Tsukuba Economics Working Papers
No. 2009-014	
 The Dynamics of R&D Network in the IT Industry
byNobuyuki Hanaki, Ryo Nakajima, Yoshiaki Ogura
November 2009

UNIVERSITY OF TSUKUBA
Department of Economics
1-1-1 Tennodai
Tsukuba, Ibaraki 305-8571
JAPANThe Dynamics of R&D Network in the IT
Industry
Nobuyuki Hanakia,b∗, Ryo Nakajimab , Yoshiaki Ogurac†a

GREQAM and Université de la MéditeranéeCentre de la Vieille Charité, 2, Rue de la Charité 13236 Marseille, cedex 02, FRANCEb
Doctoral Program in Economics,
University of Tsukuba, 1-1-1 Ten-nodai, Tsukuba, Ibaraki 305-8573, JAPANc
College of Business Administration,
Ritsumeikan University, 1-1-1 Noji Higashi, Kusatsu, Shiga 525-8577, JAPAN

August 3, 2009

Abstract
In this paper, we provide an empirical analysis of evolving networks of successful R&D collaborations in the IT industry (consisting of ﬁrms that obtained
patents in the technological category of computers and communication) in the U.S.
between 1985 and 1995. We ﬁrst show that the R&D network has become more
extensive, more clustered, and more unequal in the sense that ‘stars’ have emergedin the network. We then analyze the effect of the existing network structure in theprocess of new R&D collaboration formation. We control for unobserved similarities among ﬁrms based on the community structures within the network that thealgorithm developed by Girvan and Newman (2004) identiﬁes and ﬁnd a signiﬁcant cyclic closure and preferential attachment effect.

Keywords: Dynamic networks, R&D partnerships

1 Introduction
The interﬁrm positive spillover of research and development (R&D) activities is widely
accepted as an empirical stylized fact in the R&D literature. Existing empirical studies
have found that this spillover effect is stronger among companies in a technological or
geographical neighborhood (Jaffe, 1986; Jaffe et al., 1993) and among companies thatinvest in R&D sufﬁciently to maintain their absorptive capacity for external knowledge∗ Corresponding Author. Tel.: +33-4-91-14-07-27. Fax: +33-4-91-14-02-27.

† E-mail addresses: nobuyuki.HANAKI@univmed.fr and hanaki@dpipe.tsukuba.ac.jp (N. Hanaki), nakajima@dpipe.tsukuba.ac.jp (R. Nakajima), and yogura@ba.ritsumei.ac.jp (Y. Ogura).

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(Cohen and Levinthal, 1989). Furthermore, this spillover effect is stronger among collaborating companies than among competing companies (Branstetter and Sakakibara,
2002; Gomes-Casseres et al., 2006). These studies implicitly or explicitly recognizethat knowledge exchange among innovative companies is the key determinant of R&D
spillovers. In response to the recent surge of R&D collaborations in high-tech industries (Hagedoorn, 2002), many theorists have analyzed interﬁrm knowledge spillovers
through R&D collaborations in network settings by applying the network formation
theory (e.g., Goyal and Moraga-Gonzalez, 2001; Goyal and Joshi, 2003; Cowan andJonard, 2004; Meagher and Rogers, 2004). There is ample evidence that the positioning of companies in R&D collaboration networks substantially affects their productivity in generating new knowledge, which is embodied in artifacts such as patents andnew products (e.g., Powell et al., 1996; Ahuja, 2000; Schilling and Phelps, 2007).
Given the importance of network architecture in innovation performance, it is reasonable that innovative individuals and companies may want to form R&D collaborations strategically to control knowledge spillovers. In fact, the importance of thestrategic formation of R&D alliances has been widely recognized in the literature.1 In
recent years, the theoretical analysis of network formation has been a lively area of
research, not only in the context of R&D (e.g., Goyal and Moraga-Gonzalez, 2001)
but also in other contexts; see Jackson (2006) for a review. These studies incorporate
individual incentives to derive strategically stable network architecture and to analyze
the efﬁciency characteristics of the network. However, empirical analyses of network
formation are relatively rare.
The determinants of R&D collaboration between companies have been thus far investigated by industrial organization economists. They have found that the company’s“absorptive capacities” (Cohen and Levinthal, 1989), such as their R&D size and intensity, signiﬁcantly inﬂuence the likelihood of forming R&D alliances (e.g., Röller
et al., 1998; Hernán et al., 2003). While the characteristics of ﬁrms may explain thetypes of companies that are likely to collaborate, they provide insufﬁcient understanding of how companies interact with each other. For example, if the number of pathways
for communication between companies increases, the enhanced ﬂow of knowledge becomes attractive and, thus, any collaboration may stimulate further collaboration. Thissuggests that the network structure that is in place inﬂuences how new collaboration
links are formed. However, existing empirical studies do not address this recursive andinductive aspect of R&D network formation. Therefore, in this paper, we address thefollowing questions: How does collaboration between companies of one type inﬂuence
the actions of other types of company? What structural characteristics are more likely
to stimulate further R&D collaboration?
The goal of this paper is to study the endogenous development of R&D networks
in the U.S. Information and Technology industry (deﬁned by the technological categories of the obtained patent, as explained in the next section) by showing how companies have established new R&D collaborations with each other. Based on individual
ﬁrm-level data on R&D collaboration, which was constructed from the information on
granted patents, we estimate the conditional probability of new collaboration formation
between any pair of companies in the industry given the network structure observed in
1 For a recent review of the theoretical literature, see, for example, Bloch (2005)2

the previous period. In particular, we estimate the impact on R&D collaboration formation of certain kinds of network topology, such as cycles and stars.
Given the complexity of the subject, the empirical analysis of the formation of an
R&D network has been hampered by a scarcity of data of alliances among companies
and the members of such alliances. Existing empirical studies on this subject (e.g.,
Gulati and Gargiulo, 1999; Hagedoorn, 2002; Schilling and Phelps, 2007) have reliedon the “publicly reported alliance counting method” (Hagedoorn, 2002) for data collection; that is, information on announced interﬁrm R&D collaboration is collected fromvarious publications, such as newspapers, journal articles and books. Although such
literature-based data collection is extensive, the information is likely to be incomplete,
as only publicly announced alliances are included in the dataset.2
In this paper, we adopt a different approach. We collect information on interﬁrm
collaborations by using the NBER Patent Data File (Hall et al., 2001). Since the pioneering work of Scherer (1965) and Schmookler (1966) appeared, patent data havebeen used in a number of empirical studies of research collaboration among innovative
companies (e.g., Singh, 2005; Cantner and Graf, 2006).
The main reason for using the NBER patent data is that these data provide information about all researchers who were involved in creating the innovation along withinformation on the patenting company, its geographic location, and the types of technology involved. The names of the inventors are recorded along with the name of thecorporate assignee claiming each patent. We match the lists of inventors’ names acrossdifferent assignee companies to see if they are connected via common inventors. If
the same inventors work on a particular research project across two innovating companies, we ascribe the project to an R&D partnership and identify those companies as
collaborators through the inventors. Longitudinal data on an evolving R&D network
are created by collecting annual snapshots of instantaneous networks.
In the process of identifying inventors, an identiﬁcation error, often called the “Whois Who” problem (Trajtenberg et al., 2006) cannot be avoided. The problem refers to
the possibility that the name of an individual associated with a patent may have been
inadvertently spelled differently or that two people may have the same name, leading
to inaccuracies in the identiﬁcation process. We have deliberately used a computer
matching procedure (CMP) that was recently proposed by Trajtenberg et al. (2006) tominimize errors in identifying inventors.
We start with an empirical examination of the macro-dynamic properties of R&D
network structures. Several interesting features of the R&D collaboration network are
identiﬁed. First, R&D networks have increased in size substantially over time. The
number of nodes has increased substantially and, at the same time, the number of links
per node has steadily grown. Second, networks have become increasingly connected,
and the giant connected component has emerged and expanded. Third, the average
distance between nodes has been stable, although network sizes have increased. Fourth,
two given connected nodes tend to be linked to a common third party. The tendency
to form local circles was signiﬁcant in the 1990s. Given these ﬁndings, we can saythat the R&D network is an emerging “small world” (Watts and Strogatz, 1998). Our
2 Another problem is that the information on the termination of R&D collaborations is not usually published systematically, particularly for licensing and customer–supplier relationships.

