understanding network formation in strategy research ... · strategy research: exponential random...

Strategic Management JournalStrat. Mgmt. J., 37: 22–44 (2016)

Published online EarlyView in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/smj.2454Received 29 August 2013; Final revision received 20 January 2015

UNDERSTANDING NETWORK FORMATION INSTRATEGY RESEARCH: EXPONENTIAL RANDOMGRAPH MODELS

JI YOUN (ROSE) KIM,1 MICHAEL HOWARD,2* EMILY COX PAHNKE,3 andWARREN BOEKER3

1 Department of Management, Gatton College of Business & Economics, Universityof Kentucky, Lexington, Kentucky, U.S.A.2 Department of Management, Mays Business School, Texas A&M University,College Station, Texas, U.S.A.3 Department of Management and Organization, Michael G. Foster School ofBusiness, University of Washington, Seattle, Washington, U.S.A.

Research summary : This article uses Exponential Random Graph Models (ERGMs) to advancestrategic management research, focusing on an application to board interlock network tieformation. Networks form as the result of actor attributes as well as through the influenceof existing ties. Conventional regression models require assumptions of independence betweenobservations, and fail to incorporate endogenous structural effects of the observed network.ERGMs represent a methodological innovation for network formation research given theirability to model actor attributes along with endogenous structural processes. We illustrate theseadvantages by modeling board interlock formation among Fortune 100 firms. We also demonstratehow ERGMs offer significant opportunities to extend existing strategy research and open newpathways in multiparty alliances, microfoundations of interorganizational network formation, andmultiplexity of ties among actors.

Managerial summary: Social networks are increasingly important in the business world, not onlybetween individuals but also between organizations. Firms can obtain information, resources, andstatus through their external network connections, and understanding how these outside ties formis an important goal of strategy research. Our paper helps advance this effort by introducing a newtool for social network analysis, Exponential Random Graph Models (ERGMs) to the managementand strategy fields. We provide an example of this method, demonstrating how social network tiesform between companies when they hire common directors to their boards. Executives can benefitfrom this research through a greater understanding of how corporate relationships are built withallies as well as among competitors. Copyright © 2015 John Wiley & Sons, Ltd.

INTRODUCTION

The ubiquity of networks among industries, firms,and individuals has attracted significant researchattention as evidenced by the sheer volume of

Keywords: social networks; empirical methods; boardinterlocks; network formation; network analysis*Correspondence to: Michael Howard, Mays Business School,Texas A&M University, 420L Wehner Building, 4221 TAMU,College Station, TX 77843, U.S.A. E-mail: [email protected]

Copyright © 2015 John Wiley & Sons, Ltd.

studies that draw on network concepts and methods(Borgatti et al., 2009). One of the key themes toemerge from organizational research on social net-works is that firms are embedded in sets of rela-tionships and interactions (Granovetter, 1985) thatdetermine both their actions and outcomes (e.g.,Ahuja, Polidoro, and Mitchell, 2009; Stern, Duk-erich, and Zajac, 2014). Prior research has exam-ined numerous properties of networks, includingstructural cohesion (Moody and White, 2003) andsmall-worldness (Uzzi and Spiro, 2005; Watts,1999) as well as what kind of ties are likely to form

Understanding Network Formation in Strategy Research: ERGMs 23

between actors and which actors will become morecentral (e.g., Burkhardt and Brass, 1990; Shipilovand Li, 2012). At the same time, a better under-standing of how and why organizational networksemerge is critically important to determine how dif-ferent network structures offer distinctive benefitsor constraints to firms embedded in them (Ahuja,Soda, and Zaheer, 2012; Salancik, 1995; Stuart andSorenson, 2007).

Network formation may be driven by multipleinterdependent social processes acting simulta-neously (Hedström and Swedberg, 1998; Lusher,Koskinen, and Robins, 2013). Networks mayemerge through a process whereby actors seek part-ners with specific characteristics (e.g., homophily)or in response to opportunities made available bytheir partners’ reciprocal behaviors (Blau, 1964;Park and Luo, 2001), leading to changes in thenetwork structure (Contractor, Wasserman, andFaust, 2006). Alternatively, network ties mayresult from locally emergent structures (Gulatiand Gargiulo, 1999; Lusher et al., 2013; Zaheerand Soda, 2009), in which relationships amongactors are influenced by the presence (or absence)of other ties in the network. For example, in thecontext of the global cellular phone industry,Google’s choice to partner with Samsung and HTCaround the Android operating system and initiallypromote it through the Verizon carrier network inthe United States was strongly influenced by theexisting relationship that Apple had formed withAT&T. Google’s decision illustrates an endogenousnetwork structural effect—the choice to formnetwork ties with Samsung, HTC, and Verizonextends beyond simple considerations of their char-acteristics and involves a calculated response to theties already formed by AT&T. Observed networkstructure may thus result from the combination ofdistinct, simultaneous processes that may be inter-dependent and structurally emergent (Lusher et al.,2013) and co-evolve in a complex manner (Stuartand Sorenson, 2007; Zaheer and Soda, 2009).

Prior strategy research has rarely examined thecomplex combinations of processes that simultane-ously shape the structural characteristics of a givennetwork. Traditional network analysis uses regres-sion methodologies that are based on the assump-tion that tie formation between two actors is inde-pendent of the other ties and actors in the network.However, this assumption can be problematic formany networks, in which new tie formation isan interdependent process influenced by both the

characteristics of the actors and of their existingties (Ahuja et al., 2012; Contractor et al., 2006;Provan, Fish, and Sydow, 2007). Strategy networkresearchers often address this problem by usingmatched pair samples, rare events methods, orother advanced techniques in random effect logis-tic regression models. However, these approachesoffer only a partial solution. Moreover, conventionalstatistical methodologies are unable to account forthe endogenous structural effects that the existingrelationships between two firms have on the forma-tion of ties to a third firm (Contractor et al., 2006).In the example of the global cellular phone indus-try, existing relationships among Google, HTC, andSamsung are likely to influence Microsoft’s sub-sequent choice to partner with Nokia. As a result,without modeling such endogenous structural pro-cesses, researchers run the risk of inappropriatelyattributing observed network tie formation to firm-or dyad-specific characteristics (e.g., characteristicsof Microsoft or Nokia in our previous example),although such effects may be confounded by under-lying interdependent structural processes (e.g., theexisting relationships among Google, HTC, andSamsung).

The goal of this study is to highlight a rela-tively new analytical approach that allows scholarsto examine multiple interdependent social processesinvolved in network formation. We focus on a classof social network methodologies called Exponen-tial Random Graph Models (ERGMs) to demon-strate how they permit better specification of theprocesses underlying network formation (Frankand Strauss, 1986; Pattison and Wasserman, 1999;Snijders et al., 2006). Broadly stated, ERGM anal-ysis examines tie formation at the network level,accounting for potential cross-dependencies, emer-gent network structures (such as consortia or clus-ters of allied firms within an industry), and othereffects that cannot be addressed through conven-tional approaches, which focus primarily on dyadicrelationships. Thus, while ERGMs can model manyof the co-variates included in traditional regres-sions, they provide additional insights that increaseour understanding of how network structures form.In the example of the global cellular industry,ERGMs could provide insight into the likelihoodthat any two firms will form a tie, given the existingties between other firms in the industry.

Currently, only a small number of organizationalstudies have utilized ERGMs (e.g., Faraj and John-son, 2011; Lomi et al., 2014). In this article, we

Copyright © 2015 John Wiley & Sons, Ltd. Strat. Mgmt. J., 37: 22–44 (2016)DOI: 10.1002/smj

24 J. Y. (Rose) Kim et al.

extend this research and demonstrate how ERGMscan be effectively employed for a much broader setof research questions to study strategy network phe-nomena. We suggest that ERGMs can be used toexplicitly capture the effects of endogenous localstructures, and more generally, to understand theantecedents and mechanisms involved in networkformation. Broadly stated, this category of researchcan be expressed through two questions: (1) How doobserved network structures emerge, and (2) Whatare the underlying social processes that lead to theemergence of these observed structures? With theirdistinctive advantages, ERGMs not only extendprior research, but also open up new research oppor-tunities to enhance our understanding of strategytopics such as multipartner alliances, microfoun-dations of interorganizational network formation,and multiplexity (multiple types of ties) in socialrelationships.

