network closure or structural hole? the conditioning

Network Closure orStructural Hole? TheConditioning Effects ofNetwork-Level SocialCapital on InnovationPerformanceJustin TanHongjuan ZhangLiang Wang

This study contributes to the bonding–bridging debate in the social capital literature byexamining the conditioning effects of collective social capital. Data generated from simu-lation reveals that network density, a measure of network-level social capital, negativelymoderates the impacts of firm-level social capitals, measured separately by degree centralityand structural hole, on a firm’s innovation performance. Specifically, in low-density net-works, degree centrality and structural holes are complementary at enhancing innovationperformance. In high-density networks, the positive impact of degree centrality weakens andstructural holes turn out to be detrimental. The findings not only advance our understandingof the cross-level dynamics of social capital, but also provide a possible explanation for themixed empirical results found in previous studies.

Introduction

Social capital, a set of resources embedded in relationships, results from holdingcertain locations in social structure (Bourdieu & Wacquant, 1992; Burt, 1992, 2000;Loury, 1977). As the social capital theory suggests that better-connected individuals andorganizations tend to perform better, it is critical to determine what it means to be betterconnected (Burt). What intrigues entrepreneurship researchers is if and how positions insocial structure contributes more to new venture creation and/or innovation performance(De Carolis, Litzky, & Eddleston, 2009; Maurer & Ebers, 2006; Watson, 2007). Theliterature has highlighted network closure and structural holes as the divergent mecha-nisms underlying such advantageous locations in a social network. On one hand, as

Please send correspondence to: Hongjuan Zhang, tel.: +86-137-5233-9269; e-mail: [email protected].

PTE &

1042-2587© 2014 Baylor University

1March, 2014DOI: 10.1111/etap.12102September, 2015 1189

DOI: 10.1111/etap.12102

1042-2587VC 2014 Baylor University

cohesive social ties facilitate trust and cooperation, a more central location in a socialnetwork leads to more bonding relationships and thus more social capital (Coleman, 1988,1990). On the other hand, structural holes theory (Burt, 1997) posits that social capitalresults from information control and brokerage opportunities, available for individualswho hold a network bridge that spans otherwise disconnected groups. Parallel to suchcontrasting conceptual views, empirical evidences of the above debates are contradictory.For example, Xiao and Tsui (2007) found negative impacts of structural holes on indi-vidual performance, and Gargiulo and Benassi (2000) found detrimental effects of cohe-sive ties on cooperation.

As a reconciliation effort, Burt (2000) argued that whether social capital is more afunction of bridging than bonding depends on the context. This contingency view hasreceived growing empirical support and some conditioning factors have been investigated,including industry (Rowley, Behrens, & Krackhardt, 2000), institutional environment(Batjargal, 2010; Martinez & Aldrich, 2011), network objectives (Ahuja, 2000a), andtiming (Hite & Hesterly, 2001; Slotte-Kock & Coviello, 2010; Soda, Usai, & Zaheer,2004).

Despite these advancements, however, the contingency view of the “bonding vs.bridging” debate has not yet achieved a clear consensus over what and how contingencyfactors matter. A gap remains in the literature: If both the bonding and bridging argumentsare valid, depending on context, then under which conditions should they be complemen-tary or otherwise? As such a grand goal is beyond the scope of a single study, this paperattempts to incorporate collective social capital as a fundamental contingency factor intothe literature.

Social capital is often seen as an individual property, i.e., the sum of resources thataccrue to an individual entity (Bourdieu & Wacquant, 1992). In addition, social capital canbe viewed as a collective property (Ibarra, Kilduff, & Tsai, 2005; Shaw, Duffy, Johnson,& Lockhart, 2005). Adler and Kwon (2002, p. 19) referred to collective social capital as“a bonding form” of social capital comprising “internal ties within collectivities.” Fromthis perspective, social capital is collectively created and shared by all members in anetwork (Burt, 1992; Kwon & Arenius, 2010; Putnam, Leonardi, & Nanetti, 1993). Givensocial capital’s both individual and collective natures, however, it is surprising that theexisting literatures have overlooked the collective aspect of social capital. Except for a fewcross-level studies (Bhagavatula, Elfring, van Tilburg, & van de Bunt, 2010; Gilsing,Nooteboom, Vanhaverbeke, Duysters, & van den Oord, 2008; McEvily & Zaheer, 1999),most empirical studies often measure social capital as an individual entity’s positionwithin a social network, or the structure of its immediate alliances, without integrating thewhole network into analysis (Oh, Labianca, & Chung, 2006). As such, the investigation ofindividual social capital overlooks the possibility that the empirical contexts significantlydiffer from each other in terms of collective social capital at a higher level.

