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Journal of Geographical Sciences >

2024 , Vol. 34 >Issue 11: 2193 - 2211

DOI: https://doi.org/10.1007/s11442-024-2289-9

Research Articles

Collaboration for radical and incremental innovation: The roles of intra-region and intra-group knowledge spillover

  • XU Yan , 1, 2 ,
  • ZHU Shengjun , 1, 2, *
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  • 1. College of Urban and Environmental Sciences, Peking University, Beijing 100871, China
  • 2. Laboratory for Earth Surface Processes of the Ministry of Education, Peking University, Beijing 100871, China
* Zhu Shengjun (1984-), PhD and Associate Professor, specialized in economic geography. E-mail:

Xu Yan (2000-), Master Candidate, specialized in innovation economic geography. E-mail:

Received date: 2024-05-29

  Accepted date: 2024-09-30

  Online published: 2025-01-16

Supported by

National Natural Science Foundation of China(42122006)

National Natural Science Foundation of China(42471187)

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Abstract

Knowledge spillover via collaboration is essential to innovation, with proximity being a vital factor. Nevertheless, little consensus has been achieved on which form of proximity is more critical for innovation. Instead of reaching a definitive conclusion, we highlight the potential of addressing the argument through the lens of innovation heterogeneity. This work thus contributes to current literature by integrating two forms of innovation, radical and incremental, into the discourse of geographical and organizational proximity in knowledge spillover via collaboration. Utilizing a dataset of patents from China’s listed firms between 2001 and 2017, we first categorize radical and incremental innovation according to the characteristics of knowledge combination, encompassing the familiarity of combined knowledge and maturity of combination ways. We further investigate the heterogenous effects of intra-region and intra-group knowledge spillovers, linked to geographical and organizational proximity in collaboration, on radical and incremental innovation. Empirical findings demonstrate that innovation relies on knowledge spillover both within groups and within regions. Moreover, intra-region spillover is essential for fostering radical innovation, while intra-group spillover only facilitates incremental innovation. Our findings provide both theoretical and practical implications, suggesting that multilocational enterprises should enhance their collaborator selection to leverage diverse knowledge spillovers, thereby fostering radical and incremental innovation in distinct ways.

Key words： collaboration; proximity; intra-region spillover; intra-group spillover; radical innovation; incremental innovation

Cite this article

XU Yan , ZHU Shengjun . Collaboration for radical and incremental innovation: The roles of intra-region and intra-group knowledge spillover[J]. Journal of Geographical Sciences, 2024 , 34(11) : 2193 -2211 . DOI: 10.1007/s11442-024-2289-9

1 Introduction

Macro-level innovation can be perceived as the aggregation of firms’ behaviors at the micro level (Beugelsdijk, 2007; Zhou et al., 2019). As firms innovate, knowledge and technological resources can be disseminated among firms, individual inventors, and universities, thereby improving the capabilities of both regions and corporate groups (Mudambi and Navarra, 2004; Phene and Tallman, 2018; Yu and Lyu, 2023).
In contrast to the individual mode in the past, contemporary innovation predominantly arises via collaboration (Bernal et al., 2022). From a recombinant perspective of innovation (Fleming, 2001; Arthur, 2007), collaboration facilitates the spillover of knowledge across inventors, hence enhancing the supply of knowledge available for recombination and subsequently elevating the probability of successful innovation (Wagner et al., 2019). It is further argued that collaboration and knowledge spillover are often localized, which underscores the significance of geographical proximity in efficient knowledge diffusion and innovation (Jaffe et al., 1993). Given the opportunities for face-to-face interaction, learning by doing, and the joint acquisition of knowledge facilitated by geographical proximity (Storper and Venables, 2004; Desrochers and Leppälä, 2011; Jin et al., 2023), the knowledge profile of local environmental is crucial for shaping a firm’s future technological innovation trajectories (Zhu et al., 2018; Zhou et al., 2019).
Nevertheless, the Evolutionary Economic Geography (EEG) theory posits that proximity, extending beyond geographical dimension, also matters in promoting efficient collaboration, knowledge spillover, and innovation (Boschma, 2005; Balland et al., 2014). For multilocational firms, organizational proximity is of paramount importance. Multilocational firms can acquire knowledge not only from geographically proximate partners but also from other branches within the same corporate group that exhibit organizational proximity (Zhang et al., 2019), leading to the intra-region and intra-group knowledge spillover. Consequently, the innovation of multilocational firms is jointly influenced by both location and organization (Phene and Tallman, 2018), corresponding to the dual embeddedness in international business (Ciabuschi et al., 2014). However, the extensive current research fails to provide a definitive response about which form of proximity in knowledge spillover is more important for innovation. Our understanding of how intra-region and intra-group knowledge spillover distinctly influence innovation in multilocational firms is likewise weak. The vacuum hinders our comprehension of the distinctions in the fundamental nature of two types of knowledge spillover and proximities.
In this research, we seek to address this gap by integrating the viewpoint of radical and incremental innovation into the discourse on proximity and knowledge spillover. Radical innovation diverges from established technical trajectories to a greater extent (Anderson and Tushman, 1990; Fleming, 2001), and is essential for technology advancement, market development, and sustained growth (Ahuja and Lampert, 2001; Castaldi et al., 2015). Conversely, incremental innovation primarily enhances the existing technical paradigm, and is more apt to reinforce a firm’s current competitive advantages in particular technological domains (Sen and Ghandforoush, 2011). We anticipate that by collaborating with different partners that are geographically or organizationally close, firms can benefit from intra-region and intra-group knowledge spillovers, where distinct types of knowledge may align with the different paradigms of knowledge combination in radical and incremental innovation. Hence, instead of reaching a definitive conclusion regarding the relative significant of various proximities, the research may offer valuable insights into the heterogeneous impacts of proximities on diverse types of innovations, thus aiding in the resolution of the ongoing research debate in evolutionary economic geography.
Our research also contributes to the literature in innovation and business studies by incorporating the perspectives of intra-region and intra-group spillover in relation to radical and incremental innovation. Management and business researchers have attributed radical and incremental innovation to the results of business activities, such as human capital, management structure, and firm strategy (Gupta et al., 2018; Acemoglu et al., 2022). This strand of literature, however, has predominantly overlooked the dynamics of knowledge combination in radical and incremental innovation, thus potentially obstructing our ability to investigate implications for effectively fostering both forms of innovation. This research empirically characterizes and associates radical and incremental innovation with various knowledge spillovers in collaboration, thereby elucidating the origins of a firm's strategic competencies and competitive advantages (Jin et al., 2019). A firm may choose various collaborators, either with geographically proximate partners within the same region, or with organizationally proximate partners inside the same corporate group, to obtain diverse sorts of knowledge for radical and incremental innovation. Consequently, this research may yield practical implications for cultivating different innovations and enhancing firm’s technological capabilities.
The rest of the papers are structured as follows. Section 2 reviews important literatures and thus develop our research hypotheses. Section 3 introduces our research designs. Section 4 presents empirical results. And section 5 summarizes and concludes the paper.

