Understanding Regional Branching: Knowledge Diversification via Inventor and Firm Collaboration Networks

Abstract The diversification of regions into new technologies is driven by the degree of relatedness to existing capabilities already present in the region. In cases where opportunities for diversification are rather limited, external knowledge that spills over from neighboring regions or from farther away might become an important driver of regional diversification. Despite the relative importance of interregional knowledge flows via collaborative work, we still have a very limited understanding of how collaboration networks across regions might facilitate diversification processes. The present study investigates the diversification patterns of European metropolitan and nonmetropolitan regions into new knowledge domains via technology classes reported in patent applications to the European Patent Office. The findings indicate that externally oriented inventor collaboration networks increase the likelihood that a new technology specialization enters a region, but this external orientation is less important for related diversification than for unrelated diversification. Further, the results demonstrate that interregional collaboration networks help diversification into unrelated technologies if external knowledge sourcing is based on a diverse set of regions and if collaboration is intense within companies located in distinct regions. Within-firm collaborations across regions can compensate for missing related skills in metropolitan and in nonmetropolitan regions alike but are especially important in nonmetropolitan regions. These results provide new evidence about the importance of knowledge flows within multilocation firms in the technological knowledge diversification of regions.

Investigations into the driving factors that cause the advent of new industrial and technological activities in regional economies are central to economic geography (EG) inquiry.The diversification literature has enjoyed a renaissance via the evolutionary turn in EG (Boschma and Lambooy 1999;Grabher 2009) under various labels such as regional branching (Boschma andFrenken 2011), path creation (MacKinnon et al. 2019), path development (Grillitsch, Asheim, and Trippl 2018;Hassink, Isaksen, and Trippl 2019), among others.In evolutionary economic geography (EEG), two significant focus areas have emerged (Kogler 2015), one pertaining to the relatedness of industries and technologies (Boschma 2017;Whittle and Kogler 2020), as exemplified in the product space (Hidalgo et al. 2007), and industry space (Neffke, Henning, and Boschma 2011) and knowledge spaces (Kogler, Rigby, and Tucker 2013;Kogler, Essletzbichler, and Rigby 2017); and another one that stresses the role played by external, interregional interactions such as trade or firm investments (Boschma and Iammarino 2009;Neffke et al. 2018;Elekes, Boschma, and Lengyel 2019).Among interregional interactions, collaboration networks are important channels for local knowledge spillovers along with the influence of interregional transfer mechanisms (Funk 2014;Broekel, Brenner, and Buerger 2015;De Noni, Ganzaroli, and Orsi 2017;De Noni, Orsi, and Belussi 2018;Santoalha 2019), and therefore the role of external collaborations in regional diversification has gained recent attention (Balland and Boschma 2021;Di Iasio and Miguelez 2022).
Nevertheless, the role that relatedness, local knowledge specializations, and collaborative networks within and across regional economies plays in regional branching is rarely investigated in conjunction with and in a single research framework.This constitutes a significant research gap in the contemporary EG discourse.Indeed, the interplay of individuals', firms', and regional economies' collaborative networks in combination with local specialization and diversification activities poses significant analytical challenges.Here we propose that network indicators based on linked data are capable of pursuing a universal research framework that will offer firm linkages knowledge sourcing specialization patent data analysis JEL codes: O33 O52 R11

Acknowledgments
The authors acknowledge the help of Szabolcs Tóth-Zs in finalizing the figures.We are grateful for the comments of Gergő Tóth, Zoltán Elekes, Andrea Morrison and the three anonymous referees who contributed with very helpful suggestions.Balázs  ECONOMIC GEOGRAPHY ample empirical evidence of regional branching processes and generate opportunities for further EG and EEG theorizing (Kedron, Kogler, and Rocchetta 2020).
In pursuit of that, the advent of a newly added knowledge specialization, via technology classes reported in patent applications to the European Patent Office, in European metropolitan or nonmetropolitan regions becomes the focal point of the present investigation.We consider firms central to this analysis, given that it is almost exclusively firms that make the relevant research and development (R&D) investment decisions that ultimately decide the intensity and direction of technological change (Crescenzi, Dyèvre, and Neffke 2022) and because much of the direct knowledge sourcing activities across regions happen within the boundaries of multilocation firms (Frigon and Rigby 2022; Zhang and Rigby 2022).While our approach implies a firm-centric view, all utilized indicators in this study also capture individuals' collaborative networks in space, given that the inventive footprint of firms is determined by the location of their employees (Shin, Kogler, and Kim 2023).
We propose four networks indicators that describe the collaboration patterns of inventors within and across regions.In particular, we quantify extraregional knowledge sourcing in a technology domain by the spatial diversity of co-inventor connections that describes the accessible knowledge pool (Eriksson and Lengyel 2019) and by the intensity of collaboration within multilocation firms that describes the role of firms in interregional knowledge transfers (Alcácer and Chung 2007).In addition, we apply a number of indicators that capture the role of firms for diversification, besides the measures of relatedness and agglomeration externalities.
Our findings indicate that a higher share of external collaboration results in higher levels of technological entry along the spectrum of relatedness.Yet, external inventor collaborations are more important for unrelated than for related diversification.We find that access to diverse knowledge inputs by localities via nonlocal collaboration ties, and the intensity of intrafirm, interregional collaborative networks of firms present in a locality, can compensate for the lack of a local pool of related technological knowledge.Imported knowledge into the region by external collaboration supports diversification into more distant knowledge domains, even if a certain degree of relatedness is missing.Multilocation firms are especially helpful in this regard, since they can facilitate knowledge flows across their sites in different regions and thus can foster unrelated diversification.The findings are robust for metropolitan and nonmetropolitan regions alike.
The remainder of this article is organized as follows.The next section provides the theoretical foundation upon which we investigate the network dimensions of the regional branching thesis.In addition, it explores how these differences are manifested differently for metropolitan and nonmetropolitan regions considering policy implications.This is followed by a section describing the utilized data as well as how the variables were created along with the proposed analysis.Expanding on this, the penultimate section explores the article's primary research aims and discusses the results.The final section provides concluding remarks and offers directions for the future.