This paper investigates the impact of social capital on firms’ innovation performancewith a cross-level framework. We argue that firms’ innovation performance is not onlysubject to firm-level social capital, but also dependent upon social capital at the networklevel (Gulati, 1998). Based on simulation data, we examine how network density at thenetwork level moderates the impacts of a firm’s degree centrality and structural holes onits innovation performance. We find that degree centrality and structural holes are comple-mentary at enhancing innovation performance in low-density networks. In high-densitynetworks, however, the positive impact of degree centrality is weakened and structuralholes appears to have a negative impact. These findings clearly demonstrate the impor-tance of understanding the conditioning effects of collective social capital on how firmscan leverage individual social capital to obtain innovativeness.

2 ENTREPRENEURSHIP THEORY and PRACTICE1190 ENTREPRENEURSHIP THEORY and PRACTICE

Theory and Hypotheses

Social capital, a potential advantage (e.g., resources, information, and knowledge)that results from social structure (Bourdieu & Wacquant, 1992, p. 119), can improve theefficiency of individuals or the society by facilitating coordination (Putnam et al., 1993,p. 167). Burt (2000) proposed that the structure of the network where individuals ororganizations are embedded represents social capital, as it affects both the flow of infor-mation and what network members can do with it. In particular, inter-firm relationshipsfunction as “pipelines” through which information and knowledge flow between firms(Owen-Smith & Powell, 2004). Recently, Capaldo (2007) proposed that adoption of socialnetwork theory, cross-level analysis in particular, is essential for social capital researchersbecause their research questions usually lie at the intersection between different levels.Klein, Dansereau, and Hall (1994) and Rousseau (1985) proposed that multilevel theorywas needed to investigate how factors at one level affect the outcomes at another level.Following the call for the cross-level analysis of social capital, our study acknowledgesthe cross-level nature of social capital and incorporates two levels of analysis: the firm-level and network-level social capital.

In line with other studies (Davidsson & Honig, 2003; Mueller, 2006), our analysisacknowledges the importance of access to social capital for firms. Much research hasbeen done on the relationship between firms’ social capital and innovation performancethat has proposed that social capital can increase organizational performance (Burt,1992). Firms’ social capital essentially consists of the resources individuals obtain fromknowing others, being part of a network with them, or merely being known to them andhaving a good reputation (Nahapiet & Ghoshal, 1998). As proposed by Aarstad,Haugland, and Greve (2010, pp. 1003–1004), “Any inter-firm network has an asym-metrical distribution of individual social capital; some are rich in social capital, whereasothers have less.”

At the individual level, network structure characteristics have often been usedto capture social capital at the firm level (e.g., Burt, 1992, p. 45; 2004; Uzzi, 1996).It has been found that the amount of social capital a firm has depends on its allianceswith others (Granovetter, 1973) and position in the cooperation network (Walker,Kogut, & Shan, 1997). Following previous studies (Burt, 1992, 2004; Uzzi, 1996),we use network centrality and structural holes to operationalize as firm-level socialcapital.

At the collective level, network density has been often used to measure collectivesocial capital (Burt, 2000; Coleman, 1988). Collective social capital, by definition, isavailable to all members within a network. For example, Oh et al. (2006) define groupsocial capital as group members’ social relationships within the social structure of thegroup itself, as well as in the broader structure of the organization. From this perspective,social capital is collectively created and shared by all members in the network and canaffect the entire network as a whole. In this paper, we define collective social capital asthe resources made available to all individuals via social linkages within the collectivity.Following previous studies (e.g., Burt; Coleman), we use network density to measurecollective social capital.

In the following parts of the paper, we propose hypotheses on the relationship betweenfirm-level social capital and firms’ innovation performance, and the moderating effects ofnetwork-level social capital. We start from the often tested theoretical hypotheses of thedirect relationship between firm-level social capital and firms’ innovation performance.We then go deeper into the nature of social capital by extending it into network level ofanalysis and investigate cross-level interactions.