To demonstrate the benefits of ERGMs, we pro-vide an example examining board interlocks amongFortune 100 firms and develop models to illustratethe comparison of traditional logistic regressionmethodologies to ERGM techniques. Prior researchhas examined different firm- and dyad-specific fac-tors of interlock tie formation, yet few studies exam-ine endogenous structural processes underlying theformation of board interlock networks (Harriganand Bond, 2013). Thus, we first examine whetherthere are any structural processes that shape theboard interlock network. We also test whether theinfluence of firm-, dyad-specific factors examinedin prior research persists after explicitly account-ing for these structures. Our results show thatendogenous structural processes such as reciprocity(“returning the favor” by exchanging board inter-lock invitations) and triad closure (the greater like-lihood of a tie forming between two actors wheneach is already tied to a third actor) play a significantrole in shaping this network. These results provideinsights not offered by other regression techniquesand indicate that interlock formation may partiallystem from broader social phenomena. At the sametime, when we control for local network structuraleffects using ERGMs, some of the firm-specificcharacteristics that have most often been studied inthe past using conventional techniques prove to beless consequential. For example, prior research hasproduced inconsistent results regarding the relation-ship between profitability and interlocks (Mizruchi,1996). Our findings help clarify this issue, revealinglittle evidence that directors of large or profitable

firms are more likely to be invited for a directorshipat other firms when network structural effects aretaken into consideration. Our application shows thatthe use of ERGMs provide not only rigorous empir-ical evidence for advancing scientific research, butalso opportunities for further theorizing the socialembeddedness view of board interlock formation assuggested in prior research (Withers, Hillman, andCannella, 2012). Furthermore, we offer potentialextensions of existing strategy research that couldbe made using ERGMs in domains such as alliancesamong multiple firms, microfoundations of interor-ganizational network formation, and different typesof concurrent ties among actors.

NETWORK FORMATION

Current approaches in strategy research

Existing research in the strategy area has focusedon numerous actor and dyadic characteristics thatinfluence tie formation between organizations. Atthe actor (firm) level, a variety of firm-specific char-acteristics such as technical capability or organiza-tional reputation have been shown to be importantpredictors of a firm’s propensity to form ties withother firms, for example through alliances (e.g.,Ahuja, 2000; Gu and Lu, 2013). In a directed net-work, sender’s and receiver’s characteristics mayinfluence the likelihood of a tie being formed.

Existing research has also illustrated how theobserved network structure may be driven by char-acteristics of the dyad, showing how a relationalattribute between two parties can influence the for-mation of ties. As an illustration, homophily sug-gests that firms with similar characteristics are morelikely to have ties with one another than withother firms (McPherson, Smith-Lovin, and Cook,2001). However, homophily may sometimes limitthe benefits of connection in terms of informationor resources available in the network; thus, actorsmay partner with others who are different fromthem. For example, past research has shown howdyad-specific characteristics such as differences orsimilarities in firms’ resource endowments or theirrelative position with respect to markets, technolo-gies, or geographic location are important factorsinfluencing tie formation (Diestre and Rajagopalan,2012; Rothaermel and Boeker, 2008). Finally, net-work ties emerge as a result of other types ofshared ties between actors, that is, multiplexity. For



(a) Reciprocity (b) Popularity (c) Activity (e) Brokerage(d) Triad closure

Figure 1. Different types of network structures and associated endogenous processes

example, the presence of collaborative R&D rela-tionships between firms may subsequently influ-ence the formation of different kinds of ties such ascustomer-buyer relationships (Powell, Koput, andSmith-Doerr, 1996; Shipilov and Li, 2012). Sim-ilarly, characteristics of interlocking ties betweenindividual board members influence subsequentalliance formation between their affiliated organi-zations (Gulati and Westphal, 1999).

Endogenous structural processes

While network formation is influenced byfirm-specific and dyad-specific characteristicssuch as those highlighted above, networks can alsoemerge through broader social processes such asendogenous effects driven by the internal processesof the focal network (Lusher and Robins, 2013;Robins, 2009). For example, individual actorsmay act separately from each other without anyknowledge of or intention to shape the broadernetwork while still being influenced by each other’ssimultaneous actions (Gulati and Gargiulo, 1999;Uzzi and Spiro, 2005; Watts, 1999). In such cases,network ties are the result of endogenous processesinfluenced by existing network ties rather thanas a result of actor attributes or other exogenousfactors. Scholars have suggested five broad typesof endogenous structural processes that influencenetwork formation (Lusher and Robins, 2013), asillustrated in Figure 1.

Reciprocity (a) is the most basic, yet one ofthe most important, tendencies in social interac-tions (Blau, 1964). It explains tie formation through“returning the favor,” reciprocating an earlier inter-action with a network actor. The structure of thenetwork can also be influenced by the number anddirection of an actor’s ties. Popularity (b) illus-trates the process by which already-popular actorsmay become even more popular, analogous to thewell-known “Matthew effect” in social science

(Barabási and Albert, 1999; Merton, 1968), oftendescribed as “the rich get richer.” For example,in interorganizational networks, firms with moreextensive alliance ties are more likely to engagein future alliances, subsequently influencing theirvisibility and attractiveness as a potential partner(Podolny, 1993; Podolny and Stuart, 1995). Tiesmay also more likely be generated by actors that aresimply very active in seeking new network connec-tions, represented as Activity (c) in Figure 1. Thenetwork patterns associated with Popularity (b) andActivity (c) are often called “star” terms because oftheir star-like structures; specifically, “in-two-star”describes popularity with two incoming ties towardthe central node, and “out-two-star” refers to activ-ity with two outgoing ties from the central nodein a directed network. In an undirected network,there is no need to differentiate the direction, and wewould refer only to a general “two-star” term. (Notethat there can be multiple ties outgoing/incomingto the central node; we depict only the simplestforms for purpose of illustration.) In network terms,a triad represents the structure of ties between anyset of three actors, with Triad Closure (d) indicat-ing that two actors are likely to form a tie if theyare each tied to a separate common actor, creating atriangle connecting all three actors (Wasserman andFaust, 1994). “A friend of my friend is my friend”is an intuitive example of triad closure, which isalso referred to as the transitive influence on theformation of a tie between unconnected actors.Research suggests that firms may engage in triadclosure to obtain resources from multiple collabo-ration partners to counter the move of a competitoror to protect their own interests in an interorganiza-tional network (Gomes-Cassares, 1994; Madhavan,Gnyawali, and He, 2004). Finally, ties may occur bythe network process of Brokerage (e) where an actorconnects others who are not directly connected.There are particular advantages that brokers enjoy,as Burt (1992) discusses in terms of the power and



influence obtained by actors in a brokerage position,shown as the central node of Figure 1(e).

Network formation is the result of numerousprocesses that interact and operate simultaneously(Contractor et al., 2006; Hedström and Swedberg,1998; Lusher et al., 2013). Strategy research onnetworks and ties has largely focused on how afirm’s characteristics or dyadic-specific attributesinfluence tie formation. More complex, endogenousstructural effects such as reciprocity, triad closureand brokerage have rarely been empirically inves-tigated in a systematic fashion, although the notionthat firms’ decisions to create ties are influenced byothers’ behaviors is a central premise of networkresearch. This omission has important implicationsfor research on network formation. Failure toaccount for these endogenous structures may resultin model misspecification, attributing significanteffects to firm- or dyad-specific characteristicsthat may be confounded with structural processesindependently driving the network (Cranmer andDesmarais, 2011; Goodreau, Kitts, and Morris,2009; Harrigan and Bond, 2013). In contrast,properly accounting for these structural effects mayaid theory development, allowing us to identifycombinations of social processes underlying theemergence of network structures (Contractor et al.,2006). In the next section, we discuss why con-ventional regression models may be an inadequatetool for network formation research and introducerecent methodological advancements, ERGMs, asa better alternative.