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ﬁnal ﬁnding concerns the distribution of R&D collaborations. We ﬁnd that networks
have become more uneven. Our interpretation is that current R&D networks exhibit
a core–periphery structure in which connected companies are becoming increasinglyconnected.
These ﬁndings have led us to develop a utility-based empirical model of joint R&D
collaboration formation. Although agents behave nonstrategically, the model enables
us to condense the issues of collaboration formation to the agents’ welfare. Although
our model is simple, it exhibits two mechanisms for joint collaboration: random andnetwork-based. Hence, this model is similar to that of Jackson and Rogers (2007).
Random collaboration occurs when a pair of companies meet uniformly at random andcollaborate with each other by chance, given that the characteristics of the pair arecontrolled for. In network-based collaboration, the formation of new links depends onthe exiting network structures observed by companies in advance.
We argue that two structures are important in the context of the network-based
collaboration process. First, we focus on the cyclic structure. High search costs forcollaborating partners may promote the formation of R&D alliances involving intermediate collaboration partners, which may lead to the formation of local neighborhood
collaboration chains. Second, we focus on the star structure. Indirect beneﬁts fromspillovers may generate a positive feedback loop through which companies connect
with a handful of super-connected stars that then become increasingly connected. This
process is often called “preferential attachment” (Barabási and Albert, 1999). An empirical model that incorporates these features is compatible with the macroeconomic
empirical ﬁndings described above.
To gain more insight into the circumstances under which R&D collaboration occurs, we estimate an empirical model that controls for a number of company background characteristics. The estimation results show that similarities in the size of R&D
input have a non-monotonic impact on the probability of collaboration, which suggests that companies whose scale of R&D activity is similar but not too similar tend tocollaborate. We ﬁnd that there is a signiﬁcant relationship between network structure
and R&D collaboration. Companies with many collaborators are likely to attract further collaborations in the next period. This suggests signiﬁcant preferential attachment
in collaboration formation. At the same time, we ﬁnd evidence of signiﬁcant cyclic
closure effects, which suggests that companies are willing to collaborate with othercompanies that form part of a chain of common third-party collaborators within the
network.
There are at least two explanations for these empirical ﬁndings regarding the roleof network structure in R&D collaboration formation: the importance of referral in
the search for collaborating partners, and the effort made by ﬁrms to increase the appropriability of the fruits of joint R&D projects. Referrals from current collaborators
reduce the cost of ﬁnding new and reliable collaborators. Because referrals are madebetween ﬁrms that have collaborated before, this results in cyclic closure. In addition,
if a ﬁrm has collaborated with many others in the past, referrals can lead the ﬁrm toattract more collaboration in the future. Finding a reliable partner is important for aﬁrm entering into joint R&D projects in order to increase the appropriability of the
fruits of the project by maximizing incoming knowledge spillovers while minimizing
outgoing knowledge spillovers (Cassiman and Veugelers, 2002). Outgoing spillovers
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can also be reduced by forming a dense web of collaborations and strengthening thethreat of joint punishments against deviators. Such considerations also enable ﬁrms
to ﬁnd new partners in local circles. Unfortunately, we are unable to discriminate theeffect of these two mechanisms from our data.
Existing empirical analyses of network formation among ﬁrms (see, for example,
Gulati, 1995; Gulati and Gargiulo, 1999; Powell et al., 2005) have also found that
network-based mechanisms such as preferential attachment and cyclic closure are important. These studies, however, tend to overestimate the importance of such mechanism because of the lack of control for unobserved similarities among ﬁrms. In our
analysis, we control for unobserved similarities among ﬁrms by identifying the community structures in the existing network using the algorithm developed by Girvan
and Newman (2004). The result shows that the effect of the existing network structure remains statistically signiﬁcant even after unobserved similarities among ﬁrms arecontrolled for.
The rest of the paper is organized as follows. The data are described in Section
2. Section 3 is a discussion of the evolution of the structure of networks over time.
Section 4 is a description of the framework of our statistical analysis. The empiricalresults are discussed in Section 5. Section 6 is the conclusion.

2 Network Data
The data used for this study are drawn from NBER patent data. We restrict our attention
to the subsample of companies that have obtained patents classiﬁed as “Computers andCommunications” by Hall et al. (2001).3 This technological category is closely related
to the R&D activities of the Information and Technology (IT) industry, and we refer tothe set of ﬁrms in our dataset as the IT industry for expositional purposes.
The industry provides an interesting context for our study because companies in thisindustry actively obtained patents for their intellectual property (Levin et al., 1987). It
is also noted by Hagedoorn (2002) and others that the IT industry has been one of
the most active industries in forming R&D alliances. In fact, the IT industry has had
the highest share of newly established R&D partnerships among high-tech industries
since the late 1980s. Thus, there are a sufﬁcient number of R&D collaborations in thisindustry.
We use data on patents at the U.S. Patent and Trademark Ofﬁce that were registered
between 1985 and 1995. We choose 1985 as the initial year of our sample period
because the number of R&D collaborations established before 1985 is too small for ameaningful analysis of R&D networks.

2.1 Network Construction
We use a schematic graph to represent an R&D network, which is a collection of innovating companies (nodes) and a collection of joint collaborations (links) between
3 According to the classiﬁcation of Hall et al. (2001), this technological class includes the following
subcategories: Communications; Computer Hardware & Software; Computer Peripherals; and Information
Storage.

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Table 1: An example of the raw data.
PatentP1
P2
P3
P4

Assignee
A1
A2
A1
A3

Researchers
R 1 , R2R 1 , R3 , R4
R 1 , R4R 2 , R5

them. In what follows, network nodes consist of independent companies. Subsidiarycompanies are not included as network nodes because the contribution of intraﬁrm
R&D collaboration is considered to differ from that of interﬁrm R&D collaboration.
To identify the parent–subsidiary relationship, we supplement the NBER patent
database with corporate and noncorporate name-matching results available from Bronwyn Hall’s Web page of The Patent Name-Matching Project.4 In addition, we havesupplemented our data with SDC Platinum, the Worldwide Mergers and Acquisitions
Database, issued by Thomson-Reuters. Among all the M&As since 1979 that are reported in SDC Platinum, we select the cases in which the acquiring company obtains
all of the stock of the target company. We then consider those two companies to be ina parent–subsidiary relationship and treat them as one company after the merger.
We follow Cantner and Graf (2006) in constructing the adjacency matrix corresponding to the network graph illustrating R&D collaborations. Assuming that groupbased inventors are involved in joint R&D projects, a collaboration link is identiﬁed
between two companies if there is at least one common inventor listed in the patents
owned by the companies.
As noted in the Introduction, we have utilized the computer-matching procedure(CMP) recently proposed by Trajtenberg et al. (2006) to identify inventors. The essenceof CMP is to adjust for possible spelling errors of inventors’ names on patents to avoid
identifying one inventor as two individuals and minimize the possibility of identifying
two inventors as the same person by utilizing other information such as addresses,
assignees, and patent classes. This is a much better identiﬁcation method than using
exclusively last names, ﬁrst names, and middle initials, which have so far been used inconstructing co-authorship networks.5 Identiﬁcation methods that are similar to CMP
have been employed in several recent studies.6
The following example illustrates the methodology. Let us assume that four patents
are owned by three corporate assignees with ﬁve inventors, as shown in Table 1. The
table shows, for example, that patent P1 , which is owned by assignee company A1 ,was invented by two researchers, R1 and R2 .
Deﬁne an n × m matrix X, where n is the number of companies and m is the4 http://www.econ.berkeley.edu/

bhhall/pat/namematch.html

5 See, for example, Newman (2004); Goyal et al. (2006)
6 See, for example, McHale (2006); Schankerman et al. (2006); Marx et al. (2007); Hoisl (2007)6number of researchers recorded in the dataset. By using the above example, we have:
1 1 0 1 0
X =  1 0 1 1 0 .
0 1 0 0 1
The adjacency matrix, Γ, which summarizes all the collaboration relationships between
the assignee companies, is thus given by:


3 2 1
Γ = XX ′ =  2 3 0  .
1 0 2
The ith diagonal element of Γ represents the total number of inventors involved in thecollaborative activities between company i and the other companies. The off-diagonal
element of Γ represents the number of inventors involved in the collaborative activities
between the two companies. Thus, the larger the value of the element, the more intense
the R&D collaboration between the two companies.
Like most existing studies of network formation, the following statistical analysis
does not utilize information about the intensity of the collaborative relationships. Thus,
we focus on the following unweighted adjacency matrix, G, the off-diagonal elementsof which are either zero or unity, as follows:


0 1 1
G =  1 0 0 .
1 0 0
An entry is unity if the corresponding entry of the weighted adjacency matrix, Γ, ispositive. The unweighted adjacency matrix indicates whether there is a collaborative
relationship between a pair of companies. Note that the diagonal elements of G arezero because we do not consider intraﬁrm collaborations in our analysis.
To conduct a dynamic analysis of R&D alliance networks, we ‘slice’ the collaboration data into several snapshots. One issue is that although we know that a joint
research project existed in the year in which the patents were applied for, we have no
information about the start and end dates of the project. Given that R&D collaborations typically last for more than a year, following previous studies (e.g., Schillingand Phelps, 2007), we make the conservative assumption that R&D partnerships lastfor three years.7 In other words, we assume that the network for year t includes all
R&D collaborations represented by patents applied for during years t − 1 and t + 1. Byusing such a three-year window, we obtain information on 10 waves of instantaneous
networks between 1985 and 1995.8
Given the way we identify networks, there is a risk of creating spurious collaboration links between two companies. This happens if researchers switch their jobs
7 The three-year window may be justiﬁed by the data. For example, based on a survey of the top managersof 52 companies in the biotechnology industry, supplemented by data from Bioscan, Deeds and Hill (1998)
found that R&D collaborations lasted for an average of 3.47 years.
8 As explained above, because we use three-year moving windows, the network for 1985 is based on the
granted patents ﬁled between 1984 and 1986.

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(a) 1991(b) 1993(c) 1995

Figure 1: Evolution of IT R&D Networks
and work for different companies. For example, if the inventor of a patent owned by
a company move to another company and patents a new invention there, our method
indicates a spurious link between companies that, in fact, did not collaborate.
Because there are no comprehensive databases that track the afﬁliations of researchers, we are unable to avoid the errors arising because of inventor mobility. However, to some extent, this potential for error could be mitigated by using short spansof years to construct the window for snapshooting networks. Given empirical evidence
that researchers typically stay at one company for several years,9 the three-year window
seems sufﬁciently short to control for the noise caused by job switching. Furthermore,even if job switching does occur within the three-year period, it seems unlikely that thejob switcher, who is new to the research team, would be listed as one of the inventors ofa patent generated by an existing research project. Thus, our network data may suggest
negligible spurious links between before-job-switching and after-job-switching companies.
Based on the method of network construction described above, we ﬁnd that 6,746
companies applied for at least one patent, of which 3,315 companies (49.1 percent) had
at least one R&D collaboration link with other companies over the 10-year period from1985 to 1995.
Figure 1 illustrates a small selection of these networks to highlight both the evolving topology of the R&D networks and the processes by which new links are added.
Each presented network shows the largest cluster of companies that are linked directly
or indirectly to each other through the chain of R&D collaborations. The ﬁgures revealthat the network has grown over time. Detailed network statistics are analyzed in thenext section.

9 This can be inferred from the survey conducted by Almeida and Kogut (1999), which shows that 428
inventors switched jobs 335 times between 1974 and 1994. This suggests that each inventor averaged 1.82
jobs during this period and, thus, stayed with one company for an average of 11.05(= 20/1.82) years.
Additional support for our assumption comes from the employment tenure statistics available from the U.S.
Bureau of Labor Statistics. These data show that, for 1991, the median tenure of engineers was 6.7 years,
and that of mathematical and computer scientists was 4.2 years.

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3 Dynamics of the R&D Network
We study the following network statistics. Let N be the set of independent companies in the R&D network for a given year. The number of companies, n, is deﬁned asn = |N |. Recall that the collection of all R&D collaborations is represented by the adjacency matrix G; that is, for two companies i and j, Gij = 1 represents the existenceof an R&D partnership.
Let N (i) be the set of companies collaborating with company i. The total numberof collaborators working with company i is referred to as the degree of company i
and is deﬁned as η(i) = |N (i)|. We refer to companies that have no collaborators as
isolated nodes. We term companies that have at least one collaborator as linked nodes.
Thus, η(i) = 0 if i is an isolated node, and η(i) ≥ 1 if i is a linked node. In what
follows, we use the subscript l to denote a linked node. Thus, Gl ⊂ G denotes its
network. We use nl to denote the number of linked nodes. The proportion of all nodes
that are linked nodes is measured by nl /n.
∑
The average degree of a network G is thus deﬁned by η(G) = i∈N η(i)/n. Thereis a path between companies i and j if there is a direct connection, Gij = 1, or if there
is a set of distinct intermediate collaborators k1 , k2 , · · · , km such that Gik1 = Gk1 k2 =· · · = Gkm j = 1. Two companies are connected if there is a path between them. A
connected component is a set of companies that are connected to each other. In thissection, we focus on the giant component of a network, which is the largest connectedcomponent in the network, among connected components. The giant component isdenoted by Gg ⊂ G, and the number of member nodes is denoted by ng . We measure
the size of a giant component by the proportion of member companies that are linked
to the network, which is given by ng /nl .
We compute the clustering coefﬁcient (Watts and Strogatz, 1998) of company i,which is deﬁned as:∑∑j∈N (i)k∈N (i) Gjk
Ci (G) =.
ηi (ηi − 1)
We set Ci (G) = 0 if η(i) ≤ 1. This can be interpreted as the percentage of a company’s collaborators who are collaborating with each other. For a network G, we cancompute the average clustering coefﬁcient, which is denoted by C(G). Let dij denotethe distance between two connected companies i and j in a network G, which is deﬁned
by the length of the shortest path between them. For the largest connected componentof a network, Gg , we compute the average distance, which is deﬁned by:10∑∑i∈Ngj∈Ng dijd(Gg ) =.
ng (ng − 1)
We also compute a nodal centrality (Bonacich, 1987) measure which is deﬁned as

10 The distance between two unconnected companies is not deﬁned. Thus, when we compute the average
distance, we measure the average distance of the companies in the largest connected component of the
network G.