3March, 2014September, 2015 1191

Centrality and Innovation Performance

The Main Effect. The key proposition in the social capital literature is that networks ofrelationships constitute, or lead to, resources that can be used for the good of individuals.Shan, Walker, and Kogut (1994) found that the number of collaborative relationships waspositively related to a firm’s innovation performance. Aldrich and Fiol (1994) and Ahuja(2000b) stated that firms’ relationships with others are conduits of information, and theyestablish a pattern of obligations and expectations that are based on norms of reciprocity andequity (Koka & Prescott, 2002). The more relationships a firm has with others, the morecentral it is in the collaborative network. A firm holding a central network position canachieve higher innovation performance by not relying on mediators for access to diversifiedinformation (Burt, 2004; Powell, Koput, & Smith-Doerr, 1996; Powell, White, Koput, &Owen-Smith, 2005). As Ibarra (1993) argued, a high network centrality implies a highdegree of access over valued resources. A more central position in a social network canprovide the ego with information (Floyd & Wooldridge, 1999), status, and legitimacy (Burt,1987; Rogers, 2003). It can also reduce transaction costs between organizations, notablysearch and information costs, bargaining and decision costs, policing and enforcement costs(Maskell, 2000). It also provides firms with access to markets, ideas, information, advice,and business opportunities (Gulati, Nohria, & Zaheer, 2000; Hoang & Antoncic, 2003).Following the existing literature, we propose that the higher centrality the firm maintains inthe inter-firm network, the higher innovation performance it achieves.

The Moderating Effect. A central position in a network can bring more information andresources to the ego, which is essential to its innovation performance. These benefits areparticularly important in an inter-organizational network where network members aresparsely connected, i.e., a network with relatively low network density. In such a network,network centrality is highly unevenly distributed among network members. In otherwords, while a few firms hold relatively central positions in the network, many firms arenot well connected with other members in the network. Comparing with these looselyconnected network members, a firm with a high degree of network centrality is muchbetter positioned to benefit from information flow and to access resources in the network.In contrast, in a network with high-network density, network members are relativelyequally connected with each other, and they, on average, are actively involved in collabo-ration and interaction. In such a network, network centrality, as an indicator of socialcapital, is relatively evenly distributed among network members. Since network membersare relatively evenly endowed with social capital and much of the information andresources are accessible by most network members, a high degree of network centralitycannot significantly benefit the ego. As a result, benefits from occupying central positionsin a dense network would not be as effective as in a sparse network. Thus, we predict that:

Hypothesis 1: Network density negatively moderates the positive relationshipbetween a firm’s network centrality and its innovation performance such that the highernetwork density, the weaker positive impact will network centrality have on innovationperformance.

Structural Holes and Innovation Performance

The Main Effect. A structural hole is a gap between disconnected members in a socialnetwork. The structural hole theory (Burt, 1992, 1997, 2000) argues that the advantages of


social capital stem from the brokerage opportunities which result from bridging dis-connected members. The key underlying mechanism that determines whether a social tiewill provide such brokerage opportunities is the extent to which the tie spans a structuralhole (Burt). By holding a structural hole, the broker in a network gains two advantages:information and control (Hansen, 1999; Xiao & Tsui, 2007). On the one hand, social tiesbridging disconnected groups provide individuals the access to a broader array of ideas,non-redundant information, and opportunities (Granovetter, 1973). On the other hand, thebroker can control information flow to serve its own interest because bridges in a networkare critical in advancing information flows (Burt), and structural holes give an individuala “disproportionate say in whose interests are served” (Burt, 2000, p. 354).

Applying the structural hole theory to the firm-level management research, theempirical studies have confirmed that structural holes provide firms and organizationsaccess to new information (Beckman, Haunschild, & Phillips, 2004) and non-redundantresources (Arya & Lin, 2007). A bridging position provides a firm diversified informationand opportunities inherent in the holes and can help a firm better leverage its internalstrength and utilize external resources (Baum & Ingram, 2002; Yang, Lin, & Lin, 2010),so as to enhance innovation performance. Additionally, firms can derive benefits from thenetwork by arbitraging the resource and information flow between two otherwise discon-nected actors in the network (Burt, 1992; Shipilov & Li, 2008). A firm can also betterexploit gaps in the network and control information flow to play one network member offthe other (Yang et al., 2010).

These empirical evidences suggest that structural holes in an inter-firm networklikely will positively affect a firm’s innovation performance. However, as we will discussbelow, the impacts will be conditioned by collective social capital at the network level,and depending on context, structural holes can have detrimental impacts on innovationperformance as well.