Knowledge Production and Regional Branching
The observed and persistent uneven patterns of economic development among regions are heavily attributed to the notion that knowledge production, embodied in local skills and technological capabilities, is a place-based process for several reasons.These include the stickiness of knowledge at the spatial as well as organizational level (von Hippel 1994;Li and Hsieh 2007), the fact that knowledge flows and spillovers are localized (Jaffe, Trajtenberg, and Henderson 1993;Feldman and Kogler 2010), and the path-dependent nature of economic development altogether (Martin and Sunley 2006).On the latter, more recent discourses in economic geography have gravitated toward an evolutionary perspective of local knowledge production and in particular the relevance of path dependency (Grabher 2009;Kogler 2015).Here the notion is that the skills and industrial structure that are present at a place determine future possibilities as well as limitations on the extent a regional economy can branch out into new activities.As such, new path creation is considered an endogenous process (Henning, Stam, and Wenting 2013).
Nevertheless, in parallel there are also ongoing discussions that increasingly recognize the interplay of local and nonlocal socioeconomic networks in initiating and enabling regional branching processes beyond what might be expected on purely evolutionary connotations (Boschma 2022).Boschma and Frenken (2011) outline four knowledge transfer mechanisms through which branching processes manifest themselves, including spinoff activity, firm diversification, labor mobility, and social networking.While the relevant literature on diversification certainly speaks to these mechanisms with the help of networks across local economic and technological activities (Hidalgo et al. 2007;Neffke, Henning, and Boschma 2011;Tanner 2014;Montresor and Quatraro 2017), it is especially the social networking aspects and determinants of regional branching that have remained somewhat undertheorized and lightly supported by empirical evidence.This has important implications given the centrality of the branching thesis to contemporary economic development policy initiatives, for example, the Smart Specialization Strategies (S3) policy initiative exercised throughout the EU (Foray 2015) and the increasing importance of social and collaboration networks to further our understanding of socioeconomic outcomes in regions (Boschma 2017;Eriksson and Lengyel 2019;Whittle and Kogler 2020).
It is widely acknowledged that social and collaboration networks play an important role in the knowledge production process, and that places might draw new knowledge inputs that facilitate branching mechanisms by gaining access to geographically dispersed capabilities via collaboration (De Noni, Orsi, and Belussi 2018) or intrafirm flows of multilocational firms (Zhang, Jiang, and Cantwell 2019).It is also widely accepted that similar to regional development, the dynamics of local collaboration networks are a path-dependent process that demands external connections if the negative consequences of lock-in should be avoided (Glückler 2007;Boschma and Frenken 2010).However, it remains unclear how these networks of networks, for example, the relatedness between knowledge domains at a place and then the connections via collaboration of individuals and firms to other places that feature potentially very different relatedness constellations, possibly initiate branching processes into new spheres of the local knowledge space (Kogler, Essletzbichler, and Rigby 2017).