2 Literature review and research hypotheses

2.1 Knowledge spillover, collaboration, and proximity

Collaboration plays a crucial role in enabling successful innovation (Bernal et al., 2022). Collaborations among inventors from distinct firms, regions, and technological fields facilitate the amalgamation of diverse knowledge, resulting in the emergence of superior ideas and innovations (Lee et al., 2015). Engaging in collaboration to pursue effective knowledge spillover is therefore deemed essential for promoting innovation and improving firm capability.
Collaboration and knowledge spillover have historically been linked to geographical proximity (Jaffe et al., 1993). Multilocational firms can engage and collaborate with local business partners and integrate into the local knowledge network (Silvestre and Dalcol, 2009), in order to learn about the knowledge profile of these local agents. Geographical proximity can further facilitate the generation of innovation. This is because the disparity among various inventors can be more readily mitigated by geographical proximity, as it facilitates more opportunities for face-to-face interaction and collaborative acquisition of new knowledge (Storper and Venables, 2004; Desrochers and Leppälä, 2011; Jin et al., 2023). Familiarity and mutual understanding thus enhance the capacity for the trial and error of testing new knowledge combinations, hence significantly benefiting innovation (Galunic and Rodan, 1998; Li et al., 2020).
However, it is important to recognize that geographical proximity alone is insufficient for effective collaboration and knowledge spillover. Other dimensions of proximity, including cognitive proximity, organizational proximity, and social proximity, are also crucial (Boschma, 2005; Balland et al., 2014). Cognitive proximity is fundamental to innovation as effective communication among collaborators relies on similar knowledge foundations to foster familiarity and enhance communication efficiency (Cohen and Levinthal, 1990). An overwhelming overlap in knowledge foundations or significant cognitive distance can both impede effective communication and hinder knowledge spillover (Nooteboom, 2000). Cognitive proximity is also associated with other types of proximities. In the case of multilocational firms, cognitive proximity lays the foundation for organizational proximity. Due to the extensive interconnectivity among firms within the same corporate groups (Hollenstein and Woerter, 2008; Ma et al., 2023), internal knowledge spillover, including the transfer of knowledge from headquarters and reverse knowledge spillover from subsidiaries (Egelhoff, 2010; Chen et al., 2012), happens easily and frequently. Hence, firms within the same organizational boundary are more inclined to possess analogous knowledge profile, and to be both cognitively and organizationally proximate to one another concurrently (Boschma and Lambooy, 1999).
However, despite extensive research on geographical, organization, and cognitive proximity, the current findings remain highly inconsistent. The interplay among various forms of proximities necessitates their integration under a unified analytical framework (Hansen, 2015; Capello and Caragliu, 2018), instead of investigating their effects on innovation in isolation. Further, due to the diverse knowledge attributes and combination paradigms, the requirement for knowledge spillover may vary across different types of innovations (Schoenmakers and Duysters, 2010). It therefore underscores the necessity to examine the variability in the effects of proximities in knowledge spillover on various forms of innovation. We thus distinguish between radical and incremental innovation in the research, which will be elaborated upon in the subsequent section.