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Table 2: The evolution of the R&D collaboration network structureyear

networksize

linked node
fractionaveragedegree

t
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995

n
1503
1640
1791
1919
2059
2183
2282
2413
2672
3015
3318

nl /n
0.12
0.13
0.14
0.15
0.15
0.16
0.16
0.18
0.19
0.21
0.25

η(Gl )
1.42
1.31
1.38
1.42
1.33
1.38
1.50
1.54
1.65
1.88
2.09

giant
component
fractionng /nl
0.07
0.07
0.12
0.12
0.13
0.08
0.33
0.34
0.36
0.47
0.52

averagedistanceclustering
coefﬁcientd(Gg )
2.79
2.79
4.03
4.41
4.41
3.54
6.02
4.79
4.63
4.90
4.58

C(Gl )
0.11
0.05
0.10
0.03
0.02
0.06
0.06
0.05
0.08
0.10
0.12

variance
nodal
centrality
Var(φ)
0.26
0.27
0.33
0.38
0.39
0.37
0.47
0.60
0.72
0.80
0.86

Gl represents the network of linked nodes.
Gg represents the network of the giant connected component.

follows:11
φi =∑(a + bφj )Gij ,j∑where a is a normalization scale factor such that i φ2i = 1 and b is a decay factor thatscales down the relative weight of longer paths.12 As the above deﬁnition suggests,
the centrality of a node is recursively related to the sum of the centralities of the othernodes to which it is connected. Thus, a node that is connected to many well-connected
nodes is assigned a high degree of centrality, whereas a node that is connected with
only a few poorly connected nodes is assigned a low degree of centrality. To capture
the heterogeneity of connectedness among the nodes, or the “core–periphery” structureof the network, we compute the variance of nodal centrality Var(φi ) to characterize the
network.
Table 2 reports the basic statistics that describe the structure of R&D collaboration
networks. It shows that the number of nodes has steadily increased, which suggeststhat an increased number of companies have applied for patents (and later successfully
been granted those patents). This number more than doubled in the 10-year period
under study.
11 Ballester et al. (2006) have recently demonstrated a relationship between Bonacich centrality measuresand the Nash equilibrium action of a player in a particular class of network games.
12 Although the value of the decaying factor b can take any value between zero and unity, we follow thecommon practice of setting b to 0.1 (e.g., Haynie, 2001). Using different values of b does not greatly affectour results.

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As for the patterns of connection between nodes, the reported fraction of linked
nodes, (nl /n), increased substantially from about 10 percent to about 25 percent in
10 years. The average degree, η(Gl ), which is computed for the linked nodes, increased signiﬁcantly in the 1990s. This suggests that companies tend to collaborate
with more companies over time. The growth of the connected component, measured
by the fraction of the giant component, (ng /nl ), expanded substantially in the 1990s
as well. In fact, in the 1980s, the giant component was only less than 10 percent of thelinked nodes but, by 1995, more than 50 percent of linked nodes were included in thegiant component. These observations indicate that companies are increasingly being
connected with more than half of all linked companies through collaboration chains.
The average distance between the nodes in the giant component is given by d(Gg ).
The average distance shows an increasing trend in the 1980s and wide ﬂuctuation in1990 and 1991. However, it became rather stable between 4.5 and 5.0 after that. The
size of the giant component grew exponentially at a rate of above 20 percent in 1990.
Thus, in the 1990s, the average distance between nodes in the giant component grew
more slowly than did the logarithm of the number of nodes. Growth in the average
distance scales logarithmically with the network size represents evidence of a “smallworld” effect (Newman, 2003). The implication of a small-world network is that because many pairs of companies are connected by a few collaboration links, the spreadof information, or knowledge spillovers, is fast in the R&D network.
The degree of interconnectedness of collaboration is measured by the clustering coefﬁcient. We report the clustering coefﬁcient of the linked node, C(Gl ). The clustering
coefﬁcients reported in Table 2 are computed for linked nodes. The clustering coefﬁcients are much higher than expected when connections are made randomly among
the existing nodes in the network.13 Generally, the clustering coefﬁcient is high andhas exhibited an increasing trend since 1992. This suggests that companies tend tocollaborate with other companies that are located in their local circle.
The R&D network has two features that characterize the small-world network(Watts and Strogatz, 1998): (i) relatively short distances between nodes in the giant
component, and (ii) a large clustering coefﬁcient. This has been observed in various
social networks, such as collaborations among economists (Goyal et al., 2006) andresearchers in other ﬁelds (Newman, 2004). Deroian et al. (2007) shows similar properties for the R&D partnership networks in the pharmaceutical industry as well. 14
The variance of nodal centrality, Var(φ), increased substantially over the sample
period (last column of Table 2). A low variance of centrality implies that the relative
positions of nodes are similar to each other, whereas a high variance of centrality implies that there are small numbers of super-connected ‘center’ companies and, at thesame time, large numbers of ‘peripheral’ companies with fewer connections. Thus, as
collaborations have become more common, a few star companies have emerged in the
network.
In summary, the key empirical regularities of the R&D network are as follows.
First, the R&D network has become more extensive. The numbers of both nodes and
13 The clustering coefﬁcients of random graphs with the same number of linked nodes are less than 0.006
for the whole sampling period from 1985 to 1990, one order of magnitude lower than what is reported.
14 Deroian et al. (2007) constructs their partnership network for 1985-2005 on the basis of the SDC Platinum database. They also report the decline of inter-ﬁrm alliances after 2000.

11

links have increased substantially. Second, innovative companies are becoming increasingly connected through R&D collaborations, and distances between them areshortening. Third, R&D alliances have become locally clustered, and companies tend
to connect in local dense neighborhood circles. Fourth, the R&D network has developed unevenly, and a core–periphery structure has emerged.

4 Empirical Strategy
In this section, we turn to a statistical analysis of R&D collaboration. Although one
could allow for new link formation, dissolution, and reformation of dissolved links
at the same time, a dynamic model incorporating such simultaneous decision making
about multiple choices is too complicated, as each decision may reﬂects varying consideration of ﬁrms. Thus, we focus on newly established collaborations and formulate
the conditional probability of link formation between companies that have not collaborated before. In other words, we ignore company decisions about the maintenanceand abolition of existing links as well as the recreation of links that have existed in thepast. Given our interest in analyzing expanding R&D networks, conditioning on theformation of new links suits our purpose and simpliﬁes the estimation of the structuralparameters.
The mechanism underlying the formation of new R&D collaboration is considered to be a random matching process similar to that proposed by Jackson and Rogers(2007). Let us assume that companies that have never collaborated meet with eachother and decide simultaneously whether to collaborate. Two types of matching processes are considered. First, matching occurs randomly at each date. Under the random
matching process, the willingness of companies to collaborate may be affected by theirexogenous attributes, such as the congruence of their research interests. However, whenthese characteristics have been controlled for, the chance of joint collaboration can beconsidered to be purely random and independent of the network architecture. We referto such a process as collaboration through random matching. Second, matching occurs
on a particular topology of the existing network. For example, companies may beneﬁt
from searching locally for potential collaborators and may collaborate with their neighbors in the current network. The network-matching process illustrates how the existing
network structure inﬂuences the formation of R&D links. Such a process is referred toas collaboration through network-based matching.
In terms of the standard random-utility framework, the model of collaboration formation through random or network-based matching can be written as follows. Let us
assume that companies i and j have not collaborated with each other before period t.
Let uij (t) be the latent utility of company i derived from initiating collaboration withcompany j at time t. We assume that the potential utility derived from the collaboration, uij , is represented by the following linear function of observed and unobserved
terms:∑
ρk dk−1(1)uij (t) = α + βWij (t − 1) +ij (t − 1) + εij (t − 1),kwhere Wij (t − 1) represent the lagged background characteristics of individual com12