Relatedness, Networks, and Regional Branching
The relatedness between knowledge domains, industrial sectors, occupations, and skills, in order to highlight location-specific configurations and their associated ECONOMIC GEOGRAPHY development trajectories that are guided by evolutionary principles, and how these might result in particular socioeconomic outcomes, have become a focal interest in EG, and international development literatures over the past decade (for a recent review, see Whittle and Kogler 2020; see also Hidalgo et al. 2018).As such, a network perspective on place-based constellations of domains and their connectedness-such as the product, industry, and knowledge spaces-has developed, something that has also become a central cornerstone of advanced innovation policy ideas.For example, a key feature of the S3 policy since its inception by the original architects is an emphasis on the relative importance of size, domain, and connectedness (Foray, David, and Hall 2009).Following this argument, a number of investigations directed at the co-occurrence of specific knowledge domains at the national or pan-European level have been conducted, and subsequently derived relatedness scores have been used to explore and project the evolution of metropolitan and regional patterns of technological knowledge specializations (Kogler, Rigby, and Tucker 2013;Boschma, Balland, and Kogler 2015;Rigby 2015;Montresor and Quatraro 2017;Balland et al. 2019).Nevertheless, the vast majority of these early studies into the role of relatedness on the evolution of place-based knowledge spaces mainly focused on networks of domains that take place within urban and regional economies, rather than explicitly considering external connections of actors (Abbasiharofteh, Kogler, and Lengyel 2020).Recently, the potentially important role of interregional collaboration, and in particular in an S3 policy context, is gaining momentum (Balland and Boschma 2021).From a regional perspective, this disconnect is especially peculiar given that economic geographers have long recognized the importance of interregional linkages for regional development (Bathelt, Malmberg, and Maskell 2004).To these ends, interregional collaboration has two distinct albeit related functions.First, it ensures that regional actors are kept abreast of new ideas developed elsewhere (Fitjar and Rodríguez-Pose 2011;Neffke et al. 2018;Elekes, Boschma, and Lengyel 2019).Second, it introduces new sources of variety into the region, thereby dissuading regional lock-in while potentially facilitating relevant unrelated diversification processes (Grabher 1993).At the same time, however, evolutionary accounts have challenged this perspective by claiming that it is not sufficient enough to be connected to multiple regions per se, since differences in absorptive capacity may impede the overall learning process (Boschma and Iammarino 2009).Instead, the focus should be on developing connections to those regions that can provide related capabilities to an existing knowledge base (Miguelez and Moreno 2018;Balland and Boschma 2021).
Nevertheless, interregional knowledge production networks are certainly not independent from the path-dependent development of regional knowledge domains.Instead, inventors are more likely to collaborate across proximate regions that have similar technological portfolios (Maggioni, Nosvelli, and Uberti 2007;Hazir and Autand-Bernard 2014;Cassi and Plunket 2015), especially in the case of lasting relationships (Tóth et al. 2021).National and regional innovation systems impose further limits to innovative collaborations (Chessa et al. 2013;Aquaro, Damioli, and Lengyel 2023), stressing the need for a better understanding on the type of interregional collaboration that can facilitate regional branching.
In line with these arguments, considering networks at the region-technology level and also considering the significant role innovative firms and their associated inventive agents play need to be considered together.A unified framework should bring together the concept of relatedness with advanced network measures to disentangle the complexity of regional branching processes beyond simple relatedness scores and to better understand how interregional collaboration facilitates technological diversification.
The Role of Interregional Networks of Inventors and Firms across Region Types Regional economies can be considered coherent containers of interlinked socioeconomic activities.In general, one can differentiate between larger ones, usually composed of a city and its commuting zone, that is, functional urban areas (Dijkstra, Poelman, and Veneri 2019), or smaller nonmetropolitan regions (EU 2019).It is reasonable to expect that the degree of economic diversity, the extent of knowledge, and the level of economic complexity, and thus resulting opportunities for internal networks of relatedness as well as external collaboration networks and consequential development trajectories between these larger and smaller regions, differs in a somewhat systematic manner.For example, the network of technological relatedness is more densely connected in large metropolitan areas than in small regions (Tóth et al. 2022).Certain structural properties of co-inventor networks-such as the size of the external collaboration pool, and clustering and path length in the local co-inventor networks-correlate at least moderately with the number of inventors in the region (Fleming, King, and Juda 2007).Although regions provide a rationale for coherent innovation systems (Asheim, Isaksen, and Trippl 2019), their composition is largely determined by the individuals and firms who operate within their boundaries.Nevertheless, the innovative performance of a regional economy is not just the simple sum of those actors operating within its relative boundaries, but rather it also depends on how a region is embedded in the larger network of economic activities at the national and international level (Cortinovis and Van Oort 2019;Boschma 2022).
Firms are central to these networks given that they make R&D investment and location choices that aim at maximizing innovativeness and productivity (Crescenzi, Dyèvre, and Neffke 2022).Recent investigations into the extent that capabilities mainly reside in firms or regions provide further evidence that the knowledge structure of firms potentially is more important than the knowledge structure of places in regional diversification processes (Zhang and Rigby 2022) and stresses the role of within-firm networks across regions.
Multilocation companies have access to a wider pool of external knowledge (Leiponen and Helfat 2011) and can exploit the diversity of knowledge across the regions of their sites (Crevoisier and Jeannerat 2009).At the same time, they must develop strong internal connections across their locations in order to internalize knowledge bases of regions into an interdependent technological portfolio within the company and also to control local innovation (Alcácer and Zhao 2012).This suggests an important role of multilocation companies in facilitating interregional knowledge transfer.
Here it should be noted that a significant portion of interregional collaboration occurs within the boundaries of single multilocation firms and that this is often difficult to emulate (Singh 2008).Surprisingly, geographic contributions are somewhat scarce in this space, with most insights coming from the management studies literature (Beeby and Booth 2000).For instance, Seo, Kang, and Song (2020) demonstrate that the ECONOMIC GEOGRAPHY number of cross-border patents within US multinational corporations (MNCs) has increased from less than 7 percent in the 1990s to over 17 percent in 2015.Also, for the US, Berry (2014) shows that the number of collaborative multicountry patents has grown from one-fifth to one-third of new foreign patents by US MNCs.Furthermore, these patents draw on a wider pool of technological knowledge and are more likely to form the basis upon which new innovations are created.
However, the question whether the internal connections of multilocation firms across regions favors diversification into new activities that are related or instead are unrelated to the existing technological portfolio of a region, is still open.Indeed, one can have contradictory expectations based on the scarce empirical evidence and theoretical arguments on this matter.On the one hand, using the case of the global semiconductor industry, Wang and Zhao (2018) illustrate the controlling role of linkages within multilocation companies that help to avoid knowledge spillovers to competitors at shared locations and allows for doing R&D that is technologically similar to colocated companies.Their findings suggest that interregional collaboration within multilocation companies might facilitate related diversification in regions with the aim of exploiting the local knowledge base in the technologically diverse and unrelated portfolio of the company.On the other hand, Eriksson and Lengyel (2019) prove that extraregional links to identical but distantly located industries can substitute the network effects of the missing local capacities in the same industry.Multilocation companies often establish capacities that are new to the region (Elekes, Boschma, and Lengyel 2019;Crescenzi, Dyèvre, and Neffke 2022), and their sites are often more connected to other sites of the company across city-regions than to their local ecosystem (Lorenzen, Mudambi, and Schotter 2020).These latter insights support the expectation that internal ties of multilocation companies across regions can facilitate unrelated diversification.
In line with these arguments, a comprehensive study into the mechanisms behind regional branching activities needs to consider the networks of multilocational firms via its inventive employees and associate inventors across multiple jurisdictions.Consideration should be given to investigating how interregional collaboration within the firm is associated with the related or unrelated diversification of regional economies across the board and especially in metropolitan versus nonmetropolitan regions.
Following these lines of reasoning, the present investigation now turns to the methodological approach that is deemed suitable to conduct such a multifaceted analysis of regional economic branching processes.