2.2 Knowledge combination in radical and incremental innovation

Technological innovation is achieved by the novel combination of knowledge or the enhancement of existing combinations (Xue and Liu, 2023). This is because novel knowledge combination is essential for trial and error to identify the appropriate technical trajectory and drive technological progress (Fleming, 2001; Verhoeven et al., 2016; Li et al., 2020). The paradigm of knowledge combination and the benefits further delineate different types of innovation, among which radical and incremental innovation are particularly significant. Radical innovation is pivotal to technology progress, significantly diverging from established technical trajectories and exerting substantial influence on future innovation (Dahlin and Behrens, 2005). Conversely, incremental innovation enhances current technologies through marginal improvement and significantly contributes to innovation diffusion and marketability (Uddin, 2006).
The distinction in knowledge combination paradigms is more important for investigating their relationships with collaboration and knowledge spillover (Schoenmakers and Duysters, 2010), as it is essential to comprehend how the intrinsic nature of knowledge relates to various forms of proximities in knowledge spillover. The paradigms of knowledge combination in radical and incremental innovation differ in two respects. The initial aspect is the characteristics of combined knowledge. Radical innovation relies on unfamiliar knowledge that is cognitively distant from the inventors’ existing knowledge profile (Anderson and Tushman, 1990), while incremental innovation depends on knowledge that is familiar and cognitively proximate. Successful radical innovation necessitates that inventors transcend the limitations of technological relatedness and venture into unknown fields (Boschma et al., 2023). Conversely, familiar knowledge may enhance inventors' advantages in established technologies and solely encourage diversification into cognitively similar fields (Neffke et al., 2011; Boschma et al., 2014), which is key to the merit of incremental innovation.
The second aspect pertains to the ways of combining diverse knowledge (Fleming, 2001). Radical innovation integrates knowledge from unrelated domains. Such combination is infrequently encountered and remains immature, with its potential for practical use and economic viability still questionable (Fleming, 2001). Nevertheless, upon achieving success, it may catalyze breakthroughs in technical advancement and generate more significant outcomes (Grillitsch et al., 2018). In contrast, incremental innovation through the amalgamation of closely related knowledge entails reduced risk. This is due to the fact that disparate yet familiar knowledge may coordinate more efficiently, leading to a more seamless integration for innovators (Caviggioli, 2016). Consequently, incremental innovation occurs with greater frequency (Pinheiro et al., 2021). Furthermore, as the combination paradigm has reached maturity and is well-established, incremental innovation does not disrupt existing technological trajectories and provides only marginal enhancements.
A multitude of literature has sought to comprehend the underlying factors of radical and incremental innovation. Business scholars regard innovation as the results of firm management, such as entrepreneurial orientation, organizational innovation climate, management structure (Gupta et al., 2018; Acemoglu et al., 2022). Nonetheless, their research has not established a connection between business activities and the essential sources of knowledge required for various forms of recombination, thereby impeding the practical consequences for promoting these innovations. Another body of literature in economic geography focuses more on the roles of various types of knowledge and their characteristics. The significance of regional knowledge variety, knowledge complexity, and cross-region linkages has been established as crucial for the introduction of radical innovation at the regional level (Bathelt et al., 2004; Castaldi et al., 2015; Hesse and Fornal, 2020). Nevertheless, they have predominantly presumed that knowledge is uniformly disseminated throughout the region, neglecting to consider the various channels via which innovators obtain this knowledge. By concentrating on the knowledge of geographical and organizational proximity inherent in collaboration, our research may address the two gaps, thereby connecting the domains of economic geography, innovation study, and business.

2.3 Development of hypotheses

Considering the recombinant nature of innovation and the distinctions between radical and incremental innovation, we aim to connect them with geographical and organizational proximity in collaboration and knowledge spillover. We first posit that both intra-group and intra-region spillover positively contribute to innovation. Collaborating with partners within the same group or region facilitates knowledge acquisition (Ciabuschi et al., 2014). The growing intensity of intra-group and intra-region spillover will augment the probability of effective knowledge combination, hereby fostering greater innovation. Therefore, we first hypothesize that,
H1a: Intra-region spillover is beneficial for innovation.
H1b: Intra-group spillover is beneficial for innovation.
Further, we account for the distinction between radical and incremental innovation. We posit that intra-region knowledge spillover is more significant for radical innovation, whereas intra-group spillover mostly facilitates incremental innovation. The disparities can be elucidated by the distinction in the integrated knowledge feature and combination paradigm, as demonstrated in section 2.2. Regarding the characteristics of combined knowledge, unfamiliar knowledge that is conducive to radical innovation is likely to arise via intra-region spillover, but cognitively similar knowledge beneficial for incremental innovation is more probable to be derived from intra-group spillover. Affiliation within the same corporate group allows firms to share analogous knowledge profiles, hence enhancing their cognitive proximity (Boschma, 2005; Balland et al., 2014). Despite being situated in the same region, which facilitates communication to a degree, it has ultimately surpassed organizational boundaries, resulting in greater cognitive distance between entities. Consequently, intra-regional spillover in conjunction with local partners is more probable to provide novel information and foster radical innovation. In contrast, intra-group spillover in collaboration will encourage firms to develop vigorously in technological areas adjacent to their knowledge base (Boschma et al., 2014; Zhang et al., 2019), thereby facilitating incremental innovation.
On the other hand, regarding the ways of combining diverse knowledge, intra-region spillover will be more important for introducing immature combination. As firms within the same corporate group possess cognitive proximity, collaborators are more likely to share similar knowledge foundations, resulting in a higher degree of related and overlapping combined knowledge. Conversely, external collaborators are more inclined to possess distinct knowledge. Such collaboration may facilitate novel combinations of unrelated knowledge while curbing combinations with closely related knowledge. Consequently, the knowledge spillover derived from intra-region collaboration will predominantly facilitate the emergence of immature combination, whereas knowledge spillover from intra-group collaboration is more crucial for incremental innovation. The two reasons lead to our second hypothesis,
H2a: Intra-region spillover is more important for radical innovation.
H2b: Intra-group spillover is more important for incremental innovation.