panies and pairs of companies. To be precise, this can be expressed as Wij (t − 1) =[Xi (t − 1) Xj (t − 1) Zij (t − 1)]. Thus, βWij (t − 1) = β1 Xi (t − 1) + β2 Xj (t −1) + β3 Zij (t − 1). The individual ﬁrm-speciﬁc variables, Xi (t − 1) and Xj (t − 1),
are the lagged background characteristics of companies i and j respectively. The term
Zij (t − 1) represents lagged pair-speciﬁc common attributes. These exogenous variables determine the systematic part of the random-matching collaboration mechanism.
The idiosyncratic part is represented by an unobserved random error term, εij (t − 1),which is assumed to be independent across pairs of companies and over time. The possibility that the random error terms are correlated is discussed later. For simplicity, we
assume that the error has a logistic distribution.
In the latent-utility model describedabove, the network-based collaboration mech∑k−1
anism is represented by the term k ρk dk−1
ij (t−1). We deﬁne dij (t−1) as a dummy
variable that takes a value of unity if the shortest distance between i and j is equal tok − 1 at period t − 1 and is zero otherwise. If ρk > 0, the company obtains a positive
beneﬁt by forming a cycle of length k. Thus, the parameter ρk measures the degree towhich there is a tendency to form the kth cyclic closure; this is henceforth termed thecyclic closure preference. If the cyclic closure preference is signiﬁcant, the scope for
new collaborations is restricted to a local chain of existing collaborations.
We allow another mechanism for network-based collaboration. Given the existenceof knowledge spillovers through interﬁrm collaborations, companies may be more willing to make alliances with companies that have more collaborators and, thus, provide
more knowledge spillovers. Firms’ preference to be connected with other ﬁrms thathave many connections is referred to as “preferential attachment” following Barabási
and Albert (1999). Let us assume that the utility derived by company i from collaborating with company j is proportional to the potential partner’s number of existing
collaborators. Noting that the number of collaborators of company j at time t − 1 isgiven by the degree, ηj (t − 1), a simple variant of Equation (1) is given by:∑ρk dk−1uij (t) = α + βWij (t − 1) + ληj (t − 1) +(2)
ij (t − 1) + εij (t − 1).
kAlthough the structural model of R&D collaboration is simple, it exhibits the macrodynamic features described in the previous section. Intuitive explanations are as follows. Network-based collaboration, arising either because of a preference for cyclic
closure or a preferential attachment, may generate a feedback loop that facilitates further collaborations. For example, an increase in R&D collaboration shortens the link
between any pair of companies and, thus, promotes further links between other companies through the cyclic closure preference. Similarly, the preferential attachment
mechanism implies that an increase in the number of collaborations provides a conduit
for information, such as knowledge and skills, from collaborators and, thus, stimulates further collaboration. These positive feedback mechanisms may generate a selforganizing expansion of R&D links over time. The small-world effect may be a productof preferential attachment because the prevalence of hubs can serve as a ‘shortcut’ thatbrings many nodes into close proximity. It is apparent that local clustering in the R&D
network is a product of the cyclic closure preference. The emerging core–periphery
structure may be driven by preferential attachment. This increases collaboration with13

center nodes, which become increasingly connected, and leaves peripheral nodes relatively detached.
Without loss of generality, the utility derived from not collaborating can be normalized to zero. Thus, if uij (t) > 0, company i is willing to collaborate with company
j at time t. Using Equation(2) to represent utility, the corresponding probability ofcollaboration is
]
[
∑
k−1
Prob(uij (t) > 0) = F α + βWij (t − 1) + ληj (t − 1) +ρk dij (t − 1) , (3)kwhere F is the logistic cumulative distribution function. Given this speciﬁcation, themodel assumes that a company’s current collaboration decisions are affected by individual and joint background characteristics and existing network structures from theprevious period.
We assume that both collaborators must mutually decide to collaborate for R&D
collaboration to take place. That is, R&D collaboration only occurs if two companies
are willing and agree to collaborate with each other at the same time. Let Gij (t) denote
the R&D collaboration between company i and company j at time t. The conditional
probability that companies i and j initiate collaboration at time t, given that they havenot collaborated before, is given by
Prob(Gij (t) = 1|Gij (s) = 0; s < t) = Prob(uij (t) > 0) · Prob(uji (t) > 0).

(4)

Equality follows from the assumption that εij (t − 1) and εji (t − 1) are independent.
Given the above speciﬁcation, the likelihood of collaboration for all possible pairsof companies, which is deﬁned by∏Prob(Gij (t) = 1|Gij (s) = 0; s < t),(5)
L(θ; t) =i<jcan be written as
L(θ; t) =∏Prob(uij > 0).

(6)

i̸=j

This equation follows because uij and uji are symmetric. Equation (3) implies that theoverall sample log-likelihood function is given by
[
]
∑∑
∑
k−1
ℓ(θ) =
ln F α + βWij (t − 1) + ληj (t − 1) +ρk dij (t − 1) .
(7)
t

i̸=j

k

The structural parameter θ = (α, β, λ, ρk ) is estimated from the log-likelihood function. Because F is the logistic cumulative distribution function, the standard logistic
regression method is used for the estimation. Note that the product relates to all possible pairs of (i, j) such that i ̸= j. Hence, the observation unit for the log-likelihood
function is each pair of companies, (i, j), not the individual companies, i or j. For
maximum likelihood estimation, the sample size, N , refers to all possible pairs ofcompanies.
14

As a ﬁnal note regarding the statistical model, we discuss the identiﬁcation of somestructural parameters. It transpires that β1 and β2 , which relate to individual-speciﬁccharacteristics, cannot be separately identiﬁed from the data. The simple reason isthat because these parameters are symmetric in the log-likelihood function, any two
sets of symmetric values of (β1 , β2 ), such as (b1 , b2 ) and (b2 , b1 ), yield the same loglikelihood value for Equation (7). Thus, in the following empirical analysis, we simply
report β = (β1 + β2 )/2. The parameter β can be interpreted as the average effect onlink formation of a company’s and its collaborator’s background characteristics.

5 Empirical Results
5.1 Estimation Sample
As previously reported, the main dataset used for estimation is constructed from the
NBER patent data. In addition, we use the S&P’s COMPUSTAT database to supplement detailed information about individual companies.
Two datasets are considered in the following estimation. First, we collect the dataof all IT companies, deﬁned by the technological categories of patents, that applied forat least one patent in each year of the observation period. Second, we use the subsamples of the IT companies that are listed on the stock markets of NYSE, NASDAQ or
AMEX. The ﬁrst dataset covers substantially more companies than the second one, but
it does not contain detailed information on the ﬁrm characteristics because COMPUSTAT information is not available for companies that are not listed on the stock markets.
In what follows, we call the former the full set of companies’ data, and call the latter as
the market-listed companies’ data.
Both datasets contain the information about a pair of companies (i j) across timet. The dependent variable Gij (t) is a dummy variable that takes one if a new link isobserved between company i and j in year t. As explained in the model section, since
we focus on newly established collaborations, we only collect pairs of companies that
had never collaborated before for both datasets. 15 Hence, once companies collaborate,they are excluded from the estimation samples for subsequent periods. The data also
contain a set of independent variables Wij (t − 1), which are the lagged backgroundcharacteristics of individual companies and pairs of companies. In what follows, a timeindex is omitted for notational convenience.
We categorize the control variables Wij into three groups. The ﬁrst group is a setof variables that measures the “absorptive capacity” (Cohen and Levinthal, 1989) ofinnovating companies, which has been shown to affect companies’ R&D cooperation
decisions in previous studies. We consider both the research size and research quality
to measure the absorptive capacity. As for the “size” of research, we use the R&D
expenditure, which is available from the COMPUSTAT database for the market-listedcompanies. On the other hand, the variable is not available for non-marketed-listedcompanies, which account for the majority of the full set of companies’ data. Therefore, we instead use the number of patents for which the company applied in a given
year as a proxy for the company’s R&D size. This variable is available for the full set of
15 To check for collaborations prior to the sample period 1985–1995, we tracked back to 1975.