Methodological Approach Data
We use patent data from the European Patent Office (EPO) PATSTAT database for seven nonoverlapping five-year periods (1981-85, … , 2011-15).Besides other information, patents contain names and addresses of inventors and assignees, and CPC (Cooperative Patent Classification) codes that reflect their technological class. 1 In most cases, patents contain more CPC codes, which allow for an analysis of how particular knowledge domains are related to each other (Kogler, Rigby, and Tucker 2013;Kogler, Essletzbichler, and Rigby 2017), which is commonly used to understand regional branching (Tanner 2014).Inventors can cooperate on patents that can yield interregional collaboration networks, if co-inventors reside in more than one region (Balland and Boschma 2021;Tóth et al. 2021).The same applies to assignees, that is, a patent that has more than one assignee listed can create interregional collaboration networks at the entity level, if assignees are located in different regions (Wanzenböck et al. 2022).
The observations of our analysis are technological classes paired with regions.The former is identified by four-digit CPC codes (650).To consider cases where there are more than two four-digit CPC codes listed on a single patent, which is the case in most patent documents, the four-digit CPC proportion is applied in a similar manner to the way patents are also assigned to multiple regions based on inventor addresses as described below.In this article, we refer to four-digit CPC codes as CPC classes.
To define regions, we apply the classification of EUROSTAT's Urban Audit's Functional Urban Area,2 which distinguishes 1,151 European regions as metropolitan or nonmetropolitan.According to this definition, metropolitan regions are NUTS3 regions or combinations of adjacent NUTS3 regions of at least 250,000 inhabitants.Adjacent NUTS3 regions are grouped together in case more than 50 percent of the population commutes from one to the other creating unified labor markets3 (Pintar and Scherngell 2022).All other NUTS3 regions are considered nonmetropolitan.
We regionalize individual patent applications using inventors' addresses (Kogler, Essletzbichler, and Rigby 2017) and fractionally split those patents across regions that are authored by inventors from multiple regions.This technique enables us to look at co-inventor collaborations across regions but within company boundaries.We use assignee information to operationalize patenting firms in regions that we refer to as firms in the remainder of the article.

Dependent Variable
The main variable of interest is ENTRY that captures the emergence of new technological specializations in European metropolitan and nonmetropolitan regions.Here, we apply a measure called revealed technological advantage (RTA), which measures the level of specialization in each technological domain present in the region in a period.The RTA index is the quotient of the CPC class ratio among all patents in the region (the numerator) and of the CPC class ratio in all regions among all patents (the denominator). 4In this article, following the mainstream of diversification literature (Hidalgo et al. 2007;Neffke, Henning, and Boschma 2011), ENTRY is set equal to 1 when the CPC class in the region first has an RTA ≥ 1 and 0 otherwise.This measurement has the advantage of capturing dynamics of regional innovation through specialization, but a major limitation is its relativistic nature.For instance, a technology can emerge in a region without any increase in inventive activity when other domains shrink, but RTA can decrease in the given region if patenting in the same technology class increases in other regions.Nevertheless, because the focus here is on the relative advantage or competitiveness of regions over their counterparts, this does not pose a problem in the present investigation.The equation of RTA is provided in Appendix 1 in the online material.