3 Research design

3.1 Data

Our research concentrates on listed firms in China. A listed firm is a corporate group consisting of one headquarter and several subsidiaries, all of which are influenced by both intra-region and intra-group knowledge spillover (Frigon and Rigby, 2022; Zhang and Rigby, 2022). A key advantage of adopting listed firms as research samples is that their organizational boundaries are explicitly delineated through stock relationships in annual reports, facilitating precise classification of knowledge spillover occurrences within or outside the corporate group. The data of listed firms is obtained from the China Stock Market & Accounting Research Database, which provides comprehensive information on entity ties, financial conditions, and the establishment of branches.
Both knowledge combination in innovation and knowledge spillover are depicted by patent activity. The patent data is from China’s granted patent database. Each patent provides detailed information of its applicant, including name, affiliated firms, and geographical address, as well as its year and international patent classification (IPC) code. We first identify knowledge combination by the co-appearance of two different IPC codes in one patent. For example, patent “CN104465829B” has 3 different IPC codes, H01L31/049, H02S20/24, H02S40/34. So, there are three dyads of knowledge combinations, H01L31/049-H02S20/24, H01L31/049-H02S40/34, and H02S20/24-H02S40/34. We thus construct a dataset of knowledge combinations for all Chinese patents. The patents of sample firms and their knowledge combinations are thus extracted for further classification of radical and incremental innovation.
Regarding knowledge spillover, in accordance with previous research (Li et al., 2020; Bernal et al., 2022), we consider collaboration as the conduit for knowledge spillover. Hence, we initially extract collaborative patents from the patent dataset, and match patent applicant with the corresponding firm names in CSMAR. The matched firms, which possess a minimum of one granted collaborative patent, are considered as the research samples. We also exclude corporate groups in finance and real estate sectors, since their patents do not appropriately represent innovation activities in production and manufacturing. A sample of 1423 listed corporate groups and 3989 firms is finally retained, corresponding to 82,622 collaborative patents filed between 2001 and 2017.

3.2 Radical and incremental innovation

We define radical and incremental innovation by correlating the maturity of the combination paradigm with the familiarity of recombined knowledge, as illustrated before (Anderson and Tushman, 1990; Fleming, 2001; Schoenmakers and Duysters, 2010). The maturity of combination paradigm refers to the overall frequency of its occurrence. A combination is deemed immature, if the two pieces of knowledge have rarely been integrated previously. Following Zhang and Rigby (2021), we calculate the proximity matrix of all IPC 8-digit codes using the times of co-appearance of IPC codes at the patent level based on the knowledge combinations in all Chinese patents. The computation can be expressed as follows.
$\begin{matrix} {{\text{ }\!\!\rho\!\!\text{ }}_{\text{ij},\text{t}}}=~\frac{{{\text{N}}_{\text{ij},\text{{t}'}}}}{\sqrt{{{\text{N}}_{\text{i},\text{{t}'}}}{{\text{N}}_{\text{j},\text{{t}'}}}}} \\\end{matrix}$
$maturit{{y}_{ij,t}}=\left\{ \begin{matrix} \text{mature},\ \text{if}\ {{\text{ }\!\!\rho\!\!\text{ }}_{\text{ij},\text{t}}}\text{media}{{\text{n}}_{\text{t}}} \\ \text{immature},\ \text{if}\ {{\text{ }\!\!\rho\!\!\text{ }}_{\text{ij},\text{t}}}\le \text{media}{{\text{n}}_{\text{t}}} \\\end{matrix} \right.$
where Nij,t’ denotes numbers of patents assigned with both knowledge i and j (IPC 8-digit codes) in period t’, in which t’ includes year t-5 to t-1. Ni,t’ and Nj,t’ represent numbers of patents assigned with knowledge i and j, respectively. ρij,t refers to the proximity between knowledge i and j in year t. The maturity of knowledge i and j combined in year t (maturityij,t) is calculated by comparing with the median of all knowledge combinations’ proximity in the year (mediant). Median value, rather than mean value, is adopted as the proximity ρij,t follows a power law distribution instead of a normal distribution. If the relatedness between i and j is higher than the median, knowledge combination i-j is considered as mature; otherwise, it is considered as immature.
The second indicator, familiarity, measures whether the firm is familiar with the combined knowledge. It is calculated as the relatedness density between the combined knowledge and the firm’s knowledge stock. We construct the dataset of the sampling firms’ knowledge base at IPC 8-digit level. The relatedness density of knowledge i to firm f’s knowledge base in year t is thus calculated as follows.
$densit{{y}_{i,f,t}}=\frac{\underset{k\ne i}{\mathop{\mathop{\sum }^{}}}\,{{\rho }_{ik,t}}*{{N}_{k,f,t}}}{\underset{k\ne i}{\mathop{\mathop{\sum }^{}}}\,{{N}_{k,f,t}}}$
$densit{{y}_{ij,f,t}}=\frac{\text{ }\!\!~\!\!\text{ densit}{{\text{y}}_{i,f,t}}+\text{densit}{{\text{y}}_{j,f,t}}}{2}$
$\text{familarit}{{\text{y}}_{ij,f,t}}=\left\{ \begin{array}{*{35}{l}} ~\text{familiar}, \text{if densit}{{\text{y}}_{\text{ij},f,t}}>\text{media}{{\text{n}}_{f,t}} \\ ~\text{unfamiliar}, \text{if densit}{{\text{y}}_{ij,f,t}}\le \text{media}{{\text{n}}_{f,t}} \\\end{array} \right.$
where ρik,t denotes the proximity between knowledge i and k in year t. Nk,f,t is the number of patents assigned with knowledge k of firm f in year t. The relatedness density of combination i and j is thus calculated as their average relatedness density to firm f’s knowledge base. Whether knowledge combination i-j is familiar for firm f in year t is obtained by comparing the average density of i-j with the median of all combinations of the firm in the year (medianf,t). The selection of median value is also based on the power law distribution of average density. Combination with density higher than the median is considered as familiar; otherwise, it is considered as unfamiliar.
The two indicators enable us to categorize different types of knowledge combination, as presented in Table 1. The radical type signifies knowledge combination with immature combination and unfamiliar knowledge. The development of these immature combinations is challenging, and it is perilous for firms to venture into unfamiliar technological fields, aligning with the notion of radical innovation. The incremental type contrasts with the radical type, as firm can easily develop such combinations via related diversification from current knowledge base, and by replicating mature combinations from others. The third and fourth categories, medium 1 and medium 2, signify the intermediary forms between radical and incremental ones. The former signifies a combination with unfamiliar knowledge but mature combination, whereas the latter denotes a combination that is immature, but the knowledge has been familiar to the firm. The dependent variables, radical, medium 1, medium 2, and incremental innovation, are calculated by the numbers of patents associated with radical, medium 1, medium 2, and incremental knowledge combinations. To avoid the intervention of heteroscedasticity, logarithmic transformation is utilized.
Table 1 Definitions of different knowledge combinations