NETWORK METHODOLOGIES

Conventional regression methodologyfor network formation research

Past network research in strategy has generallyemployed regression models such as logit or pro-bit to study network formation among firms, witha focus on testing the effect of firm or dyadicco-variates (e.g., technical capability, resource com-plementarity) or some network characteristics (e.g.,centrality) on tie formation (Chung, Singh, and Lee,2000; Gulati, 1995; Gulati and Gargiulo, 1999).However, for a number of reasons, these approachesimpose significant limitations when examining net-work formation. Standard statistical methods arebased on assumptions of independence, which areproblematic for network data that are inherentlyinterdependent (Wasserman and Faust, 1994). Past

research has attempted to address this issue byemploying corrections such as the clustering ofstandard errors or the creation of separate con-trol variables to correct for autocorrelation amongobservations (Lincoln, 1984; Stuart, 1998), or ithas treated the problem as a sampling issue andtackled it by using elaborate weighting methodolo-gies (Barnett, 1993; Gulati, 1995). These techniquesmay provide an insufficient solution to the study ofnetwork formation, given the dependence of obser-vations in relational data that make it impossible tocorrectly cluster standard errors or to appropriatelycontrol for oversampling (Greene, 2008).

More importantly, standard regression methodsare generally not capable of incorporating variouslocal network structures such as triads stemmingfrom either endogenous structural effects or dyadiceffects (e.g., homophily between firms with similarattributes) because they are not independent ofeach other (Wasserman and Pattison, 1996). Thus,when conventional statistical models are used fornetwork formation research, they are likely tosuffer from model misspecification, even with theinclusion of firm- or dyad-specific co-variates.Causal inference about the influence of specificfactors may be incorrect given this confoundingeffect of the endogenous structural processes(Cranmer and Desmarais, 2011; Goodreau et al.,2009; Lusher et al., 2013). In sum, although stan-dard statistical approaches are useful for researchfrom the perspective of the individual firm (i.e.,ego-centric perspective), they are inappropriate tostudy network formation when we have the goalof examining the multiple processes that operateconcurrently to generate a global network.

Exponential random graph models

Exponential Random Graph Models (ERGMs) arewell suited to address the limitations of tradi-tional regression methodologies. ERGMs are a classof statistical models for social networks whichaccount for the presence (or absence) of net-work ties (Robins et al., 2007a; Snijders et al.,2006; Wasserman and Pattison, 1996). Relative totraditional regression models, ERGMs provide asuperior approach to study network formation byexplicitly modeling endogenous dependencies thatmay shape networks along with exogenous fac-tors such as actor- or dyad-specific characteristics(Lusher et al., 2013; Robins et al., 2007a). ERGMsmodel ties as being interdependent, resulting in a



variety of local network configurations (as repre-sented in Figure 1). These network configurationsare consequential patterns that may reflect impor-tant social processes such as reciprocity or clus-tering that simultaneously affect the formation ofa global network. The formation of ties and net-work structures is tested for statistical significancerelative to what might be expected through randomtie formation, conditioned on other effects in themodel. ERGMs do not require the assumption ofindependence between network ties and avoid theneed for a matched sample design or the bias correc-tion techniques for rare events that have been usedin prior network research.

ERGMs can incorporate different types ofnetwork configurations and estimate their effectson network formation. For instance, ERGMs candescribe the likelihood of the formation of recipro-cal ties or whether a tie between two actors, alreadytied to a common third actor, is more likely to beobserved (i.e., triad closure) in an overall network,conditioned on the structure of the network. Giventhat structural outcomes such as triad formationhave been shown to be interdependent, such aninference is problematic for standard statisticalmethods (Wasserman and Faust, 1994).

Moreover, ERGMs can accommodate any num-ber of binary, categorical, or continuous actor- ordyad-specific co-variates as well to see whether theyare associated with the formation of network ties.ERGMs can also be used to analyze different typesof networks such as directed and nondirected net-works, bipartite, and multiplex networks with vari-ous types of nodes and relationships (Lusher et al.,2013; Robins, Pattison, and Wang, 2009; Wang,2013; Wang et al., 2013). Therefore, ERGMs pro-vide a powerful, flexible tool to separate varioussocial processes operating concurrently and eval-uate the relative contribution of each on the for-mation of the observed network structure (Lusheret al., 2013; Robins et al., 2007a). At least in thisaspect, these broader capabilities of ERGMs are insome ways analogous to the advantages of statisticalanalysis tools such as structural equation modeling(SEM), which allow researchers to simultaneouslycapture wider system-level effects. For example,as SEM expands from conventional cause-effectregression modeling to the concurrent analysisof more complex co-variance structures, ERGMsgo beyond nodal and dyadic factors modeled inconventional logistic regression to capture diversefactors at the broader network level.

ERGMs trace their origins to influential work byFrank and Strauss (1986) who applied spatial statis-tical approaches to networks and proposed Markovrandom graph models to directly address the issueof interdependence. The models became widelyknown as p* models from the seminal work byWasserman and Pattison (1996), which broadenedthe use of this approach to network analysis. A num-ber of subsequent advances, including adaptationsfor local “neighborhood” network structures (Patti-son and Robins, 2002) and methods for overcomingthe problem of model degeneracy (Hunter andHandcock, 2006; Robins et al., 2009; Snijders et al.,2006) have helped develop ERGMs into a viabletool for analyzing real world network data.

Recently, ERGMs have begun to be adopted in awide range of social science disciplines, includingsociology, demography, communications, and polit-ical science (e.g., Atouba and Shumate, 2010; Cran-mer and Desmarais, 2011; Goodreau et al., 2009;Wimmer and Lewis, 2010). A small, yet grow-ing number of recent organizational studies usingERGMs demonstrates the potential of the method-ology as a useful tool for modeling multiple socialprocesses, though these techniques have seldombeen applied to empirical research focused on strat-egy questions. We provide a summary of recentstudies using ERGMs in organizational research inTable S1, along with a description of how they applyERGM techniques.

STATISTICAL INFERENCE THROUGHERGMS

Statistical framework and dependenceassumptions

ERGMs have the following form

Pr (X = x) = (1∕k) exp

[∑A

𝜂AzA (x)

], (1)

where Xij is a random variable that represents a tiebetween actor i to actor j (Xij = 1 if there is a tie fromactor i to j, and 0 otherwise). These ties are repre-sented in an n× n adjacency matrix (n= number ofactors in the network) denoted as X, and x denotes amatrix of realized ties in the network. When ties arenondirectional (edges), X is symmetric. When tiesare directional (arcs), Xij ≠Xji. The A refers to dif-ferent network configuration types. The zA(x) terms



are model co-variates, denoting any set of A networkstatistics calculated on x and theorized to affect theprobability of this network forming. Examples of zstatistics are the number of ties, the number of tiesbetween firms with a shared nodal characteristic, orthe number of closed triads and so on. Equation 1may be modified by replacing zA(x) with zA(x, P)to accommodate additional co-variate informationP such as firm- or dyad-specific characteristics. The𝜂A coefficients are unknown parameters to be esti-mated, and they determine the effect of the networkstatistics included in the model for the observednetwork. The k stands for the quantity from thenumerator summed over all possible networks withn actors. It constrains the probabilities to sum to 1.Simply put, ERGMs place more or less weight onnetworks with certain features, as determined by 𝜂A(i.e., parameters), and zA (network statistics). Theequation above can also be expressed in terms ofthe conditional log-odds (logit) of individual ties:

logit(

P(

Xij = 1 |n,Xcij

))=∑

A

𝜂A𝛿zA (x) , (2)

where Xcij denotes the rest of the network other than

the single variable Xij, and 𝛿 ZA is the amount bywhich zA changes when Xij is changed from 0 to1. The presence of Xc

ij in the conditional statementin the left-hand side of the equation represents themutual dependence of ties, showing how ERGMsexplicitly accommodate interdependent observa-tions. This alternative specification also clarifies theinterpretation of 𝜂A vector, the coefficients of inter-est. If forming a tie increases zA by 1, then all otherthings being equal, the log-odds of that tie formingincrease by 𝜂A.