15

companies. As for the “quality” of research, we take the sum of the cumulative number of patents applied by the company and the cumulative number of patent citationreferred to by other companies. For these two variables, we aggregate the information
over the past 10 years. This variable, constructed from the NBER patent database, isavailable for both market-listed and non-market-listed companies; thus, it is included
in both the market-listed companies’ data and the full set of companies’ data. It isnoteworthy that these research size and quality variables are included in the form of
the natural logarithm in the regressions.
The second group is related to similarity between two companies, which is deﬁned
in terms of technology, R&D size, and location. First, regarding technological similarity, we essentially treat the research areas of two companies as similar if the companies
applied for patents in similar technological ﬁelds. Following Jaffe (1986), we measuretechnological similarity, denoted by T Sij , by using an uncentered correlation of patentapplication subcategories between companies i and j.16 The second similarity has to
do with research size. The similarly, denoted by RSij , is given by the inverse of theabsolute difference in a measure of absorptive capacity.17 Finally, locational similarity is considered as many previous studies have stressed that geographical origin is an
important factor in collaboration decisions. We deﬁne the locational similarity measure, denoted by LSij , to be equal to one if the companies’ headquarters locate in thesame state and zero otherwise. For the market-listed companies’ data, the headquarters
information is available from COMPUSTAT data. For the full set of companies’ datathat include both market-listed and non-market-listed companies, we impute the stateof the headquarters by the state that appears most frequently as inventors’ addresses
which are available from the NBER patent data.
The third and the most important group of variables is related to network structure.
As shown in the previous section, this includes the cyclic closure structure variables
and the star structure variable, which represent a ﬁrm’s preference to form a cyclic
closure and a preferential attachment tendency, respectively. To capture the kth cyclic
closure preference effect, we compute the shortest (geodesic) path between innovatingcompanies in the R&D collaboration network and construct a dummy variable, dk−1
ij ,which is equal to unity if the shortest distance between companies i and j is k − 1 andzero otherwise. For convenience, we include up to the sixth (k = 6) cyclic closure
preference because of the rarity of network closures to more than the ﬁfth degree. To
16 To be precise, the correlation coefﬁcient, T S , is deﬁned as:ij

T Sij ≡

fi Cfj′,′[(fi Cfi )(fj Cfj′ )]1/2

where fi is a row vector of the number of patent applications in each technological subcategory taken out
by company i and C is the citation probability matrix for each technological subcategory computed from all
U.S. patent citation data from 1981 to 1999. We use the citation probability matrix, rather than the identity
matrix, as the weight so that our similarity measure reﬂects the similarities between technological categories.
17 The researsh size similarity is deﬁned by
RSij =

1,
1 + |Ri − Rj |where Ri and Rj are the research size measures of companies i and j, respectively. This similarity measure
is inspired by the “social distance” measure that was proposed by Akerlof (1997).

16

Table 3: Deﬁnitions of Controlled Variables
Variable Name
Absorptive Capacity Variables:
RD
NPATENTCUMPATENT
CITED
Similarity Variables:
TS
RS
LS
Network Variables:dk−1ηDescription
Total R&D expenditure in millions of U.S. dollars in the last period.
The number of patent applications in the last period.
The cumulative number of patent applications by the last period.
The cumulative number of cited patents by the last period.
Technological similarity, deﬁned by the uncentered correlation of patent application subcategories.
Research size similarity, deﬁned by the inverse of the difference in R&D
size.
Locational similarity, deﬁned to be one if the states of the companies headquarters coincide.
A dummy variable that takes one if the shortest distance between a pair ofcompanies is k − 1 in the last period.
The number of collaborations in the last period.

capture the preferential attachment effect, we include the natural log of the nodal degreeof R&D collaborations, which is denoted by log(ηi ) for company i. To account for the
likelihood contribution of network formation between companies i and j, the degree
variables of both companies, (log(ηi ) log(ηj )), are included. Yet, as already noted,
because the effects of own-company and partner characteristics cannot be separately
identiﬁed simultaneously, the average of the preferential attachment effect of its own
and that of the partner company is reported.
Table 3 presents the deﬁnitions of the control variables for the two datasets. In
addition to the variables explained above, we include trend variables with a base yearof 1985. Table 4 presents the descriptive statistics of the dependent and independent
variables used in our analysis.

5.2 Baseline Estimation Results
Table 5 reports the estimation results. Column (1) presents the estimates for the marketlisted companies’ data while column (2) presents the estimates for the full set of companies’ data. The robust standard error of each estimated coefﬁcient is reported inparentheses.
We ﬁnd that the estimated coefﬁcients of most variables have the expected signs.
The estimates of the absorptive-capacity-related variables, log(RD), log(N P AT EN T )and log(CU M P AT EN T + CIT ED), show that the variable representing research
size and research quality has positive and statistically signiﬁcant effects on collaboration formation. This evidence is found consistently in both the market-listed companies’ data (column (1)) and the full set of companies data (column (2)). Given thesefacts, we conclude that the absorptive capacity is an important factor that facilitates
R&D collaboration between companies.
As for similarity-related variables, we ﬁnd that technological similarity, T S, isnegative and statistically signiﬁcant in column (1), although the effect is not statistically17

Table 4: Summary Statistics

Dependent Variable:
G
Research Size:log(RD)

Market-listed
Companies

Full set ofCompanies

0.0010(0.0310)0.0002(0.0125)

3.6364(2.1399)

log(N P AT EN T )3.2323(1.6556)

Research Quality:
log(CU M P AT EN T + CIT ED)
Technological Similarity:
TS
Research Size Similarity:
RS
Locational Similarity:
LS
Cyclic Closure:third degree (k = 3)
fourth degree (k = 4)
ﬁfth degree (k = 5)
sixth degree (k = 6)
Nodal Degree :log(η)
Sample Size

5.3496(2.2283)

4.6677(1.9123)0.1738(0.1845)0.3291(0.2233)

0.3805(0.2110)0.4512(0.2155)

0.1068(0.3089)

0.0035(0.0591)0.0044(0.0658)
0.0068(0.0821)0.0055(0.0740)0.0038(0.0615)0.0010(0.0316)0.0022(0.0465)
0.0027(0.0523)
0.0022(0.0473)

0.3925(0.6603)
1856190.3003(0.5039)5494790signiﬁcant in column (2). This suggests that, at least for market-listed companies,
innovative synergy would not arise very easily if two companies had similar researchareas, and such companies would collaborate less often than those that do not shareresearch ﬁelds. However, it is consistently shown in both columns (1) and (2) thatthe research size similarity, RS, has a signiﬁcant positive impact on collaboration.
Interestingly, the relationship between similarity and collaboration is non-monotonic.
Seeing from the negative estimates of the quadratic term of the research size similarity,
it can be interpreted that companies may interact with other companies that are similar,
but not too similar, in research capacity.
It is also shown that the locational similarity, LS, has a statistically signiﬁcant effect on collaboration. This ﬁnding is robust for the results of both columns (1) and (2).
These ﬁndings suggest that companies with headquarters in the same state are more
likely to collaborate with each other. It is noteworthy, however, that the locational similarity variable in our analysis only measures the proximity of company headquarters
on the state level. Therefore, it may be more appropriate to focus attention on the proximity of company research units or business establishments. Thus, further investigation
with a focus on location will be necessary.
The estimates of the network variables indicate that the cyclic closure effects, ρk ,18

Table 5: Baseline Regression Results
Market-listed
Companies(1)−11.7681∗∗∗(0.7349)

CONSTANT
Research Size:log(RD)

0.2203∗∗∗(0.0704)log(N P AT EN T )Research Quality:
log(CU M P AT EN T + CIT ED)
Technological Similarity:
TS
T S2
Research Size Similarity:
RS
RS 2
Locational Similarity:
LS
TREND
Cyclic Closure Effect ρ:third degree ρ3fourth degree ρ4ﬁfth degree ρ5sixth degree ρ6
Preferential Attachment Effect λ:log(η)
Log-likelihood
Sample Size

Full set ofCompanies(2)−12.7136∗∗∗(0.4257)

0.2848∗∗∗(0.0414)0.2078∗∗∗(0.0754)0.1831∗∗∗(0.0304)−2.5537∗∗(1.0037)
1.9821(1.4185)−0.0949(0.5486)
0.0611(0.6526)

6.2846∗∗∗(1.7398)−4.6214∗∗∗(1.6377)

4.9020∗∗∗(1.1125)−4.8361∗∗∗(1.0481)0.8560∗∗∗(0.1817)0.0222(0.0359)

0.8439∗∗∗(0.2576)
0.0567∗∗∗(0.0165)2.5991∗∗∗(0.2489)
2.1358∗∗∗(0.2439)2.2072∗∗∗(0.2869)
1.2148∗∗(0.5245)3.4289∗∗∗(0.1440)2.4342∗∗∗(0.1475)
1.7809∗∗∗(0.1892)
1.8651∗∗∗(0.2156)

0.4946∗∗∗(0.1533)−1090.4146
1856190.3790∗∗∗(0.0721)−7150.1950
5494790

are positive and statistically signiﬁcant for all k at the one percent signiﬁcance level.
This evidence is consistently found in columns (1) and (2). Furthermore, the triadic
closure effect ρ3 has the largest effect among other cyclic closure effects. This suggests that companies that have mutual third-party collaborators in their network neighborhood tend to establish a new R&D collaboration. The mechanism seem to work
consistently, irrespective of whether or not they are listed on the stock market.
We consider at least two reasons that R&D collaborations are more likely to be undertaken between companies that have mutual third-party collaborators. First, previous
collaborators may play a referral role for new collaborators. Companies would probably gain by reducing any uncertainty about whether a potential partner would behave
opportunistically. 18 Given such uncertainty, companies may want to use preexisting
18 For example, a potential collaborator may free-ride by limiting contributions to a collaboration and/or
may take advantage of a close relationship to use resources or information in ways that may damage theirinterests.