 Familiarity
Unfamiliar Familiar
Maturity Immature Radical Medium 2
Mature Medium 1 Incremental

3.3 Intra-group and intra-region spillover

The independent variables contain intra-group and intra-region knowledge spillover. As we have considered patent collaboration as the channel of spillover, the knowledge that could be potentially diffused in each collaboration corresponds the knowledge stock of collaborators. Therefore, for each sample firm, we first calculate the collaborator’s knowledge stock in each collaboration, measured by the number of collaborator’s granted patents in the past five years, as the strength of knowledge spillover.
$\begin{matrix} Knowledge\ Spillove{{r}_{{{f}_{p}},{{c}_{pq}},\text{t}}}=\text{ln}\left( {{\text{N}}_{\text{q},\ {{\text{c}}_{\text{pq}}},\text{t}-5\text{ }\!\!\tilde{\ }\!\!\text{ t}-1}}\text{+}1 \right) \\\end{matrix}$
$Knowledge\ Spillove{{r}_{{{f}_{p}},{{c}_{pq}},\text{t}}}$measures the strength of knowledge spillover in collaboration cpq between sample firm fp and its collaborator q in the year t.${{\text{N}}_{\text{q},\ {{\text{c}}_{\text{pq}}},\text{t}-5\text{ }\!\!\tilde{\ }\!\!\text{ t}-1}}$is the number of collaborator q’s patents between year t-5 and t-1. Logarithm is utilized to avoid heteroscedasticity.
Further, we consider whether the collaboration happens within the geographical boundary and organizational boundary to define intra-region and intra-group knowledge spillover. Specifically, intra-region knowledge spillover is considered as the knowledge spillover that happens between collaborators within the same prefectural city. It is calculated as follows,
$\begin{matrix} Intra\ Region\ Spillove{{r}_{{{f}_{p}}\text{,}{{c}_{pq}}\text{,}t}}=Knowledge\ Spillove{{r}_{{{f}_{p}}\text{,}{{c}_{pq}}\text{,}t}}*\vartheta _{pq}^{region} \\\end{matrix}$
$\begin{matrix} \vartheta _{pq}^{region}=\left\{ \begin{matrix} 1,\ \text{if}\ \text{firm}\ {{\text{f}}_{\text{p}}}\ \text{and}\ \text{collaborator}\ \text{q}\ \text{locate}\ \text{in}\ \text{the}\ \text{same}\ \text{city} \\ 0,\text{else} \\\end{matrix} \right. \\\end{matrix}$
$Intra\ Region\ Spillove{{r}_{{{f}_{p}}\text{,}{{c}_{pq}}\text{,}t}}$denotes the strength of intra-region knowledge spillover for sample firm fp in collaboration cpq.$\vartheta _{pq}^{region}$is a dummy variable denoting whether sample firm fp and the collaborator q locate in the same prefectural city.
Intra-group knowledge spillover is calculated similarly, which considers knowledge spillover that happens within the same corporate group. The calculation can be expressed as follows,
$Intra \ Group \ Spillove{{r}_{{{f}_{p}},{{c}_{pq}},t}}=~Knowledge \ Spillove{{r}_{{{f}_{p}},{{c}_{pq}},\text{t}}}*\vartheta _{pq}^{\text{group}}$
$\vartheta _{pq}^{group~}=\left\{ \begin{matrix} 1,if \ firm{{f}_{p}} \ and \ collaborator\ q \ belong\ to\ the\ same\ corporate\ group \\ 0, else \\\end{matrix} \right.$
where $Intra Group Spillove{{r}_{{{f}_{p}},{{c}_{pq}}t}}$ represents the strength of intra-group knowledge spillover for sample firm fp in collaboration cpq.$\vartheta _{pq}^{group~}$is also a dummy variable denoting whether firm fp and the collaborator q belongs to the same corporate group.