To implement ERGMs, it is important to under-stand the dependence assumptions that define theways in which the observed ties may be related(Brandes et al., 2013; Pattison and Robins, 2002;Robins et al., 2007a). A particular dependenceassumption determines the different types of net-work configurations to be included in a model(Lusher et al., 2013; Robins et al., 2007a). The sim-plest dependence assumption is that all possible dis-tinct ties are independent of one another; they occurrandomly with a certain fixed probability. A sec-ond assumption is that dyads are independent of oneanother. For example, reciprocity in a directed net-work is a form of dependency assumption where thetwo possible directed ties within a dyad are depen-dent on each other. This assumption is sometimes

referred to as “dyadic independence” because thereare no other effects outside the dyad that influencethe formation of ties, and so the dyads are inde-pendent of each other. However, these two assump-tions are usually implausible in most of the observedsocial networks (Snijders et al., 2006). For example,if we believe that ties do not depend on each other,there would be no local network configurationsformed such as stars or triangles other than a recip-rocated tie. A more realistic assumption is Markovdependence (Frank and Strauss, 1986), where tiesmay depend on the presence of a common actor.For example, the relationship between A and B maywell be dependent on the presence or absence of arelationship between B and C. As explained in thefollowing section, models exclusively based on theMarkov dependence assumption do not representthe observed network data well due to the problemof model degeneracy (Handcock, 2003a, b). Finally,the most common assumption is the “social circuitmodel”, in combination with Markov dependence(Pattison and Robins, 2002). In this model, somedyads are conditionally dependent on the presenceof other ties, even without a common actor (seeKoskinen and Daraganova, 2013a, b) for more com-prehensive explanations on the different types ofdependence assumptions).

Model estimation

Parameters in ERGMs were initially estimatedusing maximum pseudo-likelihood (Strauss andIkeda, 1990), yet this approach tends to performpoorly, particularly with dyad-dependent models.Instead, Markov Chain Monte Carlo maximumlikelihood estimation (MCMC-MLE) procedureshave been used (Geyer and Thompson, 1992;Snijders, 2002). Monte Carlo estimation sim-ulates a distribution of random graphs usingstarting values of parameter estimates generatedby pseudo-likelihood, and it repeats the process toget refined values by comparing simulated distri-butions of graphs with the observed data (Snijders,2002). The benefit of the MCMC-MLE approachis that with an infinite number of draws from thedistribution of network configurations, it gives esti-mates equivalent to the MLE and provides reliablestandard errors while including dyad-dependentterms (for a review, see Wasserman and Robins,2005). Currently, the MCMC-MLE approach is thedefault for most software packages. One drawbackassociated with the use of this procedure is that



resulting networks generated by parameter esti-mates with Markov dependence assumptions wereoften degenerate—that is, the model producedestimates that created a graph with no ties at all ora complete graph with ties connecting every node.This problem of model degeneracy is primarilydue to poor model specification and often occursamong networks with a high level of triangles(Handcock, 2003a, b). Scholars have developed aseries of new network specifications called socialcircuit dependence (Pattison and Robins, 2002)that significantly curtail such issues (Hunter andHandcock, 2006; Robins et al., 2009; Snijderset al., 2006). Thus, in our application, we adoptthese new specifications to examine structuraleffects, following prior research (Goodreau et al.,2009; Wimmer and Lewis, 2010).

APPLICATION

To illustrate the capabilities of ERGMs and theirapplication in the field of strategy, we examine thephenomenon of board interlocks, interorganiza-tional ties that are formed between firms sharingexecutives on their boards of directors (Mizruchi,1996). Prior research has identified a variety offactors that influence dyadic interlock tie forma-tion (Beckman, Haunschild, and Phillips, 2004;Mizruchi and Stearns, 1988; Pfeffer and Salancik,1978), yet few studies explicitly account for theinfluence of endogenous structural processes—thatis, the existing set of board interlocks—in theformation of future interlock ties (Harrigan andBond, 2013). Thus, we explore whether the influ-ence of firm- and dyad-specific characteristicspersists while structural effects are taken intoaccount.

Sample and data

We chose to focus our study on the network of inter-locks formed between the boards of directors ofU.S. firms belonging to the Fortune 100 in 2005to predict the subsequent formation of interlockties among these companies from 2006 to 2010.Long-established research has argued that directorties among the most important firms in the U.S.economy result in the formation and persistence of acorporate elite (Mills, 1956; Palmer, Friedland, andSingh, 1986), who act to ensure the maintenanceof their privileged position in the economy as well

as offering a platform for the diffusion of infor-mation and new managerial practices (Davis, 1996;Haunschild, 1994; Haunschild and Beckman, 1998;Mizruchi, 1996). We use 2005 as the reference yearfor firm and dyadic attributes and track the subse-quent formation of interlock ties between compa-nies in our sample during the period of 2006–2010.The Sarbanes-Oxley legislation passed in 2002 ledto substantive changes in board composition andmembership. Our study period lags this change andcaptures boards after changes made in responseto the legislation related to the availability andwillingness of directors to sit on multiple boards(Green, 2005; Linck, Netter, and Yang, 2009). Fol-lowing prior research (Beckman et al., 2004), weomit privately held organizations such as insurancefirms from our sample to ensure the consistency offinancial information in our analysis, resulting in afinal sample size of 95 firms.

We capture a new board interlock tie for eachinstance in which a director or executive of a firmaccepts a directorship with another firm in the sam-ple. We draw interlock data from the GMI Ratingscorporate governance database (formerly knownas the Corporate Library), a third-party resourcetracking board membership in publicly traded U.S.firms. The resulting binary ties recorded among allpotential dyads are then assembled into a 95× 95binary sociomatrix (essentially, a grid listing allfirms on the vertical and horizontal axes, capturingthe presence or lack of board interlock ties for eachpossible dyadic combination of sample firms) to beanalyzed by ERGMs. This is a directed network,given that the focal firm essentially initiates atie by inviting a director from another firm toserve on its board. We observe a total of 129 newinterlock ties formed between sample firms duringthe 2006–2010 period of our study.

We also collected data on our independent vari-ables from a variety of additional sources. Data forfirm size and all financial measures were obtainedfrom COMPUSTAT. Alliance data were obtainedthrough the SDC Platinum database.

Variables and measures

The dependent variable in our study is tie formationthrough board interlocks among the 95 sampledfirms. Our key independent variables examine theeffect of board characteristics at different levels ofanalysis—firm characteristics, dyad–co-variates,and structural effects—on subsequent board ties.



Firm level characteristics

Prior research on boards of directors has empha-sized the role that firm characteristics play indetermining what interlock relationships may form.Research has shown that geographic proximity isan important determinant for network formation ofcorporate interlocks (Kono et al., 1998). We exam-ine the influence of geography by modeling whethera tie is more likely between firms located in thesame State, while accounting for geographic levelsof tie formation. Empirically, we include a series ofindicator variables for the 10 states most commonlyrepresented in our data, which cover 74 percent ofour sample population. The remaining firms aregrouped into the reference category. We also includea term to capture homophily effects of colocationin a common state. This approach is analogous toincluding both main effect and interaction termsin a regression. The main effect in this case isto control for the propensity of firms located in aparticular geographic region to make ties, whereasthe interaction effect tests whether firms locatedin the same region are more likely to make tieswith each other, over the variance explained bythe main effect. We include Firm size by mea-suring the number of employees in each firm asreported in the reference year of 2005. Managersand directors of successful firms may be more likelyform ties (Davis, 1993; Withers et al., 2012); thus,we include Profitability of a company by measur-ing its ROA, again in 2005. We include Marketuncertainty, which has been shown to influencea firm’s propensity to pursue interorganizationalrelationships as it seeks to lessen its dependenceand alleviate environmental uncertainty (Pfeffer andSalancik, 1978). We measure this variable as theaverage monthly volatility across all companies inthe focal firm’s industry using four-digit SIC code(Beckman et al., 2004). Prior experience in externalinterorganizational relationships may influence afirm’s motivation to make additional ties (Beckmanet al., 2004; Yue, 2012). Therefore, we also includea measure of the Number of prior alliances in whicheach firm engaged during the period from 2001to 2005.