Independent Variables
According to the central tenet, technological relatedness is the major engine of regional diversification because a new technology is more likely to emerge in a region when related knowledge domains are already present.Originally popularized by Hidalgo et al. (2007), this general schema has been adapted by economic geographers to analyze the diversification patterns of economic activities at the subnational level (Kogler, Rigby, and Tucker 2013;Boschma, Balland, and Kogler 2015;Rigby 2015;Balland 2017;Kogler, Essletzbichler, and Rigby 2017;Kogler and Whittle 2018).Here, we calculate the RELATEDNESS index using the network-based knowledge space representation of technological relatedness across CPC classes (Kogler, Rigby, and Tucker 2013).In the knowledge space, two CPC classes are connected by the degree of their technological relatedness measured as pairwise conditional probability that the regions are specialized in both.Then, RELATEDNESS is calculated at the level of the CPC class in the focal region by taking the sum of technological relatedness to existing other CPC classes in the region that have RTA ≥ 1 in the period, divided by the sum of technological relatedness of the CPC class to all the other CPC classes in the knowledge space.By design, this index can take a value between 0 percent and 100 percent.The value 0 percent indicates that the region is not specialized in any of the technologies related to the focal CPC class, while an increase in RELATEDNESS means that related technologies are present in the region's knowledge space.Appendix 1 in the online material contains a formal description of this indicator.
The knowledge space generated using the above cospecialization approach has been used extensively in the diversification literature (Tanner 2014;Boschma, Balland, and Kogler 2015;Kogler and Whittle 2018;Balland et al. 2019).One advantage of this technique is that it directly builds upon the regions' ability to specialize in pairs of technologies.Given the substantial variations in size within and across observed periods, on both technological class and regional unit observations, the RTA approach offers the opportunity to make sensible comparisons while also drawing particular attention to a region's capabilities as they relate to its specialization core.Another useful approach to generate the knowledge space uses coclassification of patents into pairs of technologies (e.g., Breschi, Lissoni, and Malerba 2003;Kogler, Rigby, and Tucker 2013).Since our primary aim is to contribute to the regional diversification literature with our co-inventor network approach, we apply the former measure and will call for further research to leverage the latter techniques.
Regional controllers are important to include because related and unrelated diversification is conditioned by the development of local economies (Boschma and Capone 2015;Petralia, Balland, and Morrison 2017).Thus, we have calculated and tested many indicators of regional economic and technological development that unfortunately violated the rules of multicollinearity. 5An important indicator that withstood multicollinearity tests is EMPLOYMENT, which denotes the total number of employees in the region reflecting the degree of agglomeration externalities (Ciccone 2002).
To identify the role of patenting firms in technological diversification, we introduce several variables at the region-technology level.FIRMS captures the number of firms that have been assigned a patent in the given CPC class and the region.The higher this number, the greater value of absolute specialization in patenting in a given technology in the region (Kemeny and Storper 2015).NEWFIRMS is the number of firms that patent in the region and technology class for the first time.This indicator captures the capacity of new firms that might diversify the region into new technologies (Neffke et al. 2018).To reflect the phenomenon that firm size correlates with innovation advantages within the specific industry (Acs and Audretsch 1987), we quantify INVPER-FIRM, which equals the number of inventors divided by the number of firms.6MULTILOC is the share of companies that patent in the given CPC class and region by employing local inventors but employ inventors living in other regions as well.Multilocation firms have been found to exploit external knowledge sources in their innovation (Leiponen and Helfat 2011) and can transfer knowledge across units at different locations (Lahiri 2010;Shin et al. 2023), especially in case of strong internal connections (Alcácer and Zhao 2012).
To investigate the role of co-inventor collaboration in technological diversification of regions, we construct the regional inventor network.In this network, inventors are connected if they have worked together, that is, if they are listed as co-inventors on a single patent application, and depending on the location of their collaborators, these connections can remain within regions or can span regional boundaries.
Figure 1 illustrates the backbone of the aggregate interregional co-inventor network in Europe containing all CPC classes over the entire period, investigated by depicting the most likely network path (in network science terms, the maximum spanning tree) between any pairs of regional economies.This network representation is a simplification of the full network, which keeps all regions and their typical co-inventor links with other European regions.One can observe a hierarchy in this network in which nonmetro regions tend to connect to neighboring metro counterparts that link to major (mostly national) hubs.Some of the largest centers, like Paris, Milano, Stockholm, or Berlin, are important connections for more distant nonmetro regions as well.Less innovative regions in the periphery of Europe connect directly, but weakly, to innovative central regions.
Taking the four-digit CPC classes that inventors patent in, we construct four network indicators to describe collaboration patterns of inventors in given technological domains in regions.The formal definitions of these network indicators can be found in Appendix 1 in the online material.
DENSITY is the number of collaboration links that the inventors in the given CPC class have to all inventors in the region, including all CPC classes, divided by the potential maximum number of collaboration links within the region.This index captures the magnitude of co-inventor collaboration, considering the total number of inventors in the region, and is widely used to characterize the knowledge transmission capacity of collaboration networks (Fritsch and Kauffeld-Monz 2010;Tortoriello, Reagans, and McEvily 2012).We use this indicator as a control variable to sort out the effect of local collaborations on technological diversification.
Our first explanatory network variable is the EXTCOLLAB indicator, which quantifies the share of external co-inventor collaborations in the total number of collaborations the inventors in the region-technology class have.The index can take a value from 0 (the region has no external connections) to 1 (all connections are with external entities).The Note: The network depicts aggregated co-inventor ties across regions over the entire period of the investigation using the maximum spanning tree representation.We keep only one path between any two regions such that the sum of tie weights is maximal.
EXTCOLLAB index quantifies the access to knowledge residing in other regions through individual collaborations.We apply the relative share in this formula to recognize the importance of external collaborations in diversification.Scholars have frequently argued in favor of external collaboration as the primary engine by which novelty is brought into the region (Bathelt, Malmberg, and Maskell 2004;Boschma and Iammarino 2009;Neffke et al. 2018) but also claimed that its unison with local collaborations was optimal (Isaksen 2015).
Next, we quantify the DIVERSITY index, which is the spatial diversity of the technology-region pairs by aggregating the co-inventor links that a technology-region has to other regions and calculating the entropy of the aggregated tie strength distribution.Providing access to new diversity might play a central role for interregional collaboration and subsequent regional branching (Bathelt, Malmberg, and Maskell 2004).A diverse set of links provides the opportunity to combine distinct pieces of knowledge and to come up with innovative ideas (Granovetter 1985;Burt 2004).In this sense, geographic diversity in social networks captures the potential variety in the pool of knowledge that resides in various locations and that the entity in focus has access to.For example, individuals who have spatially diverse communication networks and connections to many places are typically wealthier than those who do not (Eagle, Macy, and Claxton 2010).On a more aggregate level, Eriksson and Lengyel (2019) find that spatially diverse co-worker links facilitate the growth of those industry-region pairs that have a low degree of specialization.We expect that the diversity of external knowledge access facilitates diversification into new technologies.
Our final network variable is INTENSITY, which aims to capture the phenomenon that most of interregional co-inventor collaboration happens within boundaries of firms that have R&D branches in many regions or at least work with many inventors distributed across regions.From the perspective of regional diversification, these firms act as sources of external knowledge exchange (Neffke et al. 2018;Elekes, Boschma, and Lengyel 2019), since the transfer of information is easier to orchestrate within firms that share the same overarching organizational structure (Lengyel and Leskó 2016;Crescenzi, Dyèvre, and Neffke 2022).However, firms are also known to employ specific (spatial) R&D strategies, and therefore the intensity of intrafirm knowledge transfer is likely to vary by region (Alcácer and Chung 2007;Shin et al. 2023).To capture this heterogeneity, we quantify the intensity of intrafirm collaboration to other regions by calculating the density of collaboration ties within firms as the ratio of observed withinfirm collaboration in all possible within-firm collaborations.
Table 1 summarizes the indicators described above.We present summary statistics, VIF values, and pairwise correlations in Table 2. Except for the strong correlation between EXTCOLLAB and INTENSITY, which are not included in the regression models together, multicollinearity does not distort our estimation.

Analysis
The analysis contains three steps that build on each other and aim to uncover the role of co-inventor collaborations for the technological diversification of regions.
In the first step, we calculate the probability of ENTRY at levels of RELATEDNESS as a ratio of observed diversification among all possible cases, following the earlier ECONOMIC GEOGRAPHY literature on diversification (Hidalgo et al. 2007;Neffke, Henning, and Boschma 2011).We contribute to this generally accepted technique by calculating these probabilities by levels of EXTCOLLAB that the probabilities of ENTRY in subsets sum up to the overall probability of ENTRY.We use the twenty-fifth and seventy-fifth percentile of EXTCOL-LAB to distinguish region-technologies that had a low, medium, or high share of external collaboration among all co-inventor links and compare their ENTRY probability with probabilities of all observed entries in regions at each RELATEDNESS value.
Next, we analyze the role of interregional co-inventor collaboration on technological diversification with a fixed-effect regression approach by estimating ENTRY in a linear probability model (LPM) where X i,r,t−1 stands for independent variables on the level of CPC class i and region r RELATEDNESS, FIRMS, NEWFIRMS, INVPERFIRM, MULTILOC, and DENSITY, E r,t-1 represents region-level EMPLOYMENT, while Z i,r,t−1 denotes interregional collaboration network variables EXTCOLLAB, DIVERSITY, and INTENSITY, m i,r,t is region-technology fixed effect-that can control for unobserved variations across regions such as institutions-and 1 i,r,t is the error term.Period-fixed effects are introduced as a robustness check to evaluate whether the main findings hold, even if we control for time-specific circumstances.To test whether the network indicators of interregional co-inventor collaboration facilitate related diversification, we introduce the interactions of RELATEDNESS and these variables.Regressions are run on a panel of technology-regions in which observations are traced only until the event of entry.All variables are standardized to have a mean of 0 and a standard deviation of 1.