3.4 Model specification

We adopt a fixed-effect regression model to estimate the effects of intra-group and intra-region knowledge spillover on firm’s ability to develop innovation, as well the heterogeneity between radical and incremental innovation. The model can be expressed as follows.
$\begin{align} & \begin{matrix} Innovation_{{{f}_{p}},{{c}_{pq}},t}^{Type~}={{\beta }_{1}}~Intra\ Region\ Spillove{{r}_{{{f}_{p}},{{c}_{pq}},t}}+{{\beta }_{2}}~Intra\ Group\ Spillove{{r}_{{{f}_{p}},{{c}_{pq}},t}} \\\end{matrix} \\ & \text{ }+{{\text{ }\!\!\beta\!\!\text{ }}_{3}}Controls+{{\vartheta }_{{{\text{f}}_{\text{p}}}}}+{{\vartheta }_{\text{q}}}+{{\vartheta }_{\text{t}}}+\varepsilon \end{align}$
where the dependent variable,$Innovation_{{{f}_{p}},{{c}_{pq}},t}^{Type~}$, refers to the ability of firm fp in introducing innovation after collaboration cpq in year t. The superscript, Type, differentiate the four types of innovation, i.e. radical, medium 1, medium 2, and incremental. It is calculated as the number of firm fp’s patents in year t+1 and t+2, that is, two years after the collaboration. $Intra\ Region \ Spillove{{r}_{{{f}_{p}},{{c}_{pq}},t}}$ and $Intra\ Group\ Spillove{{r}_{{{f}_{p}},{{c}_{pq}},t}}$ denote the strength of intra-region spillover and intra-group spillover in collaboration cpq.${{\vartheta }_{{{\text{f}}_{\text{p}}}}}$,${{\vartheta }_{\text{q}}}$,${{\vartheta }_{\text{t}}}$represent fixed effect of firm fp, collaborator q, and year t, respectively.
It is important to acknowledge that knowledge spillover beyond collaboration may bias the identification of its effect on innovation. On the one hand, some branches may disproportionately rely on intra-region spillover for breakthrough innovation and path creation (Phene and Tallman, 2018), whilst other branches may excessively depend on intra-group spillover to sustain current knowledge advantages. The disproportionate reliance on various knowledge spillover may lead to bias in empirical results. On the other hand, due to the stronger knowledge capacity of listed firms, as well as their geographically dispersed shareholders, listed firms may be simultaneously more profoundly influenced by both intra-group and intra-region spillover, as well as spillover from its own knowledge base. Such circumstances may also cause challenges in the selection of listed firms as our research samples.
To mitigate these difficulties, we also include a set of control variables in the model. We identify three sources of potential spillover. First, the reliance on the existing knowledge base may profoundly impact a firm’s future innovation trajectories (Neffke et al., 2011; Balland et al., 2019). To control for the potential effect of spillover from own knowledge base, we include both its magnitude and diversity. The former is calculated as the number of granted patents in the past five years ($Firm\ Base\ Siz{{e}_{{{f}_{p}}\text{,}t}}$), whilst the latter is assessed by the number of different IPC codes in all granted patents in the past five years ($Firm\ Base\ Diversit{{y}_{{{f}_{p}}\text{,}t}}$).
Second, other firms within the same region and corporate group, despite not directly engaging in the focal collaboration, may still facilitate potential knowledge spillover due to the convenience of knowledge diffusion afforded by geographical proximity and organizational proximity (Boschma, 2005; Balland et al., 2014). Hence, we also calculate the size ($Region\ Base\ Siz{{e}_{{{f}_{p}}\text{,}t}}$, $Group\ Base\ Siz{{e}_{{{f}_{p}}\text{,}t}}$), and diversity ($Region\ Base\ diverit{{y}_{{{f}_{p}}\text{,}t}}$, $Group\ Base\ diversit{{y}_{{{f}_{p}}\text{,}t}}$) of knowledge base for all other firms situated in the same prefectural city and belonging to the same corporate group, to control for additional geographical and organizational knowledge spillover that extend beyond the focal collaboration. To avoid heteroscedasticity, logarithmic transformation is also utilized. Descriptive statistics of variables are given in Table 2.
Table 2 Descriptive statistics of variables
Variables Num Mean Sd Min Max
All innovation 82,622 4.447 3.347 0 10.37
Radical innovation 82,622 3.374 2.851 0 8.843
Medium innovation 82,622 3.707 3.001 0 9.316
Incremental innovation 82,622 3.626 3.172 0 9.536
Intra-region spillover 82,622 0.709 2.032 0 8.915
Intra-group spillover 82,622 2.499 2.792 0 9.354
Firm knowledge size 82,622 4.700 2.663 0 9.420
Firm knowledge diversity 82,622 4.620 2.236 0 8.278
Region knowledge size 82,622 9.865 1.793 0 12.00
Region knowledge diversity 82,622 9.187 1.135 0 10.29
Group knowledge size 82,622 6.159 2.247 0 9.434
Group knowledge diversity 82,622 5.691 1.742 0 8.280

4 Empirical results

4.1 Spatial and temporal evolution of innovation and collaboration

We first examine the evolution of the patterns of innovation, including radical, medium 1, medium 2, and incremental innovation. Figure 1 illustrates the annual quantities of various forms of innovation from 2007 to 2018. The total number of innovations has steadily risen during the research period. In relation to the four types of innovation, radical innovation initially holds the largest percentage, signifying that the majority of knowledge is unfamiliar for sample firms, and the combination of this knowledge is immature and challenging. However, the medium 1, medium 2, and incremental types swiftly escalate and eventually catch up with the radical type. This may be due to prior knowledge combinations diminishing the barriers to combining unrelated knowledge, hence facilitating the progression from immature to mature combination. Also, the expansion of knowledge base has enabled firm to acquire more familiarity with knowledge, thus increasing the likelihood of introducing medium and incremental innovation. The spatial pattern (Figure 2) reveals that radical, medium 1, medium 2, and incremental innovations exhibit a notable characteristic of spatial agglomeration, aligning with the distribution of sample firms.
Figure 1 Annual numbers of different types of innovation
Figure 2 Spatial pattern of different types of innovations in China
We further look into the spatial and temporal patterns of collaboration, which is intricately linked to knowledge spillover. The yearly frequency of collaborations and the percentage of intra-city and intra-group collaborations are plotted in Figure 3. We find that the growing number of collaborations correlates with a rising share of intra-city and intra-group spillover, both exceeding 50% at the end of the research period. It can thus be inferred that the geographical and organizational proximity have prompted firms to seek more collaborations with partners within the same region and the same corporate group, thereby reducing communication barriers and facilitating seamless collaboration.
Figure 3 Annual number of collaborations and share of intra-city and intra-group collaboration
Both the spatial pattern of intra-city collaboration (Figure 4) and the distribution of intra-group collaboration (Figure 5) exhibit significant concentration. The intra-city collaboration is predominantly concentrated in certain developed cities, such as Beijing, Shanghai, Shenzhen, and Hangzhou. On the other hand, the majority of intra-group collaboration disproportionately occurs inside the range beyond 500, which only pertains to just a limited number of corporate groups. The uneven distributions suggest that the strong knowledge profile of a few cities and groups may enable firms to derive greater advantages from collaboration and knowledge spillover from geographically proximate and organizationally proximate partners.
Figure 4 Spatial pattern of intra-city collaboration in China
Figure 5 Distribution of intra-group collaborations in different intervals