Dyad level characteristics

The presence of existing relationships among firmscan influence their subsequent tie formation. Thus,we examine whether firms in our sample had any

previous interlock ties with each other before theperiod of our study. Prior interlocks is operational-ized as a binary sociomatrix valued as 1 for thepresence of one or more prior ties between a pairof sample firms and 0 otherwise. We draw fromthe GMI Ratings corporate governance database,using 2001–2005 as the reference period for thisvariable. We also examine whether firms that aresimilar in size may be more likely to make inter-lock ties with each other. Size difference is a dyadicco-variate consisting of the absolute difference infirm size operationalized by the number of employ-ees for each firm.

Structural effects

Structural processes can also be important driversof board network formation, but empirical exam-ination of such effects has been largely absent inprior board interlock research. To facilitate under-standing of each of the structural terms we includein the model, we provide a graphical presentationof each structural term in Figure 2. We follow inthe path of prior research suggesting that modelsshould include at least a parameter for density,some control over the degree distribution and triadclosure to properly capture the features of the net-work in general (Robins and Lusher, 2013; Robinset al., 2009; Snijders et al., 2006). We includethe following set of structural effects that mayoccur independent of firm or dyad characteristics.Reciprocity captures the tendency of a tie beingreciprocated from j to i when firm i has an existingtie to firm j; in our study, it represents the likelihoodthat firm i that already has a director of firm j onits board will subsequently place a member of itsboard on the board of firm j. Ties are directional,with one actor initiating them and another receivingthem. In the interlock context, the initiator is thefirm that puts another firm’s director on its ownboard while the firm that originally had the boardmember is the receiver. We use two measuresto capture the differences between senders andreceivers. Popularity and activity spread (star-likeconfigurations) capture the tendency of networkcentralization in the in- and out-degree distributions(Pattison and Robins, 2002). Popularity spreadmeasures how often a firm’s director is invited fora directorship from multiple firms, while Activityspread captures how often a firm initiates aninterlock tie by inviting a director from other firms.Triads represent an important intermediate level in



Parameter Diagram Social Process statnet term

Purely structural effects

Arc edges

Reciprocity Firm A's tendency toward inviting a director of firm B whose director is already on Firm A's board

mutual

Popularity Spread gwidegree

Activity Spread gwodegree

Generalized transitive closure gwesp

Multiple Connectivity gwdsp

Actor relation effects (black nodes indicates actor with attribute)

Sender (firm size) nodeocov (firm size)

Sender (profitability) nodeocov (profitability)

Sender (prior alliance activities) nodeocov (prior alliance activities)

Sender (uncertainty) nodeocov (uncertainty)

Receiver (firm size) nodeicov (firm size)

Receiver (profitability) nodeicov (profitability)

Receiver (prior alliance activities) nodeicov (prior alliance activities)

Receiver (uncertainty) nodeicov (uncertainty)

Homophily (state) nodematch (state)

Covariate network

Prior interlocks edgecov (prior interlocks)

Tendency of firms with a certain level of size, profitability, prior alliance activities or facing a certain level of uncertainty to be invited by other firms

Tendency of managers from firms located in the same geographic location to sit on common boards

Tendency for a dyad of firms that had prior interlocking ties to make a new tie through board interlock

Baseline tendency for interlock tie formation

Tendency toward variation in the degree to which a manager of firm A is invited to sit on multiple boards.

Tendency toward variation in the degree to which firm A invites a director from multiple firms to sit on its boardTendency for the closure of transitive triads (when firm A's board has a director from firm B, and when firm B's board has a director from C, firm A is more likely to invite a director from firm C)Tendency for the formation of multiple 2-paths connecting firms in the board interlocking network

Tendency of firms with a certain level of size, profitability, prior alliance activities or facing a certain level of uncertainty to invite a director from other firms

Figure 2. Summary of structural effects included in the ERGM estimation for board interlocks



network analysis between the individual dyads andlarger network structures (Madhavan et al., 2004;Wasserman and Faust, 1994). In our context, triadclosure refers to the likelihood that a board inter-lock will form between two firms that both haveexisting ties with a third firm. We capture this effectusing the term Generalized ransitive closure (otherforms of triad closure may be modeled in a directednetwork—Robins et al. (2009) provide greaterdetail on these alternative terms). Finally, Multipleconnectivity captures a tendency for the formationof nonclosure structures where two actors areconnected by multiple paths: in our context, inwhich firm A and firm B are indirectly connectedthrough other organizations that share board inter-locks with the two firms. Research suggests thatinclusion of this term permits refined inferencesabout transitivity effects because a triad closurecontains other lower-order configurations such aspopularity and activity spread (Robins et al., 2009).

We use new specifications to incorporate thesestructural effects (Goodreau et al., 2009; Hunter,2007; Wimmer and Lewis, 2010) and to overcomethe problem of model degeneracy discussed earlier.Popularity spread and activity spread are includedby using geometrically weighted in-degree dis-tribution (GWID) and geometrically weightedout-degree distribution (GWOD), respectively.They model the shape of the in- and out-degreedistribution. A large, positive coefficient for theseparameters suggests a network with high-degreenodes. The GWID statistic models a tendencytoward variation in the degree to which firm A’sdirector is invited to join multiple external boards.The GWOD statistic indicates, on the other hand, atendency toward variation in the degree to whichfirm A invites directors from multiple externalfirms to join its board. Basic triangles are includedin ERGMs by a geometrically weighted sharedpartner (GWESP) statistic. This term indicates ageneral tendency for network closure of transitivetriads (i.e., when firm A has a board interlockwith firm B, and firm B has an interlock with firmC, A is more likely to form an interlock tie withC). Finally, multiple connectivity is included bygeometrically weighted dyad-wise shared partnerdistribution (GWDSP) statistics. This statisticmodels a tendency for the formation of multipletwo-paths connecting firms in the board interlocknetwork.

Adding structural effects to the examination andestimation of board interlock formation provides

several distinct advantages. A co-variate–onlymodel without structural terms tends to overesti-mate the effect of firm- or dyad-level characteristics,whereas a full model that includes the structuralterms can specifically estimate the unique effects ofthose factors. As a result, estimates of the effects offirm and dyadic co-variates may be smaller in thefull model than in the co-variate–only model. Wealso predict that the full model will fit the observednetwork better than the co-variate–only modelbecause at least some of the structural effects suchas reciprocity and triad closure are important socialprocesses influencing board interlock formation.We estimate our models using MCMC-MLE inthe ERGM package, a part of the statnet suite ofpackages for R (Hunter et al., 2008b). There areother useful software packages available for ERGManalysis, such as the PNet suite of programs forERGMs (Wang, Robins, and Pattison, 2009) orSIENA-p* in StOCNET (Snijders et al., 2008).

Analysis and results

For the main descriptive statistics of the networkof board interlocks, the probability that any pairof firms has a board interlock tie at some pointduring the study period is 1.4 percent (i.e., networkdensity= 0.014). The average degree is 2.72. Thestandard deviation of out-degree (1.57) is slightlygreater than that of in-degree (1.33). Thus, thesample firms are more heterogeneous in termsof initiating ties (i.e., inviting new directors whocurrently sit on the boards of other firms) than interms of receiving ties.