Variable Description
Variable Name Description RELATEDNESS Relatedness density (Hidalgo et al. 2007) calculated on the knowledge-space network.Measure of how close an emerging technology i is to other existing technologies in the region at time t.EMPLOYMENT Total number of employees in a region.

FIRMS
The number of firms in a region and CPC class that have been assigned at least one patent until t.

NEWFIRMS
The number of firms in a region and CPC class that have been assigned a first patent since t-1.

MULTILOC
The share of firms in the region and CPC class that employ inventors in other regions as well.

INVPERFIRM
The number of inventors per number of firms that are assignees of patents in the region and CPC class at period t.

EXTCOLLAB
The ratio of interregional collaborations among all collaborations of the inventors living in the region and patenting in a CPC class in period t.

DENSITY
The ratio of observed co-inventor collaboration among all possible collaborations the inventors in a specific CPC class could have within the region.DIVERSITY Entropy of the aggregated co-inventor connections from a CPC class and the region to other regions at period t.

INTENSITY
The ratio of observed links within the firm to other regions among all possible such links.This measure is calculated at the CPC and region level at period t.Lagging explanatory variables is a well-accepted technique in the diversification literature (Neffke, Henning, and Boschma 2011).Although interregional knowledge transfer might have a faster influence on regional diversification, especially when interregional co-inventorship and submission of patent application coincides with the event of diversification, lagging all variables is the best strategy to reduce the likelihood of reversed causality.Yet, we have also tested models in which network variables are not lagged, and the results of these tests are in line with the main findings presented here.
The linear probability model (LPM) approach utilized here has the advantage over logistic regressions in estimating binary outcomes in terms of interpretability of coefficients and interaction terms.However, probabilities predicted by the LPM can be negative or can exceed one.We report in Appendix 2 in the online material that this is hardly the case in our estimation.However, since it is a common practice in the regional diversification literature (e.g., Neffke, Henning, and Boschma 2011), we report the significance and sign of the coefficients of the full model in a logistic regression specification in the main text.
Finally, fixing all other variables at their mean, we calculate the marginal effects of RELATEDNESS on ENTRY at levels of the network variables EXTCOLLAB, DIVER-SITY, and INTENSITY.This exercise enables us to investigate the joint effect of inventor collaboration, and technological relatedness in catalyzing regional diversification, and to better understand which characteristics of the interregional co-inventor networks can compensate for the lack of related technologies in a region.

Interregional Collaborations and Related Diversification
Figure 2 illustrates how entry probabilities change along the spectrum of technological relatedness and differentiate those region-technologies where co-inventor collaboration is dominantly external.Following Boschma, Balland, and Kogler (2015) we focus only on those observations, where RELATEDNESS is between 5 percent and 35 percent, since the value of the index is smaller than 35 percent for more than 90 percent of our observations.
As expected from previous results (Boschma, Balland, and Kogler 2015;Rigby 2015;Kogler, Essletzbichler, and Rigby 2017), ENTRY increases sharply with technological relatedness in the full set of region-technologies.Further, the probability of entry increases in all three subsets.The high share of external collaboration (EXTCOLLAB is above 75 percent, hollow hexagon) is associated with higher probability of technological entry along the spectrum of RELATEDNESS as opposed to the medium (hollow square) or low (hollow triangle) share.
This finding supports the importance of interregional collaboration in regional diversification.The result is in line with the mainstream thinking in economic geography: novelty is easier to access through extraregional collaboration or global pipelines than locally (Bathelt, Malmberg, and Maskell 2004;Boschma, Eriksson, and Lindgren 2009;Fitjar and Rodríguez-Pose 2011).Previous results on productivity growth suggest that interregional co-worker links can compensate for a missing knowledge base in the region (Eriksson and Lengyel 2019).On the individual level, a recent study shows that workers who have high shares of external contacts can import new Vol.99 No. 5 2023 DIVERSIFICATION VIA COLLABORATION NETWORKS skills to the region (Lőrincz et al. 2020).Lastly, Asheim and Isaksen (2002) advance a more qualitative perspective, demonstrating that the need to develop external linkages can arise in instances when local firms outgrow their region.Our new evidence contributes to this literature by illustrating that interregional collaboration is important for technological diversification in regions.

