170	−0.0168	0.0171
Number of obs	270		270		270		270
Hausman chi2 Test	18.52, p < 0.01		16.94, p < 0.01		2.98, p > 0.1		3.24, p > 0.1
Model effects	fixed effect		fixed effect		random effect		random effect

Note: Statistical significance levels: *** p ≤ 0.01, ** p ≤ 0.05. KNOW_PY, knowledge productivity; COM_EY, technology transfer productivity.

).

This could be because R&D activities rely more on interregional collaborations that can easily transmit knowledge over time and space. Interregional collaboration is the main channel for knowledge diffusion across long distances, and it enables innovators to source activities and inputs regionally and to benefit from spatial knowledge spillovers and complementary networks that are conducive to local R&D activities. Complementary learning and exchange across dispersed geographical units brings more diverse knowledge reorganization and inspires creativity, fostering R&D performance [72].

The regression coefficients of the control variables are as we expected, Open (p < 0.01) and Int (p < 0.05) are positive and significant in Model 1, and Eco (p < 0.05), Gov (p < 0.01), and Int (p < 0.05) are positive and significant in Model 3. Among the four models, their regression coefficients and signs remained stable, suggesting that the results are robust and there is no multicollinearity in these regression models.

Models 5 and 6 show the impact of interregional collaboration on the interregional gaps of knowledge productivity and technology transfer productivity, respectively, to test our second hypotheses (H3 and H4) (

Table 3. Econometric results: The impact of Co_Col on the interregional gaps of knowledge productivity and technology transfer productivity.

Independent Variables	Gap_KNOW_PY (5)		Gap_TECH_PY (6)
	Coefficient	S.E	Coefficient	S.E
Gap_Eco	0.0060 ***	0.0051	0.0126 ***	0.0055
Gap_Open	0.0233 ***	0.0036	−0.0082 **	0.0039
Gap_Gov	0.0234 ***	0.0030	0.0054 *	0.0032
Gap_Hum	0.5864 ***	0.1372	0.4453 ***	0.1495
Gap_Int	−0.0061 ***	0.0011	−0.0056 ***	0.0011
Dis	−0.1667 ***	0.0211	−0.0404 **	0.0168
Co_Col	−0.0022 **	0.0010	0.0015	0.0011
Constant	0.9502 ***	0.0292	−0.6768 **	0.0318
Number of obs	3915		3915
Hausman chi2 Test	21.09, p < 0.01		31.33, p < 0.01
Model effects	fixed effect		fixed effect

Note: Statistical significance levels: *** p ≤ 0.01, ** p ≤ 0.05, * p ≤ 0.1. Gap_KNOW_PY, knowledge productivity gap; Gap_TECH_PY, technology transfer productivity gap.

). In Model 5, higher interregional collaboration has a negative and significant (β₃ = −0.0022, p < 0.05) effect on the interregional gaps of knowledge productivity. Thus, the greater the innovator’s capability to support interregional knowledge flows and to collaborate with other regions, the smaller the interregional gaps in the potential for generating new knowledge. Therefore, H3 is confirmed.

However, Model 6 pinpoints a positive but not statistically significant impact (p > 0.1) of interregional collaboration on the interregional gaps of technology transfer productivity. This implies that the knowledge spillovers between regions do not necessary narrow the technology–transfer gap between regions, and thus, H4 is not confirmed.

Nonetheless, we believe that interregional collaboration plays a vital role in promoting knowledge spillovers and R&D productivity. The insignificance of the result may depend on the demand for different types of knowledge at different R&D stages [73]. The process of technology transfer often has a high degree of uncertainty and complexity and has even been called “the valley of death.” Its success is difficult to predict exactly [74]. To reduce such uncertainty and complexity, frequent interaction between industry and academia is required to obtain knowledge related to the transformation of R&D achievements. This kind of knowledge is more likely to be tacit knowledge based on personal experience and its spillover needing face-to-face communication or even apprenticeship [75]. Interregional collaboration enables people to exchange codified knowledge more easily than tacit knowledge, which has an important effect on its relevance to different R&D stages [76].