4.2 Baseline regression results

Empirical results of the baseline regression are shown in Table 3. All variables have been standardized prior to running the regression model. The baseline model adopts all forms of innovation as a dependent variable, without distinguishing between radical, medium, and incremental innovation. Models (1)-(3) utilize the strength of knowledge spillover as independent variable. Model (1) demonstrates that collaboration with partners possessing a robust knowledge base significantly and positively influences a firm’s future innovation through knowledge spillover. In model (2), we control for the potential effect of the firm’s own knowledge base, then subsequently address the potential spillover from other firms in the same region and the same corporate group in model (3). The regression coefficients of knowledge spillover remain robust.
Table 3 Regression results for the effects of intra-region and intra-group spillover on innovation
Variables (1) (2) (3) (4) (5) (6)
All innovation
Knowledge spillover 0.405*** 0.013*** 0.018***
(0.004) (0.003) (0.002)
Intra-region spillover 0.038*** 0.028*** 0.024***
(0.002) (0.002) (0.002)
Intra-group spillover 0.163*** 0.143*** 0.057***
(0.003) (0.003) (0.003)
Firm base size 1.368*** 0.512*** 0.802*** 0.644***
(0.015) (0.022) (0.014) (0.014)
Firm base diversity -0.610*** -0.209*** -0.661*** -0.389***
(-0.015) (-0.016) (-0.012) (-0.012)
City base size 1.778*** 1.698***
(0.036) (0.035)
City base diversity -2.001*** -1.766***
(-0.025) (-0.024)
Group base size -0.383*** -0.245***
(-0.024) (-0.02)
Group base diversity -0.265*** -0.270***
(-0.019) (-0.018)
Constant 0.144*** 0.180*** 0.098*** 0.099*** 0.123*** 0.101***
(0.003) (0.003) (0.002) (0.002) (0.002) (0.002)
Observations 82,622 82,622 82,622 82,622 82,622 82,622
R2 0.170 0.511 0.891 0.838 0.844 0.867
Year FE Yes Yes Yes Yes Yes Yes
Firm FE Yes Yes Yes Yes Yes Yes
Collaborator FE Yes Yes Yes Yes Yes Yes

Notes: Standard errors in parentheses; *** p<0.01, ** p<0.05, * p<0.1; all variables have been standardized.

In models (4)-(6), we categorize knowledge spillover into intra-region spillover and intra-group spillover. Both intra-region and intra-group knowledge spillover are advantageous for innovation, evidenced by their statistically significant and positive regression coefficients. This aligns with our research hypothesis 1a and 1b, suggesting that both geographical and organizational proximity are essential for knowledge spillover and innovation. Moreover, having standardized all variables before running the model, the results facilitate the comparison of the relative magnitude of their effects through the examination of the regression coefficients. The coefficient of intra-group spillover exceeds that of intra-region spillover, signifying the former is more significant in promoting innovation. The cognitive proximity resulting from continuous interaction through equity relationships and organizational proximity within the corporate group may be more significant for innovation, as it substantially diminishes barriers to mutual understanding and communication in collaboration, thereby facilitating knowledge spillover and future innovation. Conversely, while geographical proximity facilitates increased opportunities for collaborative connection, its efficacy in diminishing cognitive distance may be less pronounced, hence contributing a comparatively minor role in knowledge spillover and innovation.

4.3 Heterogeneity among different types of innovation

We further examine whether the effects of intra-region spillover and intra-group spillover vary across different types of innovation. We employ the same model to perform the regressions for radical, medium 1, medium 2, and incremental innovation, respectively. The results are shown in Table 4. Model (1) indicates that only intra-region spillover fosters radical innovation, whereas intra-group spillover exerts a considerably adverse effect. The results remain consistent upon the inclusion of control variables in model (2). This is in line with our research hypothesis 2a. On the one hand, collaborating with geographically proximate partners enhances opportunities for face-to-face interaction and co-learning of new knowledge, hence improving the likelihood of combining distant knowledge and creating immature knowledge combination. On the other hand, local partners frequently exist beyond the organizational boundary of corporate group, thereby assisting firms in acquiring unfamiliar knowledge and generating novel combination. Both elements are beneficial for promoting radical innovation. Conversely, while intra-group spillover with organizational proximity can foster chances for mutual understanding and extensive contact, collaboration with overly familiar firms within the same corporate group may impede the introduction of unfamiliar knowledge and immature combination. Thus, intra-group spillover may be harmful for radical innovation.
Table 4 Regression results of the heterogeneity among different types of innovation
VARIABLES (1) (2) (3) (4) (5) (6) (7) (8)
Radical innovation Medium 1 innovation Medium 2 innovation Incremental innovation
Intra-region spillover 0.536*** 0.185*** 0.007*** 0.005*** 0.005*** 0.002 0.001 0.002
(0.003) (0.003) (0.002) (0.002) (0.002) (0.001) (0.002) (0.002)
Intra-group spillover -0.269*** -0.405*** -0.065*** 0.015*** -0.024*** 0.041*** 0.017*** 0.013***
(-0.003) (-0.003) (-0.004) (0.004) (-0.003) (0.003) (0.004) (0.004)
Firm base size 1.132*** 0.580*** 0.360*** 0.589***
(0.018) (0.023) (0.020) (0.024)
Firm base diversity -0.669*** -0.266*** -0.054*** -0.283***
(-0.016) (-0.017) (-0.015) (-0.018)
City base size 0.068*** 1.873*** 1.010*** 2.209***
(0.012) (0.038) (0.032) (0.04)
City base diversity -0.035*** -2.130*** -1.345*** -2.354***
(-0.011) (0.026) (-0.022) (-0.027)
Group base size -0.048*** -0.418*** -0.380*** -0.383***
(-0.017) (0.025) (-0.021) (-0.026)
Group base diversity 0.310*** -0.264*** -0.201*** -0.297***
(0.014) (0.020) (-0.017) (-0.021)
Constant 0.080*** 0.142*** 0.113*** 0.095*** 0.117*** 0.088*** 0.116*** 0.105***
(0.003) (0.002) (0.002) (0.002) (0.001) (0.002) (0.002) (0.002)
Observations 82,622 82,622 82,622 82,622 82,622 82,622 82,622 82,622
R2 0.351 0.656 0.848 0.877 0.899 0.913 0.868 0.870
Year FE Yes Yes Yes Yes Yes Yes Yes Yes
Firm FE Yes Yes Yes Yes Yes Yes Yes Yes
Collaborator FE Yes Yes Yes Yes Yes Yes Yes Yes