The Role of Diverse and Intrafirm Collaborations across Regions
Knowledge can be transferred across units within multilocation firms (Lahiri 2010;Alcácer and Zhao 2012).We estimate equation (1) to better understand how such knowledge transfers facilitate diversification processes in regions where these firms reside.
In Table 3, we introduce regression results in a stepwise manner such that models 1-5 and 8-9 are estimated on the full sample of regions, whereas models 6-7 focus on subsamples of metro and nonmetro regions.
Model 1 is our baseline model including all but the explanatory variables.All of these variables are significantly related to ENTRY, and their coefficients remain stable over the various model specifications.As expected, RELATEDNESS has a strong and positive correlation with ENTRY, a finding that supports the vast literature on diversification Note: Markers denote the number of entries over all possible entry options binned into technological relatedness categories (deciles of relatedness density).RELATEDNESS is decomposed into low, medium, and high share of external collaboration by applying the twenty-fifth and seventy-fifth percentiles of the EXTCOLLAB measure.Observations are aggregated to the full period.150,348.7 150,329.5 149,423.6 150,348.5 149,314.0 254,731.8 -169,679.4 138,328.0 520,371.7 511,581.8 ll -75,167.3 -75,156.8 -74,702.8 -75,165.2 -74,659.5 -127,354.9 84,850.7 -69,148.0 -260,174.9 -255,774.9Note: Coefficients are presented in LPM models and log-odds ratios in LOGIT models.Standard errors in parenthesis.In case of LPM, heteroscedasticity-robust standard errors are reported.*, **, *** denote significance at the 0.1, 0.05, 0.01 level.(Neffke, Henning, and Boschma 2011;Whittle and Kogler 2020).The positive and significant coefficient of EMPLOYMENT signals that large regions diversify into new technologies with higher likelihood because these agglomerations already have diversified technological portfolios and dense knowledge spaces (Boschma, Balland, and Kogler 2015).Essentially, a regional knowledge space that already consists of a variety of specialized competencies provides a good point of departure for adding on even further, albeit related, knowledge domains.On the other hand, the knowledge spaces of smaller regional economies, which naturally contain fewer specialized competencies, are much more constrained in terms of the number of possibly strongly related knowledge domains that are within reach and thus might further diversification processes.While this might imply that diversification opportunities are simply driven by the sheer size of a place, this is not necessarily the case.Rather it is more so the actual structure of regional knowledge spaces in terms of related variety and average clustering (Tóth et al. 2022) or the overall coherence (Rocchetta et al. 2022) that significantly shape regional diversification opportunities and the resilience thereof.

ECONOMIC GEOGRAPHY
The FIRMS variable, which captures the number of firms that have been assigned a patent in the given CPC class at the region level, is negatively related to ENTRY.In other words, a high value of FIRMS indicates a saturation at the CPC class level and thus to some extent implies a degree of local overspecialization.This in turn might result in limited diversification opportunities given that regional technological knowledge production activities are concentrated in fewer spheres of the regional knowledge space.Contrary, in a scenario where the regional cohort of firms specializes across a large and diverse set of knowledge domains, which in turn of course also increases the number of potentially related classes, diversification opportunities will be higher.Furthermore, we find that two types of firms can boost diversification as it is widely discussed in the innovation literature (e.g., Acs and Audretsch 1987).First, small new firms can enter technological areas new to the region that is suggested by the negative coefficient of INVPERFIRM and the positive coefficient of NEWFIRMS.Second, those firms that are active in the region but have branches outside the region as well can contribute to diversification.The positive coefficient of MULTILOC highlights that multilocation firms can build pipelines across regions that can foster the transfer of new knowledge and facilitate diversification.This latter finding forecasts our final message regarding the role of interregional collaborations.
DENSITY is a significant positive predictor of ENTRY, suggesting that dense networks of local co-inventor collaboration favor diversification in regions compared to sparse networks.Such networks facilitate the emergence of a new technology because local knowledge flows are faster, more effective in dense networks, and complex knowledge is easier to transmit (Sorenson Rivkin, and Fleming 2006;Abbasiharofteh, Kogler, and Lengyel 2020).
Starting from model 2, we investigate the role of interregional co-inventor collaborations.The positive coefficient of EXTCOLLAB verifies our previous finding observed in Figure 2. Regions tend to diversify into new technologies with higher likelihood in case inventors collaborate with peers outside the regions.The negative interaction terms between EXTCOLLAB and RELATEDNESS in model 3 confirm that external collaborations can compensate for the lack of local related technologies.If related knowledge is missing in the region, inventors can still develop an emerging knowledge base by collaborating externally.Therein, external co-inventor collaboration is shown to provide access to technologies that are new to the region (Bathelt, Malmberg, and Maskell 2004;Boschma and Iammarino 2009).
Next, we analyze two qualitative aspects of interregional collaborations from model 4. From this model on, we exclude EXTCOLLAB due to its high correlation with IN-TENSITY.Neither DIVERSITY nor INTENSITY have a significant relationship with ENTRY in model 4. Their coefficients turn positive significant only when their interaction term with RELATEDNESS is introduced in model 5.The interaction term is significant and negative with a similar value to the main effects of DIVERSITY and INTENSITY.This suggests that the role diverse knowledge access and intrafirm interregional knowledge transfer play in regional diversification is not independent from the level of relatedness the technology has to other existing technologies in the region.Appendix 2 in the online material illustrates that predicted probabilities using the estimation of model 5 are below 0 in very few cases only and that the bulk of predictions range between 0 and 0.4.
These results highlight that regions can benefit from diverse knowledge access for developing those technologies that have weak local bases.Similarly, knowledge transfer within firms across regions helps the emergence of those new technologies that are not related to existing technologies in the region.This compensation of within-firm knowledge transfer for the missing local capabilities is in line with previous findings that stressed other sources of knowledge transfer on unrelated diversification like mobile inventors, entrepreneurs, or foreign-owned firms (Neffke et al. 2018;Elekes, Boschma, and Lengyel 2019;Miguelez and Morrison 2023).We can confirm that, like in the case of mobility-induced co-worker relations (Eriksson and Lengyel 2019), those technologies can enjoy the benefits of geographically diverse connections and strong withinfirm links across places that miss related specializations in the region.
In models 6 and 7, we find that the above pattern is true for both metropolitan regions without further limitations.However, DIVERSITY and its interaction with RELATED-NESS lose significance in nonmetropolitan regions.This is not surprising, since large metropolitan areas typically have more diverse connections than small regions.Yet, within-firm knowledge transfer across regions remains effective in triggering unrelated diversification in both metropolitan and nonmetropolitan regions.In Appendix 3 in the online material, we apply the OECD definition of small-medium-metro-large metro region classification (OECD 2022).Results reported there confirm that DIVERSITY can substitute RELATEDNESS only in large metro regions, while INTENSITY is found to compensate for missing RELATEDNESS in all regional types.
The period-fixed effect introduced in model 8 takes unobserved time-specific shocks and deteriorates the significance of INTENSITY but leaves all other explanatory coefficients unchanged.Appendix 4 in the online material contains a regression table that includes period-fixed effects in further models.These regressions support our main findings regarding the role of EXTCOLLAB and its interaction with RELATEDNESS.However, introducing the period-fixed effect distinguishes useful external collaboration by region types.DIVERSITY seems to compensate for missing RELATEDNESS in metro regions, while INTENSITY can substitute for the lack of related technologies in nonmetro regions.We discuss the potential policy implications of these results in metro and nonmetro regions in the concluding section.