5. Conclusions

This study examined the contribution of interregional collaboration to R&D productivity in China from a multistage perspective. The empirical analysis draws two main findings.

First, there are certain spatiotemporal mismatches between R&D productivity and interregional collaboration. Specifically, although knowledge productivity and technology transfer productivity show high spatial heterogeneity at a regional level, overall R&D productivity has significantly increased, and high-value regions tend to agglomerate in southeastern China. This phenomenon is repeated in the interregional collaboration network, in which the provinces with much interregional collaboration are mainly located in eastern China. However, such high-frequency interregional collaboration might not lead to high-value R&D productivity. It can be seen on the map as mentioned before that the eastern provinces with the highest level of collaboration with other regions, such as Beijing, Shanghai, and Guangdong, had a relatively slow improvement in R&D productivity.

Second, econometric estimates suggest the existence of a simultaneous positive effect of interregional collaboration on knowledge productivity and technology transfer productivity. However, the extent to which the interregional R&D gaps are impacted seems to be associated with the demands of each sub-stage for different knowledge types. Specifically, interregional collaboration contributes more to narrowing the interregional gap of knowledge productivity, confirming the importance of codified knowledge spillover in interregional collaboration. The participation of external knowledge, as well as of external inventors from knowledge-intensive regions, appears to be more effectively narrow regional differences in knowledge production compared to technology transfer.

These results provide some evidence for implementation of regional innovation cooperation policy in China. The formation and development of the regional innovation cooperation network has deepened the knowledge connection between provinces, and the complex networked relationship formed thereby can improve the knowledge productivity of nodes in the network and promote regional collaborative innovation. During the 14th Five-Year Plan period, the construction of an interregional innovation cooperation network is one of China’s in-depth implementations of major national regional development strategies. The overall direction of China’s regional innovation cooperation network construction should be to build a high-level open regional collaborative innovation cooperation system, which can effectively reduce the cost of knowledge flow, accumulation, acquisition and transformation, and promote the coordinated development of interregional knowledge production capacity.

According to our findings, policymakers can implement regional innovation cooperation policies from two aspects to help regional coordinated development. Regional innovation policies give full play to the multi-center effect of interregional innovation cooperation networks. With the construction of Comprehensive National Science Centers and regional Science and Technology Innovation Centers (STIC), the network structure of interregional innovation cooperation in China has gradually evolved from the “partial drive” of the four major STIC to a “multi-center drive” centered on Beijing, Tianjin, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Hubei, Guangdong, and Chongqing. Such a network structure can promote the improvement of overall knowledge production capacity in China. Conversely, policymakers should fully consider the radiation effect of interregional innovation networks. From the innovation development stage of “pioneering innovation” to “leading innovation”, innovation-leading regions such as Beijing, Shanghai, Guangdong and Chongqing use interregional innovation cooperation networks to improve the knowledge productivity of innovation-lagging regions, thereby narrowing the gap between interregional knowledge productivity.

This study on R&D productivity has economic effects to a certain extent. The analysis of R&D productivity is not only used to influence R&D output, but is used to achieve low cost of R&D activities. With a declining national economy in China, improving R&D productivity is an essential process, because it releases insufficient input and output redundancy in different provinces. It needs to be promoted by major national innovation policies. Based on an in-depth understanding of the current situation of existing R&D productivity in Chinese, such innovation policies are mainly committed to optimizing the spatial allocation of R&D resources and realizing the most economical R&D production activities.

The study’s findings are subject to limitations. Due to data limitations, our analysis was limited to a specific nine-year time frame. Regarding the longevity of R&D activities, this time frame may not be sufficient to capture all sides of the relationship between interregional collaboration and R&D activities. It is probable that the effects of interregional collaboration unfold over even longer periods, and that interregional collaboration and R&D interact in a co-evolutionary process crossing more than ten years.

The purpose of this study is to explore the paths for improving R&D productivity and narrowing interregional gaps of innovation performance. The study is exploratory and only provides a preliminary explanation for their impact of interregional collaboration. A promising avenue for future research could be systematic investigation based on global scales. Study in this direction is dedicated to narrowing the innovation gaps among countries and exploring paths for the realization of a global innovation community.