The Moderating Effect. The structural hole theory emphasizes the brokerage opportuni-ties within a social network, and posits that a bridging position can bring the ego diverseand non-redundant information, as well as control of information flow (Gargiulo &Benassi, 2000). As such, it is critical to understand under which conditions these advan-tages will be more pronounced.

On one hand, the information benefits from spanning structural holes will diminishwhen a network becomes too dense, or in other words, when collective social capitalsbecome too high. Having access to diverse information is essential for a network member,particularly when the information is not widely available to all other network members.Firms holding these bridging positions in a sparsely connected network have moreexclusive access to diverse information, and thus are in a better position for innovation. Incontrast, a dense network consists of members who are better connected with each other.In such a network, firms are relatively well connected with each other. Since mostfirms are directly or indirectly connected, interaction among these well-linked networkmembers increases the probability that firms within the network have access to the sameinformation. As much of the information in dense networks is likely redundant andavailable to other network members, firms spanning structural holes have only limitedinformation advantages.

On the other hand, the control benefits from spanning structural holes can turn into adisadvantage in dense networks. Such a detrimental effect of structural holes will rise upwhen the control behavior of a broker gets sanctioned. As Burt (1992) noted, the controlbehavior of a broker, i.e., playing the peers against one another, erodes the value of socialcapital of the peers. Furthermore, structural holes in a network weaken communication


and coordination among network members, and thus dampen the whole network’s abilityto take advantage of opportunities beyond the network (Burt, 2000). Therefore, when amember realizes the control benefits of structural holes by manipulating information flow,the advantage enjoyed by the individual member comes at the expense of other membersand sometimes the entire network as a whole.

Such a controlling manipulation for self-interest is not likely to be sanctioned in asparsely connected network, which usually lacks strong norms, collective trust, peerpressure and governance structure. In other words, when a network is short of collectivesocial capital, the network likely does not have the necessary mechanisms, either volun-tary or mandatory, to sanction wrongdoers and ensure the group’s interests. In contrast,in a cohesive network with high density, the control behavior and the manipulation of abroker are more likely to be discovered by other members because they are betterconnected than in a sparsely connected network. Additionally, the malpractice of a broker,once discovered, is more likely to receive sanction in a high-density network, which isoften associated with reciprocity, trust, obligations, and sanction mechanisms. Forexample, Xiao and Tsui (2007) found that structural holes are detrimental to the careerperformance of employees in the collectivistic culture of China, where social capital ismore a function of network closure rather than structural holes. In their words, “spanningstructural holes, as a Chinese saying has it, is like standing on two boats, which is oneof the most socially disparaged behaviors and subject to heavy social sanctions” (Xiao &Tsui, p. 5). Applying the same logic to firm-level innovation performance, we proposedthat:

Hypothesis 2: Network density negatively moderates the relationship between afirm’s possession of structural holes in a network and its innovation performance suchthat structural holes affect innovation performance positively when network density islow, but negatively when network density is high.

Research Design and Simulation

We used data generated by computer simulation to test the hypotheses for the follow-ing reasons. First, simulation allows researchers to model complex phenomena. It hasbeen increasingly adopted as a methodological approach for theory development inthe literature (e.g., Adner, 2002; Lant & Mezias, 1990; Repenning, 2002; Rivkin &Siggelkow, 2003; Zott, 2003). In particular, simulation has been advocated as a powerfulmethod to study strategic alliances and inter-firm networks, as it allows researchers tomodel firm properties, behaviors, and outcomes in a complete network (Lin, Yang, &Demirkan, 2007, p. 1652). Second, simulation can be used for theory development whensimple theory exists (Rivkin, 2000; Rodolph & Repenning, 2002), or when researchershave basic and limited understanding of the phenomenon (Davis, Eisenhardt, & Bingham,2007; Rivkin). This applies to our study because the cross-level mechanism of socialcapital is under-theorized, although much research has been done on social capital at theindividual level. Third, more importantly, simulation is useful when traditional data-collection methods do not facilitate empirical test of certain phenomena (Zott).To empirically test the cross-level mechanisms (i.e., how collective social capital at thenetwork level interacts with individual social capital at the firm level), it is necessary tocollect empirical data covering a sufficient number of inter-firm networks. This presentsan empirical challenge, because only a few existing databases consistently track alliancesand the sample size of networks is not big enough for statistical testing. For example,


Rosenkopf and Schilling (2007) used Thomson’s SDC database to analyze networkstructure across 32 industries, but the small sample does not allow them to statistically testtheir propositions. Additionally, simulation enables experimentation across a wide rangeof conditions by modifying the programming code (Bruderer & Singh, 1996; Zott). Wecan thus simulate different industries with different network characteristics to generatedata for investigation.