The results of the ERGMs are shown inTable 1. Model 1 includes firm characteristics anddyad-specific co-variates without any structuralterms. It is important to note that when ERGMsinclude only firm- or dyad-specific characteristics,the results are the same as what would be obtainedfrom conventional logistic regression analysis fre-quently used in prior research (Koehly, Goodreau,and Morris, 2004). Thus, Model 1 provides abenchmark for comparison to the model withstructural terms included. Model 2 adds a varietyof structural terms explained earlier, along with thefirm characteristics and dyad-specific co-variates.

We first consider whether a full model with thestructural terms shows improvement with respect tomodel fit based on Akaike’s Information Criterion(AIC) (Akaike, 1998). The smaller the value of AIC,the better the model fits the data. The AIC of Model



Table 1. Formation of board interlock in Fortune 100 firms

ParameterModel 1 co-variates–only

(no structural term)Model 2 co-variatesand structural term

Purely structural effectsArc −13.23*** −10.39***Reciprocity — 2.72***Popularity spread — −0.07Activity spread — −0.57Generalized transitive closure — 0.83***Multiple connectivity — −0.12+Actor relation effectsSender (firm size) 0.49*** 0.35***Sender (profitability) 8.46*** 6.25**Sender (prior alliance activities) 0.002 0.002Sender (market uncertainty) 1.56 1.61Receiver (firm size) 0.23** 0.15+Receiver (profitability) 4.81* 3.42Receiver (prior alliance activities) 0.001 0.001Receiver (market uncertainty) −3.17+ −3.01+Homophily (state) 1.08*** 0.79***Homophily (firm size) −0.09 −0.05Co-variate networkPrior interlocks 0.74** 0.59*Akaike information criterion (AIC) goodness of fit 1,264 1,196

+p< 0.1; *p< 0.05; **p< 0.01; ***p< 0.001.

2 is substantially smaller than Model 1, suggestingthat systematic network properties are important inproducing the observed network of board interlocksin our sample.

We are interested in the underlying processes oftie formation or how the observed network couldhave been formed (Lusher et al., 2013). Thus, inaddition to model selection criteria such as AIC,we also employ graphical evaluations of goodnessof fit to visualize the match between the predictedand observed networks in Figure 3(a, b) (Goodreauet al., 2009; Hunter, Goodreau, and Handcock,2008a). Each plot compares the observed datato 100 randomly generated simulated networksobtained from the fitted models we examined. Thisallows the researcher to gain a visual sense of modelfit by observing how well the distribution of plot-ted points of networks randomly generated from thefitted models match the actual observed network(represented by the dark line) in terms of key struc-tural properties of the network such as the propor-tion of incoming or outgoing ties to other actors. Weshow the logit of relative frequency on the y-axis forgreater ease of interpretation.

The first and second plots in Figure 3(a, b) rep-resent the out-degree distribution (the number ofconnections a focal node has sent to other nodes)

and in-degree distribution (the number of connec-tions a focal node has received from other nodes).Model 2 fits slightly better than Model 1 with thedark line of Model 2 passing through the medianpoint of the box plots for the range, yet Model 1also does a relatively good job of producing net-works that reflect the actual degree distribution.The third plot shows the distribution of the triadcensus, which captures 16 different forms of tri-ads (see Holland and Leinhardt, 1970, for detailson the 16 triad forms). While Model 1 underes-timates several types of triangle structures in theobserved network (suggesting a relatively poor fit),Model 2 appears to provide an improvement withsimulated numbers of each type of triad closely fol-lowing the pattern of the observed network. Thefourth plot in Figure 3(a, b) shows the distribution ofshared partners (number of third-party interlock tiesin common between a given pair of firms), whichindicates the level and scale of clustering. Here,we also see a noticeable difference between Mod-els 1 and 2. By directly modeling the local struc-ture with the inclusion of a term for shared partners,the plot illustrates that Model 2 provides a good fitbetween the simulated and observed networks. Incontrast, Model 1 appears to be more divergent interms of this network characteristic. Finally, the fifth



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Figure 3. (a) Goodness-of-fit diagnostics for Model 1 (without structural effects). The dark solid line represents a givenstatistic from the observed board interlock network. The boxplots represent the same statistic from the 100 simulatednetworks; they include the median and interquartile range. The light-gray lines represent the range in which 95 percentof simulated networks fall. The Y-axis is expressed as a loglikelihood to facilitate interpretation. In summary, Model 1without any structural effects shows a lack of fit, particularly in terms of “triad census” and “edge-wise shared partners”model statistics, as evidenced by the gap between the dark solid line and the trend of the boxplots. (b) Goodness-of-fitdiagnostics for Model 2 (with structural effects). Compared to Model 1, Model 2 with structural effects shows a noticeableimprovement of model fit by explicitly capturing additional structural effects through the GWESP and GWDSP termsincluded in the model. In each network statistic, the pattern of the boxplots from simulated networks are largely in line

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Figure 3. Continued.

plot examines a higher-order network statistic, thedistribution of geodesic distances, tabulated acrossall actors. Geodesic distances represent the pairwiseshortest distances between firms. Both Models 1and 2 appear to provide a relatively good for thelower range of the plot, yet beyond the middle pointthe observed distribution diverges from the modelprediction. Note that geodesic distance is a globalproperty of the network (Goodreau et al., 2009), andour models (both Models 1 and 2) do not include

a specific structural term to capture this propertybecause we do not propose specific examples offactors in the interlock context that would explainglobal network properties. Thus, although we pro-vide the plots for geodesic distances as one of theways to graphically demonstrate model fit, it is notsurprising to see little improvement of Model 2 overModel 1 for this particular network characteristic.Depending on the goals of their study, researchersmay explicitly capture this higher-order property in



their models (Morris, Handcock, and Hunter, 2008,provide a discussion of ERGM terms related to thisproperty).

Because Model 2 provides a better fit withthe observed data, we further examine the modelcoefficients in order to assess the drivers of boardinterlock formation. In ERGMs, a positive coef-ficient suggests greater prevalence of a givenconfiguration in the network than that which wouldbe expected, conditional on the other effects in themodel, whereas a negative coefficient indicates thatthe configuration occurs less often than expected(Lusher et al., 2013). Returning to the results inTable 1, the negative, significant coefficient ofArc in Model 2 suggests that interlock ties occurrelatively rarely, especially if a given pair of firmsis not part of a higher order structure such as a staror triad. The Arc term in ERGMs is equivalent toan intercept term or a grand mean in regression orANOVA, indicating the baseline propensity for tieformation in the network (Strauss and Ikeda, 1990;Wasserman and Pattison, 1996). The Reciprocityterm represents the strength of reciprocity withindyads. The coefficient of Reciprocity in Model 2is positive and highly significant, suggesting thatfirms are likely to reciprocate board membershipwith each other (e.g., a director/executive of firmA is more likely to hold a directorship in firm Bwhose director/executive has already been on firmA’s board). The popularity spread and activityspread terms account for dispersion in the in-and out-degree distribution in the network. Thecoefficients for both terms are not significant. Thepositive, significant coefficient on the GeneralizedTransitive Closure term indicates that controllingfor the tendency to reciprocate ties and for multipleconnectivity, board interlock ties tend to take placein transitive structures. The results also imply thatclusters in this network are driven by groups ofoverlapping triangles rather than clusters of firmsthat are either particularly popular or active. Interms of firm-specific characteristics, the positive,significant coefficient for Sender (Firm size) sug-gests that, when structural effects are accounted for,large firms are more likely to invite directors to joinfrom other firms. The results also suggest that highperforming firms (positive, significant coefficientfor Sender [Profitability]) are more likely to inviteexternal directors to join their boards, conditionalon the other effects in the model. The positive, sig-nificant coefficient on Homophily (State) suggeststhat firms located in the same states are more likely

to make interlocking ties with each other. Finally,firms are more likely to make interlock ties whenthey have shared interlock ties previously (positive,significant coefficient for Prior interlocks).