Notes: Standard errors in parentheses; *** p<0.01, ** p<0.05, * p<0.1; all variables have been standardized.

In models (3)-(6), we change the dependent variable to medium innovation. The result of model (3) demonstrate that intra-region spillover remains advantageous for medium 1 innovation, whereas intra-group spillover exerts a detrimental effect. Upon adjusting for additional sources of knowledge spillover beyond collaboration in model (4), the coefficient of intra-region spillover remains robust, while the coefficient of intra-group spillover exhibits a reversal. It may be concluded that intra-region spillover remains advantageous for the introduction of unfamiliar knowledge, notwithstanding the maturity of the combination, whereas the impact of intra-group spillover is not consistent. In models (5) and (6), we find that both effects of intra-group and intra-region spillover on medium 2 innovation that with familiar knowledge but immature combination are not robust, as their coefficients invert upon the inclusion of control variables
Finally, models (7)-(8) adopt the number of incremental innovations as the dependent variable. We find that the effect of intra-region spillover is no longer statistically significant, while the effect of intra-group spillover is positive and robust. This aligns with our hypothesis 2b. While collaboration among firms in the same corporate group may hinder the introduction of radical innovation, cognitive proximity might enhance related diversification and the integration of familiar knowledge, so promoting incremental innovation.

5 Conclusion and discussion

Collaboration and knowledge spillover are vital sources of innovation, wherein various types of proximity, including geographical, cognitive, organizational, and social proximity, play the essential role. Nonetheless, current research does not achieve a definitive consensus on which sort of proximity is more significant. In this research, we highlight that different types of proximities in collaboration and knowledge spillover align with the diverse paradigms of knowledge combination, hence contributing positively to distinct types of innovation. The argument is examined in the case of multilocational firms, which are simultaneously influenced by geographical proximity and organizational proximity, and have to develop either radical or incremental innovation. On the one hand, multilocation firms may collaborate with both internal partners within the organizational boundary and external partners in the same regions, thus reaping advantages from both intra-region and intra-group knowledge spillover. On the other hand, radical innovation fosters the development of new technological trajectories and mitigates lock-in by combining unfamiliar knowledge and immature combinations (Ahuja et al., 2001; Castaldi et al., 2015), whereas incremental innovation enhances existing technologies and solidifies a firm’s competitive advantages in established domains through its reliance on familiar knowledge and mature combination paradigms (Sen and Ghandforoush, 2011). This case may provide value insights into the relationship between collaboration, knowledge spillover, and various proximities and innovations.
Utilizing patent data of China’s listed firm, we first depict the evolution of collaboration patterns and different types of innovation, i.e. radical, medium, and incremental innovation. Additionally, we associate them with intra-region and intra-group information spillover, demonstrating that both geographical and organizational proximity in knowledge spillover enhance innovation. Nonetheless, the impacts range across various categories of innovations. Intra-region knowledge spillover, resulting from collaboration with geographically proximate partners within the same region, is essential for radical innovation. Conversely, intra-group knowledge spillover, central to collaboration with organizationally proximate partners inside the same corporate group, is more critical for medium and incremental innovation. Therefore, instead of achieving a uniform consensus, we emphasize the necessity of acknowledging the diversity of various forms of proximities and innovations.
Our research yields implications for fostering radical and incremental innovation in corporate groups. To succeed in radical innovation, firms should be positively embedded into the local network of the host region to capitalize on intra-region knowledge spillovers. This can be achieved by extensive collaboration with local agents (Silvestre and Dalcol, 2009; Zhang and Rigby, 2021; Jin et al., 2023), such as customers, suppliers, and competitors (Albis et al., 2021). The knowledge profile of these agents can thus be diffused and help firms achieve advantages in radical innovation. Regarding incremental innovation, it is preferable for firms to engage in extensive collaboration with other firms in the corporate groups. By sharing knowledge in intra-group network (Egelhoff, 2010; Chen et al., 2012), more familiar knowledge and mature combination can be accessed through intra-group spillover to promote incremental innovation.
This research also has several limitations. First, our research focus is confined to Chinese listed firms and their domestic subsidiaries. The applicability of the findings to non-listed firms and multinational enterprises remains uncertain. Further, we do not account for the moderating effect of additional factors in the relationship between knowledge spillover and innovation, such as knowledge base complexity, local institutional context, and characteristics of collaboration network. We leave them for future research.

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