Simulation Model

The development of an inter-firm network is a dynamic process through which firmscontinuously make strategic decisions and interact with one another (Courdier, Guerrin,Andriamasinoro, & Paillat, 2002). Simulation models of network evolution therefore haveto consist of heterogeneous agents (i.e., firms for an inter-firm network) that have adaptivecapability and are able to take adaptive actions accordingly (Volberda & Lewin, 2003).We use simulation based on multi-agents (each agent represents one firm), who makestrategic decisions to maximize their performance according to their own properties andthe surrounding context. The simulation model is designed with the following features.First, firms are active and can make decisions on their own, i.e., changing their outgoingalliances at will. Second, the simulation model incorporates the evolution process ofinter-firm network and feedback loops. The output at each stage is the input of the nextstage, and the current state of the network determines probabilistically its future evolution.Third, a firm can enter or exit the inter-firm network by building or ending allianceswith the other firms, depending on whether the alliance contributes to its performance(Barabasi & Albert, 1999; Jackson & Rogers, 2007).

Modeling Performance Landscape. Conceptualizing firms as agents that can make deci-sions on their activities, we assume that a firm has to make decisions on differentactivities, i.e., building new alliances, strengthening an existing alliance, weakening anexisting alliance, relieving an existing alliance, and exiting the network. It is assumed thatfirms have to choose only one activity at each round. A firm calculates its performanceresulting from taking different actions, and the calculation continues until it takes anoption to maximize performance (For details, see the Appendix).

Feedback Loops. The simulation process is designed to start at a certain condition,including firms (agents), knowledge capital possessed by each firm, inter-firm alliances,and development of the inter-firm network. Then the firms experience as many as Mrounds of interaction, and at each round firms take turns in making decisions. The orderof firms’ decision making is determined by the knowledge capital they possessed at eachstage. A firm takes the actions that can increase its performance, and meanwhile, a firm’sactions not only directly affect itself but also the development of the inter-firm networkand decision making of other firms. When firms make decisions in the next round, theywill re-analyze the renewed inter-firm network conditions and rectify their recognition ofthe industry environment.

Firms’ Entry and Exit Strategies. Given the fact that firms can enter and exit a networkduring network evolution, it is surprising to find that such an entry/exit mechanism hasoften been overlooked in most previous studies (Lin et al., 2007; Rosenkopf & Tushman,1998). To make the simulation model as close as possible to reality, we incorporated firm’sentry and exit in the simulation model. During the evolution process of each network inour simulation model, at each round there is a certain amount of potential entrants which


enter the network by building alliances with the incumbents. If firms’ industrial status (fordefinition, see the Appendix) is lower than a certain threshold level, it will take the actionof relieving existing alliances and exiting the network.

Based on the above assumptions, we build a simulation model with the programm-ing language Java (see details in the Appendix). The simulation results of each stage werecompiled into a dataset containing each firm’s knowledge capital, strategic alliances andperformance. We also incorporate the time-lag between network characteristics and firms’innovation performance; firm-level actions at time T collectively shape the networkcharacteristics and individual firms’ innovation performance at time T + 1.

Dependent Variable

Innovation Performance. Firms take actions of cooperation in the simulation model, tomaximize their performance, which was affected by its knowledge capital, network status,and prospects of the technological standardization (for details, see the Appendix). Wheneach firm enters the inter-firm network, its knowledge capital was randomly set. Aftertaking specific actions, a firm’s knowledge capital changes. We define Innovation Per-formance as the change of a firm’s knowledge capital (i.e., knowledge capital finallyreported each round minus original knowledge capital and then divided by its originalknowledge capital).

Independent Variables

Firm-level social capital is measured by Degree Centrality (Ahuja, 2000b) andStructural Hole (Burt, 1992; Xiao & Tsui, 2007). UCINET VI was used to calculate thetwo variables (Borgatti, Everett, & Freeman, 2002).

Degree Centrality is the number of alliances a firm has with its partners. The degreecentrality measure is a well-adopted measure and is widely used in the existing studies offirms’ alliance activity and performance (Ahuja, 2000a; Mintz & Schwartz, 1985; Powellet al., 1996).