In fact, the comparison of Models 1 and 2shows the striking change in terms of the effectsof some co-variates. The coefficient associatedwith Receiver (Firm size) is highly significant inModel 1 (p< 0.01); however, it is only marginallysignificant in Model 2. In other words, afterexplicitly accounting for endogenous structuraleffects, the significance of the tendency to invitedirectors of large firms to join external boards issubstantially reduced. The magnitude of the coef-ficient is also decreased. Similarly, the influenceof Receiver (Profitability) also loses significance.While some firm-level characteristics (Firm sizeand Profitability in initiating board interlock ties)and dyad-level characteristics (homophily [State],prior interlocks) are shown to be influential inModel 2, the comparison of Models 1 and 2 showsa general pattern that the magnitude of coefficientsand their significance level diminish with theinclusion of structural effects, as we anticipated.From a theoretical standpoint, these findings maysupport the notion that social processes relatedto reciprocity or information obtained throughcommon third-party ties (i.e., transitivity) actu-ally explain variation in interlock tie formationthat would otherwise be attributed to target firmcharacteristics of prominence and success.

Overall, these results suggest that a varietyof structural processes have unique explanatorypower for board interlock tie formation among thelargest, public U.S. firms, indicating that networkformation models that fail to control for endoge-nous processes provide only a partial picture of thedynamics in this network. This analysis emphasizesthe importance of simultaneously accounting fornetwork–self-organizing processes as well as otherfirm- and dyad-specific co-variates in order togain an accurate understanding of the complicatedmechanisms of network formation, a task uniquelysuited to ERGM techniques.

DISCUSSION

Network formation is the result of critical socialprocesses driven by numerous factors. Whileprior research has employed traditional regres-sion methods to empirically examine network



formation, we propose the use of ERGMs as asuperior alternative that offers several advantages.The primary advantage of ERGMs is that theyallow accurate specification of multiple processesthat simultaneously influence the creation of anobserved network structure. In particular, ERGMsallow the incorporation of purely endogenous struc-tural processes such as reciprocity, triad closure andhigher-order dependencies while accounting forother actor and dyad specific attributes. In addition,ERGMs do not require the assumption of indepen-dence that underlies conventional models, enablingresearchers to analyze complex relational data,and disentangle concurrent effects in a rigorousmanner. Using ERGMs, strategy researchers mayconstruct hypotheses of distinct social processesand test them directly to evaluate their relativecontribution to network formation (Robins et al.,2007a).

We provided a brief overview of recent networkresearch, discussed some of the limitations of cur-rent methodological approaches and elaborated thebasic concepts underlying ERGMs and how theyoffer unique strengths for studying network for-mation. Our application example demonstrates theadvantages of ERGMs, uncovering interesting find-ings that would not have been possible using con-ventional techniques. For example, there has beenlittle empirical research explicitly examining theinfluence of endogenous structural processes onboard interlock formation even though social net-work theory has been a dominant theoretical lensin the literature (Withers et al., 2012). ERGMs pro-vide a useful tool to address these processes, and ourresults show that the board interlock network is inpart a function of endogenous structural processessuch as reciprocity and triad closure. Our examina-tion of board interlocks using ERGM demonstrateshow the failure to account for multiple processesor simultaneously include endogenous structuraleffects can lead to incorrect or incomplete infer-ences regarding the role of factors influencing net-work tie formation. We find that the influenceof firm- and dyad-level characteristics diminishessubstantially in magnitude and significance afteraccounting for structural effects, making an impor-tant contribution to our empirical analysis. Ourresults also help resolve the inconsistent findingsregarding the influence of firm profitability on inter-lock formation, providing evidence that profitabilitymay not play a significant role when network struc-tural effects are considered.

Despite their advantages, ERGMs do have spe-cific limitations as an empirical methodology fornetwork analysis. One limitation is that they canonly be used to model binary outcomes—the pres-ence or lack of ties among actors in a network.Consequently, when ties vary in strength, they mustbe dichotomized in order to be analyzed usingERGMs. In our application, we operationalizedties using board interlocks. It is rare for mul-tiple directors or executives of a given firm tooverlap in their directorships in another specificfirm simultaneously. As a result, the creation ofa binary variable is appropriate for our sampleand research question. For other applications wherethere is important variance in the value of the tie,researchers may want to first consider the distribu-tion of the values and understand how the opera-tionalized variable can be dichotomized (e.g., val-ues either above or below the median for the over-all sample). Another limitation of ERGMs, par-ticularly the MCMC-MLE procedures we used inour examples, is that they can be computation-ally intensive, requiring substantial computationalresources (especially with large-scale data). Fur-thermore, model degeneracy—cases in which thefitted model does not offer a good fit to the observeddata due to model misspecification (Handcock,2003a, b)—remains a challenge. However, recent(and continuing) development of these models hasresulted in new network specifications that havelimited the problem of model degeneracy and facil-itated the adoption of the methodology (Robinset al., 2007b). We employed these new networkspecifications in our empirical study and our pre-dicted model provided a generally good fit to theobserved data without the problem of model degen-eracy, as shown in Figure 3(b).

Potential use of ERGMs in strategy research

Several features of ERGM methodology providesignificant opportunities to extend strategy researchin meaningful ways. First, the ability of ERGMsto directly account for tie dependencies in networkdata allows more precise analysis of the effect offactors that have been examined in prior research.Because ERGMs do not assume independenceamong observations and account for endogeneity,they can be used to test theories of tie formationto establish rigorous empirical evidence, a criticalingredient to develop models that are not onlyappealing, but also scientifically valid (Colquitt



and Zapata-Phelan, 2007). For example, muchprior research has examined the influence of orga-nizational resources on alliance formation. Whilefirms with more resources have more opportunitiesto form ties, their greater level of resources mayalso eliminate the need for collaboration throughalliance.

To try to understand the competing effects ofresources, some researchers have proposed an inte-gration of both perspectives, resulting in a curvi-linear relationship between resources and allianceformation (e.g., Gu and Lu, 2013). Of course, firmsmay also be more likely to form ties because oftheir extensive histories of alliance formation (i.e.,activity) or their popularity as an alliance part-ner from the perspective of other potential part-ners. In such analyses, it may be important tofirst establish whether organizational resources haveany independent effect beyond other factors thatmay simultaneously influence the formation ofan observed network. ERGMs can test the maineffect of organizational resources while explic-itly controlling for numerous forms of structuraleffects. Because ERGMs avoid the need to usea matched sample design or analysis of only asubset of firms by modeling tie formation acrossthe entire network, the inferences drawn as aresult of the empirical analysis are significantlyimproved.

ERGMs may also help us better understand dif-ferent types of local network patterns that generatethe observed structure of the overall network. Forexample, brokerage is an important phenomenonthat directly relates to network formation and struc-ture. Research has demonstrated that status and cen-trality influence the formation of structural holes(Zaheer and Soda, 2009) and that firms that arein brokerage positions with heterogeneous partnersare more likely to sustain their network position(Yin, Wu, and Tsai, 2012). ERGMs offer importantadvantages over conventional methods to extendresearch into brokerage and other structural effectsby modeling brokerage directly.

ERGMs’ flexibility to model exogenous firm-and dyad-specific attributes as well as endogenousstructural effects allows researchers to hypothe-size among competing explanations for networkformation to isolate the specific effects of inter-est in their study with enhanced methodologicalrigor. To highlight and demonstrate how ERGMsmay be used to extend past strategy research, weprovide a summary of recent strategy work on tie

formation in Table S2 with some specific commentson the potential use of ERGMs to extend eachwork.

ERGMs also open up a host of new and interest-ing questions that can advance strategy research.For example, ERGMs allow for the study of multi-partner alliances that involve three or more actors(Das and Teng, 2002; Lavie, Lechner, and Singh,2007; Li et al., 2012). While multiparty allianceshave become more prevalent recently, especiallyin high technology industries where differentgroups of firms may work together, relatively littleis known about their formation (Li et al., 2012).Given the empirical complexities inherent in thestudy of multipartner alliances, scholars havecalled for the development of methodologies thatcan more effectively investigate these types ofstructures (Rosenkopf and Padula, 2008). BecauseERGMs can directly model local network structuressuch as triad and multipartner connectivity whileaccounting for other types of endogenous effectsand exogenous factors, they provide a useful tool tobetter understand the antecedents of multipartneralliance formation.