ECONOMIC GEOGRAPHY
The logistic regressions in models 9 and 10 further confirm the stability of the findings.Unreported robustness checks cover models in which network variables are not lagged, while yet further models included variables like concentration of patents in firms or certain CPC classes and number of inventors in the region that correlate with other independent variables.The sign and significance of explanatory variables in those robustness checks remain stable across all model specifications.

Co-inventor Networks and Unrelated Diversification
The interaction terms between RELATEDNESS and interregional network indicators reported in Table 3 point toward a potential substitution effect.Extraregional collaboration might compensate for the lack of related technologies in the region similar to labor flows (Neffke et al. 2018;Miguelez and Morrison 2023), international trade (Boschma and Iammarino 2009), or multinational companies (Elekes, Boschma, and Lengyel 2019).To better understand whether such substitution effect exists, we calculate the marginal effect of RELATEDNESS on ENTRY at the levels of interregional network indicators.
Figure 3A illustrates that the effect of RELATEDNESS on ENTRY decreases as EXTCOLLAB grows.However, the marginal effects remain positive along the full spectrum.This means that interregional collaboration mitigates the need for related technologies to be present but still facilitates related diversification.We do not find that interregional collaboration in general can substitute the local pool of related technological knowledge, but we find that externally oriented co-inventor networks require a smaller degree of local relatedness to diversify into a certain technology.
However, we do find that certain types of interregional collaboration can indeed substitute for related knowledge in the region.Figure 3B and C demonstrate that the effect of RELATEDNESS on ENTRY decreases as DIVERSITY and INTENSITY increase.Yet, at medium levels of these indicators, the marginal effect of RELATEDNESS turns negative.This means that a wide knowledge pool accessible through diverse connections and knowledge transfers facilitated by strong collaborations within multilocation firms can enable local inventors to diversify the regional patent portfolio into unrelated technologies.inventors and firms interacts with different granularities of technological relatedness in the knowledge space created from cospecialization patterns of regions as well as co-occurrence of technology classes in patents.
In a further consideration, it should be noted that the effect of technological diversification on regional productivity might be a nonlinear one, and therefore the process of branching per se is unlikely to directly translate into increased economic rents from the local innovation system (Rocchetta, Ortega-Argilés, and Kogler 2022).In line with this, the interplay of entry-relatedness and entry-potential, the latter referring to knowledge recombination activities that ultimately drive relatedness measures while also being more closely associated with the development of novel products and processes of economic value, is yet another aspect that further research ambitions in this direction should take into account (Kogler et al. 2023).Essentially, not each branching process might provide equal opportunities for development.Further research is needed to uncover how the role of collaboration networks in regional branching depends on national policy that might concentrate on specific technologies with various abilities to exploit interregional networks and time-specific conditions that can change the efficiency of nonlocal collaboration.Finally, future efforts to aid our understanding of regional path creation and branching processes could pursue a geographical political economy (GPE) approach along the integrative framework that MacKinnon et al. (2019) suggest.Such a GPE framework not only considers insights from literatures that are complementary to EEG thinking, which dominates this line of inquiry, but also suggests further key elements that might significantly determine path creation and branching processes.
The present investigation offers some highly relevant insights for future policy initiatives geared toward regional economic development and upgrading.In particular, the findings indicate how a region might pursue unrelated diversification of its core capabilities.Nevertheless, the study also indicates that not all connections carry the same value and that these might even further vary across regional types.This line of reasoning resonates with recent S3 policy making, which acknowledges the importance of complementary linkages and access to centers of excellence.We find connections with a diverse set of regions favor technological diversification in metropolitan areas that are more capable of benefiting from diverse pools of knowledge.On the contrary, nonmetro, small, and peripheral regions often struggle to create such diverse connections and therefore run the risk of lagging behind in the race for technological development.Our results however indicate that these smaller regions can still benefit from the presence of multilocation companies that can foster diversification into new technologies that are completely new to the regional portfolio.Policy initiatives in these regions should foster the collaboration of local company units with remote sites in order to maximize knowledge transfer processes within companies that might be capable of translating extralocal knowledge into tangible local technological development.

Figure 1 .
Figure 1.The backbone of interregional co-inventor networks in Europe, 1981-2015.Note: The network depicts aggregated co-inventor ties across regions over the entire period of the investigation using the maximum spanning tree representation.We keep only one path between any two regions such that the sum of tie weights is maximal.

Figure 2 .
Figure 2. Diversification by technological relatedness and interregional collaboration.Note: Markers denote the number of entries over all possible entry options binned into technological relatedness categories (deciles of relatedness density).RELATEDNESS is decomposed into low, medium, and high share of external collaboration by applying the twenty-fifth and seventy-fifth percentiles of the EXTCOLLAB measure.Observations are aggregated to the full period.

Figure 3 .
Figure 3. Marginal effects of technological relatedness at levels of interregional co-inventor collaboration.Note: Average marginal effects have been calculated at standardized levels of (A) external collaboration rate (EXTCOLLAB), (B) diversity of connections across regions (DIVESRITY), (C) collaboration across regions but within firms (INTENSITY) by keeping all other variables at their means.Markers denote estimates and whiskers denote standard errors.

Table 2
Descriptive Statistics and Pearson Correlation of Variables

Table 3
Fixed-effect Regressions with the Dependent Variable ENTRY