Structural Holes was first proposed by Burt (1992) and measured by “effective size,”“efficiency,” “constraint,” and “hierarchy,” among which “constraint” is the most impor-tant. We choose “constraint” to measure structural holes (Yang et al., 2010). Networkconstraint is an index that measures the extent to which a network member’s contacts areredundant (Burt). The higher an actor’s constraint value, the fewer structural holes exist inits network. Since constraint has a range between 0 and 1, following Xiao and Tsui (2007),we use one constraint to directly measure the number of structural holes. We multipliedthe scores by 10 to facilitate the discussion of the results (Reagan & Zuckerman, 2001).

Network-level social capital is measured by Network Density, which has been used inexisting literature to measure the social capital of the entire network (Abrahamson &Rosenkopf, 1997). We calculate a network’s Network Density as the average frequency ofcommunication among the firms in the inter-firm network. The higher density a network,the more it resembles a clique in which all members communicate and interact with eachother. It was calculated with UCINET VI as follows, where Nij is the number of links inthe network, N is the number of firms in it, and N(N − 1)/2 is the maximum number oflinks that can be formed in the network.

DensityN

N N

ij=∗

−2

1( )


Control Variables

Industry represents the different activities a firm is engaged in along the value chainof an industrial network. Assuming that almost any industrial network is comprised ofdifferent firms specializing in certain part of the value chain, we categorize firms into fiveindustries along the value chain. Firm Size is the knowledge capital possessed by eachfirm when it entered the inter-firm network, and it is randomly set. Network Size is thenumber of firms in an inter-firm network.

Statistical Approach

Given the cross-level level nature of our theoretical framework, i.e., dependent vari-able at firm level (level 1) and predictors at both the firm level (level 1) and the networklevel (level 2), we used the hierarchical linear regression models (HLM) (Bryk &Raudenbush, 1992) to test the hypotheses. The network-level variable is used to predictthe intercept (main effect model) and slope (cross-level interaction) relating to firmlevel (Yu, Yu, & Yu, 2013). HLM computes an empirical Bayes estimate of the level 1intercepts and slopes for each inter-firm network and offers the best estimate of the level1 coefficient for a particular network. In addition, HLM uses a generalized least squares(GLS) estimate for level 2 parameters and thereby provides a weighted level 2 regression(Wu, Su, & Lee, 2008).

We grand-mean centered firm-level (level 1) variables. This approach facilitates theinterpretation of the HLM results. It ensures that the firm-level effects are controlled forduring the test of the effects of the network-level variables, and controls multicollinearityin network-level estimation by reducing the correlation between the network-levelintercept and slope estimates (Liao & Chuang, 2007). Considering the potential confound-ing effects of using grand-mean centering in cross-level interactions, we also used group-mean centering for firm-level predictors and the results were consistent (Hofmann &Gavin, 1998; Zatzick & Iverson, 2011).

Results

Table 1 shows the descriptive statistics and the correlation results variables used inthis study. We attach network-level indicators to each firm to calculate correlation coef-ficients both within and across levels of analysis.

Table 2 presents the regression models. We followed the procedure of HLM analysisoutlined by Bryk and Raudenbush (1992). First, we estimated a null model in Model 1that had no predictors at either firm level or network level to partition the firm innovationperformance variance into within- and between-networks components. The between-network variance of firms’ innovation performance was 15.33. The within-network varia-tion of firms’ differences is 100.85. The intra-class correlation for firms’ innovationperformance was 13.20% (15.33/[15.33 + 100.85]), which shows that 13.19% of thevariation in firms’ innovation performance is derived from between-network variation,whereas 86.80% (100.854/[15.33 + 100.85]) is derived from within-network variation (Yuet al., 2013). This indicates the cross-level analysis framework and use of hierarchicallinear modeling is necessary (Shin, Kim, Lee, & Bian, 2012).

Second, we specified a random coefficient regression model in Model 2, where weadded firm-level control variables and predictors, to examine the main effects of DegreeCentrality and Structural Hole on a firm’s Innovation Performance.


Tab

le1

Des

crip

tive

Sta

tist

ics

and

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Corr

elat

ions

Var

iable

Mea

nS

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12

34

56

79

10

Inn

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ion

per

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ance

8.8

91

0.7

8

Fir

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ze1

.57

0.6

1.1

7*

*

Ind

ust

ry1

0.0

10

.08

.01

.27

**

Ind

ust

ry2

0.2

50

.43

−.0

5*

*.0

0−.