Another promising area for the use of ERGMs isresearch on the microfoundations of interorganiza-tional network formation. Prior research has high-lighted the important role of existing ties amongindividuals for the subsequent formation of tiesbetween their firms (Gulati and Westphal, 1999;Rosenkopf, Metiu, and George, 2001). For example,in an entrepreneurial setting, new startups areoften founded by individuals who were previouslyemployed by industry incumbents and subsequentlyleft them to begin independent ventures (Klepper,2001; Phillips, 2002). Thus, founders’ employmentrelationships with their previous employers mayhave an important influence on the types of tiesthey form between their new ventures and the par-ent firms. ERGMs are well suited to study thesesituations as they allow for analysis of ties at twolevels—where the network is represented simul-taneously through a set of ties between individualactors and as a set of ties between organizations.This permits the modeling of both sets of char-acteristics, and their reciprocal effects on eachother, simultaneously. Such modeling approachesensure the preservation of the dualistic nature ofthe structure rather than constraining relationshipsinto one form of tie or another (a network offirms or a network of individuals) (Harrigan andBond, 2013). This methodological improvement is



important because research focused on only individ-ual or firm attributes, while simultaneously ignor-ing social processes behind network formation, mayoverestimate the impact of each of these attributes inisolation. ERGMs provide a more accurate assess-ment and understanding of the relative importanceof different factors leading to network formation atthe firm and individual levels.

Past network research in strategy has oftenassumed that all ties formed between actors reflecta single type of relationship. However, actors oftenmaintain qualitatively different relationships toother actors connected with them both directlyand indirectly (Baker and Faulkner, 2002). In fact,many interesting research questions in strategyinvolve firms engaged in multiple types of tieswhere the influence of such ties may span differ-ent networks (e.g., Shipilov and Li, 2012). Forexample, two firms may have an R&D alliancewith each other while at the same time bothbeing suppliers to a third firm (Gimeno, 2004;Gulati and Gargiulo, 1999). Given the flexibilityof ERGMs to accommodate different roles foreach organization as actor attributes and differenttypes of relationships as dyad-co-variate or exoge-nous networks, ERGMs provide an opportunityto examine the influence of tie multiplexity onthe formation of networks among organizations(Wang et al., 2013). In the discussion section, wehighlight recent extensions of ERGM techniquesthat enable the study of multiplex ties in strategyresearch.

Extensions of ERGM methodology

ERGMs are primarily used with cross-sectionaldata and do not model longitudinal effects in a man-ner directly analogous to conventional panel regres-sion techniques. However, endogenous structuralprocesses can still be examined and demonstratedover time using ERGMs with cross-sectionaldata (Lusher et al., 2013). For example, to detectwhether homophily has an influence on the net-work, researchers can observe the network atdifferent points in time and observe whether tieswere being formed among actors sharing similarcharacteristics. As a result, analysis using ERGMswith cross-sectional observations still offers impor-tant insights regarding the effect of homophily onthe formation of the given network. Nonetheless,networks evolve and are subject to change, andmore insight will be gained from longitudinal

network data. Recent developments have creatednew opportunities for longitudinal analysis oforganizational networks using newer ERGMtechniques. For example, longitudinal ERGMsincorporate parameters for dynamic change, focus-ing on network ties (Snijders and Koskinen, 2013).This approach has been demonstrated in the studyof changes in friendship networks (Igarashi, 2013)and could be meaningfully applied to a varietyof time-based network phenomena in strategy,such as the creation and dissolution of allianceties or changes in board interlocks. Note thatwhile ERGMs are primarily tie-oriented models,stochastic actor-oriented models (SAOM) focus onactor characteristics in network dynamics (Snijders,2001; Snijders and van Duijn, 1997). Dependingon the research questions explored, SAOM may bebetter suited than a tie-based approach for studiesfocused on actor-driven theory and social processes(Lusher et al., 2013).

Many interesting questions in strategy researchinvolve firms’ simultaneous participation in multi-ple relational networks, connecting them to externalorganizations through different types of ties. ERGMtechniques have recently been extended to addressthe dynamics of such multiplex ties (Wang, 2013).This allows the exploration of social processesunique to multiplex networks, including theco-occurrence of multiplex ties, reciprocity acrossdifferent types of ties, and entrainment, in which thepresence of one connection leads to the formationof a different type of tie. Zhao and Rank (2013)illustrate the capabilities of multiplex ERGM meth-ods in an organizational setting, studying networksof advice and employee satisfaction within bankbranches. They find evidence of cross-networkentrainment and reciprocity in these relation-ships, processes that could not be tested throughconventional network analysis methodologies. Theoccurrence of multiplex ties is quite common instrategy network research, given that firms may belinked through alliances, board interlocks, tradeassociations, or other types of concurrent ties.Recent work in strategy has begun to exploresuch concurrent network effects (Ranganathan andRosenkopf, 2014; Shipilov et al., 2014; Wang et al.,2014). Multiplex ERGM techniques can enhancethis stream of work, providing a sound methodologyfor capturing the influence of cross-network rela-tionships and offering a more realistic understand-ing of the many linkages that may form betweenorganizations.



Another potentially useful extension is multilevelERGMs, which allows the simultaneous examina-tion of networks among individuals at one level,organizations at another level, and cross-level net-works between the organizations and individuals.This methodology can be particularly useful if onemay be interested in how interdependencies amongdifferent levels of networks influence network for-mation. For example, Wang et al. (2013) examineda collaboration network of French cancer scien-tists and their affiliations with research laboratoriesusing multilevel ERGMs, demonstrating how mod-eling of each network at the level of the researcher,lab, and ties among researchers and labs providesa more comprehensive understanding of networkformation.

Another model closely related to ERGMs isthe Autologistic Actor Attribute Model (ALAAM)(Robins, Pattison, and Elliott, 2001). This techniqueis designed to model behaviors of individuals as afunction of an underlying network structure that istreated as exogenous. Although it is a social influ-ence model that focuses on the attributes of nodes,whereas ERGMs are a social selection model fornetwork structure, ALAAM follows similar logic tothat of ERGMs. Further development in these andrelated techniques will permit researchers to betterunderstand network structure and its influence of thepractices and characteristics of network members(Daraganova and Pattison, 2013) in areas such asthe diffusion and contagion of firm actions and prac-tices in strategy research (e.g., Davis, 1991; Strangand Soule, 1998).

In conclusion, ERGMs represent an importanttechnique that will allow strategy researchers toempirically examine a wider host of phenom-ena that have heretofore been inaccessible usingconventional methodological techniques. As theconnectedness among individuals, organizations,and societies continues to increase, a better under-standing of how network structures emerge is crit-ical to our knowledge of network mechanismsand outcomes. ERGMs allow scholars to buildon the considerable foundation of existing net-work research while advancing our understandingof networks even further. Our discussion of theuse of ERGMs demonstrates how strategy researchfocused on the emergence of networks can be moreappropriately examined using ERGMs. We hope tostimulate more interest in ERGMs among strategyscholars and help to realize the promise of ERGMs

to advance our understanding of the genesis of orga-nizational networks.

ACKNOWLEDGEMENTS

We are grateful to David Gomulya, Steven M.Goodreau, Dennis Park, Miruna Petrescu-Prahova,Kevin Steensma, Dan Wang, and Mike Withersfor their helpful comments and feedback on themanuscript.

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SUPPORTING INFORMATION

Additional supporting information may be foundin the online version of this article:

Table S1. Research using ERGMs in organizational,nonstrategy researchTable S2. Prior strategy research on network forma-tion and possible extensions using ERGMs


understanding network formation in strategy research ... · strategy research: exponential random...

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