19

collaboration as conduits of information about the reliability of potential partners, andthus, they would prefer to establish “secure” relationships with known local partners intheir close circle rather than begin relationships with new collaborators with unknown
behavior.19 Second, it may be motivated by the appropriability of the fruits of joint
R&D, about which companies might be seriously concerned when starting joint R&D
projects (Cassiman and Veugelers, 2002). To prevent collaborators from appropriating the technology generated by joint R&D projects for their own interests against theinterests of others, collaborating ﬁrms must be able to punish deviators.20 The existence of an indirect link through mutual collaborators may enhance the effectiveness ofpenalties and improve the appropriability of the fruits of joint R&D projects.21
We also ﬁnd in Table 5 that the preferential attachment effect, λ, is positive andstatistically signiﬁcant at the one percent level in columns (1) and (2). This ﬁnding
reinforces our argument that the attractiveness of collaboration is determined by the
resources and capabilities that a potential partner possesses. It has been argued thatcollaboration ties are key vehicles through which companies obtain access to external knowledge, including technical breakthroughs and new insights to problems andfailures (e.g., Powell et al., 1996). Our estimation results conﬁrm that access to theresources of potential partners may promote R&D collaboration. In addition, companies that have knowledge repositories from previous collaborations are likely to attract
more collaborators and, thus, more opportunities for collaboration. However, it is also
possible that companies’ unobserved capabilities for R&D collaboration are capturedby the preferential-attachment variable.
The results presented above clearly indicate that two types of mechanisms may explain R&D collaboration formation between IT companies. First, companies decideto establish a new R&D collaboration with each other because of their cyclic closure
preference or preferential attachment predisposition. Such a collaboration mechanism
is considered as structural or endogenous. Secondly, companies collaborate “contextually” with each other even without taking into account the generated network structure.
For example, as shown in estimation results, companies with similar research size, orcompanies that are located in the same state, will collaborate with each other. Such collaboration due to characteristic similarities is considered contextual or exogenous. The
distinction between the structural and contextual mechanisms is important. Whereas
the structural effect generates an additional mechanism that facilitates further collaborations with others, the contextual effect does not.
19 The same idea is found in Gulati and Gargiulo (1999).
20 For example, if two companies are collaborating on an R&D project and this is the only connection
between them, then the only way to penalize malicious technology diverters is to expel them from current
collaborations and exclude them from future ones. However, if these two companies are connected not only
directly but also indirectly through mutual third-party collaborators, it is possible for deviators to be punishedby all other collaborators who are aware of such behavior; deviators could be punished by being ostracizedfrom the alliance comprising third-party collaborators.
21 A similar sanctioning logic has been widely proposed by several sociologists (e.g., Coleman, 1990;
Putnam, 1992; Walker et al., 1997), who hypothesize that such punishments are more easily enforced among
agents belonging to a closely knit network. In the literature of economics, Spagnolo (1999) uses a repeatedgame framework to analyze transfers of trust from social to production relationships that facilitate cooperation in production and shows that the amount of credible punishment, as embodied in social capital,
strengthens cooperation. Lippert and Spagnolo (2004) provides rigorous support for the sanctioning role of
network closure by using a game-theoretic model of networks of relational contracts.

20

0.0008

0.000160.00070.000140.00060.000120.00050.00010.00040.00008

contextual

contextual

structural

structural

0.00030.00006

0.00020.00004

0.00010.00002

0

0

3

4

5

6

3

(a) market-listed companies’ data

4

5

6

(b) all companies’ data

Figure 2: Decomposition of the Collaboration Probability into Structural and Contextual Effects
To disentangle these effects, we decompose the collaboration probability into two
components: (i) the structural effect, which arises because of cyclic closure preferences
or preferential attachment, and (ii) the contextual effect, which arises because of nonstructural factors. Figure 2 presents the results of the decomposition for the marketlisted companies’ data (a) and the full set of companies’ data (b). The height of eachbar graph represents the average predicted probability that a new R&D collaboration
is established between two companies that never collaborated before and is computedwith the parameter estimates presented above. For ﬁgures (a) and (b), we present thepredicted probabilities with up to d = 5 network distances. The structural part ofthe collaboration probability between companies with d network distance is computedby the probability that is attributable to the cyclic closure preference with (d + 1)
degree after controlling for the effect of similarity-related variables so that the effect iszero. The contextual part is given by the residual part of the probability that cannot be
explained by the structural part.
The ﬁgures show that, for the market-listed companies’ data (a), the structural effect on collaboration formation exceeds the contextual effect, while the magnitude relationship is reversed for the full set of companies’ data (b). It thus can be said the R&D
collaboration formation of market-listed companies is driven, for the most part, by the
structural mechanism that facilitates further collaboration formation in a self-fulﬁllingmanner. In contrast, the structural mechanism is less important than the contextual
mechanism for non-market-listed companies.
In summary, we have established three main ﬁndings. First, a company’s absorptive capacities are important determinants of R&D collaboration. Second, companies
with similar, but not too similar, research capacity are highly likely to collaborate witheach other. Third, network-based collaboration is signiﬁcant. Companies with morecollaborators are more likely to collaborate with each other. Furthermore, companies
that are closer in the existing R&D network are more likely to collaborate with eachother.
21

5.3 Controlling for Unobserved Common Factors
Although evidence of a strong cyclic closure preference is found, there may be an
omitted-variables problem. If there are unobserved common shocks that affect the decisions of a group of companies, the effect of those omitted factors might be incorporated
into the cyclic closure preference effect. For example, let us assume that a company’s
research managers formerly worked for a nearby company. The two companies may be
more likely to collaborate in R&D activities because of this personal association.22 If
the predisposition of research managers is not observed by researchers, the effect may
be mistakenly attributed to a cyclic closure preference.
To address this problem, we modify the model to incorporate a group-speciﬁc unobserved factor. The primary assumption underlying this speciﬁcation is that suchcommon factors, which are unobservable to researchers, affect all companies in thesame group. Let us assume that company i and company j both belong to group g.
Then, the utility function isuij (t) = α + βWij (t − 1) + ληj (t − 1) +∑ρk dk−1ij (t − 1) + δg (t − 1) + εij (t − 1),(8)kwhere δg (t − 1) is a ﬁxed effect that is common to companies i and j belonging togroup g; other companies probably also belong to the group. The ﬁxed effect, δg , if nottaken into account, causes the overall error term, δg + εij , to be correlated between thecompanies in group g.
The omitted group-speciﬁc factor can arise from the endogenous group formation of companies based on unobserved characteristics. Companies are likely to sortthemselves into groups in which members share common unobserved characteristics.
Hence, the group structure should capture hidden sorting across companies and theirshared attributes. We employ a simple strategy to identify hidden group structures.
In other words, each group is identiﬁed by a “community structure”, as referred to by
Girvan and Newman (2004). Essentially, a community is a subset of nodes within a network such that connections between them are deeper than connections to other nodes
in the network.23 Our group identiﬁcation strategy relies on the assumption that companies are densely connected with each other because they share common unobserved
group-level attributes. Using the algorithm proposed by Girvan and Newman (2004),
we identify 161 and 48 communities for the all companies’ dataset and market-listedcompanies’ dataset, respectively, in the sample period between 1985 and 1995. The
ﬁxed effect term δg is assigned to each pair of companies i and j if both companies
belong to group g.
22 See Saxenian (1994) for anecdotal evidence in this regard.
23 Girvan and Newman’s community detection algorithm is based on the idea of the “betweenness” oflinks in the network, in which this betweenness is a measure that emphasizes links between communities.
They propose using a modularity index to determine the number of communities. The modularity index
measures the difference between the proportion of edges in the network that connect nodes within the samecommunity and the expected value of the proportion of edges that have the same community division but inwhich the connections between nodes are random. We use the community structure that provides the highest
modularity.

22

Table 6: Community Fixed Effects Regression Estimation Results
Market-listed
Companies(3)
Research Size:log(RD)

0.2245∗∗∗(0.0755)

log(N P AT EN T )Research Quality:
log(CU M P AT EN T + CIT ED)
Technological Similarity:
TS
T S2
Research Size Similarity:
RS
RS 2
Locational Similarity:
LS
TREND
Cyclic Closure Effect ρ:third degree ρ3fourth degree ρ4ﬁfth degree ρ5sixth degree ρ6
Preferential Attachment Effect λ:log(η)
Log-likelihood
Sample Size23

Full set ofCompanies(4)

0.2731∗∗∗(0.0381)0.2215∗∗∗(0.0679)

0.1882∗∗∗(0.0255)−2.6361∗∗(1.1783)
1.7260(2.0805)−0.1885(0.4959)
0.0470(0.5643)5.9228∗∗∗(1.6811)−4.2508∗∗∗(1.6148)

4.9421∗∗∗(1.4123)−5.2924∗∗∗(1.2646)0.8541∗∗∗(0.1848)0.0372(0.0402)0.2633(1.0602)
0.0750∗∗∗(0.0200)

2.5944∗∗∗(0.2717)
2.1589∗∗∗(0.2599)2.2452∗∗∗(0.2816)1.2261∗∗(0.5216)3.2356∗∗∗(0.1622)2.3347∗∗∗(0.1552)
1.7691∗∗∗(0.2100)
1.8549∗∗∗(0.1851)0.4463∗∗∗(0.1548)-1049.9447
1852280.3863∗∗∗(0.0577)—
10% bootstrapGiven the utility speciﬁcation by Equation (8), the log-likelihood function for new
collaboration links is derived analogously to Equation (7). Because the cumulative
distribution function of the error term is assumed to be logistic, the ﬁxed effects logit
estimator is used to estimate the model.
Table 6 reports the estimation results for the ﬁxed effects model. Column (4)presents the estimates for the market-listed companies’ dataset. We use the same variable speciﬁcation as that used for the baseline estimation. For the data of market-listedcompanies, 6 community-speciﬁc ﬁxed effects are included in the estimation.24
We also tried the same ﬁxed effects estimation to the full set of companies’ data.
However, because of the immense sample size (N = 5, 494, 790) and the lack ofmachine power, the estimation could not be implemented. We, thus, instead used 10%
bootstrapped samples of the original sample and estimated the ﬁxed effects model forthe subsample. We repeated this subsample estimation procedure for 50 times with thesubsample being bootstrapped each round and computed the average of the parameter
estimate. Column (4) in Table 6 reports the bootstrap estimates, and the bootstrap
estimates of the standard errors are shown in parentheses. 25
It is shown that the coefﬁcients of most of the variables are similar to those fromthe baseline speciﬁcation but less precisely estimated. The qualitative results are thesame as before with one exception: the variables measuring locational similarity are
not signiﬁcant for the full set of companies’ data.
The estimated effects of the network variables are statistically signiﬁcant and havethe predicted signs. The effect of preferential attachment remains positive and significant. The point estimates are similar to those from the baseline speciﬁcation. Hence,
the inclusion of group-speciﬁc effects does not negate these network effects. Thissuggests that closure preference is not primarily driven by unobserved group characteristics. Furthermore, triadic closure preference continues to have the strongest effect.
Thus, provided we are allowed to assume that most of the omitted variables only vary at
the community level, our results suggest evidence of positive triadic closure preference.

6 Conclusion
In this paper, we have studied the evolution of successful R&D collaboration in the
U.S. IT industry between 1985 and 1995 by using information on patents granted in the
U.S. The descriptive statistics on R&D networks provide insights into how networks
have evolved. Put simply, collaboration has become more extensive, more locally clustered, connected over shorter distances, and increasingly unequal. Considering the lawsthat guide these macrodynamic features, through regression analysis, we found, having
controlled for as many company characteristics as possible, that the choice of collaboration partners is signiﬁcantly affected by cyclic closure preference and preferential
24 The ﬁxed effects of communities in which no collaboration links are observed are dropped from theestimation sample. To estimate the ﬁxed effects model, within-group variation in the response variable isrequired.
25 We employ the subsampling bootstrap method proposed by Politis and Romano (1994). In the subsampling bootstrap procedure, resampling should be implemented without replacement. For details, see Theorem
2.1 in Politis and Romano (1994) and Politis et al. (1999).

24

attachment preference. Our results support the following two hypotheses relating tointerﬁrm collaboration formation: (1) the local partner search hypothesis, according
to which the connected get more interconnected; and (2) the accumulation advantage
hypothesis, according to which the connected get more connected.
Our paper makes a unique contribution to the literature on R&D alliances by measuring the impact of existing collaboration structures on the formation of new collaborations and by explaining how the collaboration network emerges. Although many
previous studies have analyzed interﬁrm collaboration structures that can enhance innovation, none has explained how the collaboration network can be systematicallystructured among companies that are uncoordinated ex ante. Our ﬁndings suggest thatﬁrms search for reliable collaboration partners through referrals from previous collaborators. The results also suggest that companies attempt to form dense webs of local
collaborators to increase the threat of joint punishment to minimize the risk of malicious behavior by their collaboration partners. However, our results do not identify theseparate roles of these factors in explaining the behavior of ﬁrms. More theoreticalwork is needed to identify the different dynamic structural effects produced by ﬁrms’
networking strategies.
By focusing on the formation of new collaborations, we did not analyze the patterns and determinants of the dissolution of existing collaborations. The question of
how companies decide to terminate existing partnerships and start new ones was not
examined. We have based our empirical framework on rather myopic and adaptive
agents making decision about with whom to make a new link. Forward-looking agentscan be considered in a more dynamic context. In such a set-up, there is possible endogeneity between a ﬁrm’s current position in the network and its future decision about
the termination of existing links or the creation of new links. Future research on boththe creation and dissolution of ties must also address this endogeneity issue as well togain a full understanding of the dynamics of networks.
Although we have information on the intensity of collaboration measured by the
number of researchers common to both companies, we did not utilize it in our analysis.
We have treated all links as homogeneous and abstracted from the strength of ties andtheir types. The strength and types of ties, however, are known to play important roles
in information ﬂows (See Granovetter (1973) for an example from the labor market).
The manner in which the strength and type of existing links will affect the creationand termination of ties needs to be examined. The dynamics of the strength of the ties
will need to be examined as well. The ﬁrst step to answer such questions is to establish a framework for analyzing the dynamics of weighted, as opposed to unweighted,
networks. We leave this important and interesting task to future research.

25

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Acknowledgment
We would like to thank for vaulable comments from Gueorgi Kossinets, Hidehiko
Ichimura, Daiji Kawaguchi, Tomoya Mori, Ryo Kambayashi, Reiko Aoki, Hiroyuki
Chuma, Sadao Nagaoka, and anonymous referees. Of course, the responsibility of allremaining errors is ours. Financial support from the Japan Securities Scholarship Foundation, Inamori Foundation and the Kikawada Foundation (21-seiki bunka gakujyutsu
zaidann) are gratefully acknowledged. This research was also supported by Grant-inAid for Young Scientists (B)awarded from The Ministry of Education, Culture, Sports,
Science, and Technology of Japan (Grant. No. 19730165)

30