05

**

Ind

ust

ry3

0.2

50

.44

−.0

4*

*−.

01

−.0

5*

*−.

34

**

Ind

ust

ry4

0.2

40

.43

−.0

3*

.00

−.0

5*

*−.

33

**

−.3

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Fir

m-l

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deg

ree

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tral

ity

4.3

76

.39

.38

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.28

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06

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57

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Tab

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Det

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Per

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Lev

elan

dvar

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Model

1M

odel

2M

odel

3M

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4b

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(13

.78

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)9

.99

(11

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)3

9.7

3*

*(1

0.3

9*

*)

28

.66

*(1

0.9

5*

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msi

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.87

*(1

.64

**

)0

.87

**

(1.5

6*

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0.8

6*

*(1

.64

**

)0

.87

**

(1.6

6*

*)

Ind

ust

ry1

−16

.03

**

(23

2.3

0*

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Third, we estimated an intercepts-as-outcomes model to assess and control forthe main effects of the network-level predictor, i.e., Network Size and Network Density,in Model 3 by regressing the intercept estimates obtained from firm level (level 1) asoutcome variables.

Fourth, we estimate slope-as-outcome model to regress the slope estimates obtainedfrom firm level on the network-level predictor to examine cross-level interaction effects inModel 4a and Model 4b. To assess the moderating effect of network density on firms’innovation performance, we incorporate two levels in Model 4a and Model 4b. The level1 model estimated the relationship between firms’ Innovation Performance and firm-levelvariables of Degree Centrality and Structural Hole (including the control variables FirmSize and Industry). The level 2 model is a slope-as-outcome model, which addresses theissue of whether the collective social capital (Network Density) moderates the relation-ships between the firm-level predictors and firms’ Innovation Performance (Hirst,Knippenberg, Chen, & Sacramento, 2011; Parboteeah & Cullen, 2003). Furthermore, weinclude Network-level Degree Centrality and its interaction term with Network Density inModel 4a, and Network-level Structural Hole and its interaction term with NetworkDensity in Model 4b, to control for the between-network interactions (Hofmann & Gavin,1998; Liao & Chuang, 2007). Network-level Degree Centrality/Structural Hole is theaverage of the firm-level Degree Centrality/Structural Hole in the network.

In Model 2, we found a significant and positive relationship between the firms’Degree Centrality and Innovation Performance (β = 0.76, p < 0.01), which supportsthe prediction of a positive main effect of Degree Centrality on a firm’s InnovationPerformance. In Model 4a, we find that the coefficient of firm-level Degree Central-ity × Network Density is negative and significant (β = −6.00, p < 0.01). These results areconsistent with hypothesis 1, which posits that the positive effect of Degree Centrality ona firm’s Innovation Performance declines as Network Density increases.

We find a negative (β = −0.62, p < 0.01) relationship between firms’ Structural Holeand Innovation Performance in Model 2, which is opposite to most existing empiricalstudies. However, when incorporating Structural Hole × Network Density in Model 4b,the coefficient of Structural Hole turns to be positive (β = 0.65, p < 0.01), which suggeststhat the marginal effect of Structural Hole on Innovation Performance is positive whenNetwork Density is zero. Additionally, we find that the coefficient of firm-level StructuralHole × Network Density is negative and significant (β = −8.06, p < 0.01) in Model 4b.These results are consistent with hypothesis 2, which posits that the impact of structuralhole on innovation performance is positive in low-density networks but negative inhigh-density network.

While the information in Table 2 is informative, it remains somewhat limited.After all, the results do not indicate whether the marginal impact of degree centralityor structural holes on a firm’s innovation performance is significantly positive or negativeat specific values of network density. To examine the moderating effects, we follow thesuggestion of Brambor, Clark, and Golder (2006) to compute the marginal effects ofboth degree centrality and structural holes on a firm’s innovation performance, as well asstandard errors, at all feasible values of network density.1 We summarize the results bygraphically illustrating the marginal effects across the observed range of the moderatorin Figures 1 and 2. The solid sloping lines in Figures 1 and 2 indicate how the marginaleffects of Degree Centrality and Structural Hole on innovation performance, respectively,change as Network Density increases. One can see whether the effect of Degree Centrality

1. We thank the reviewer for the suggestion.


or Structural Hole is significant by considering the two-tailed 95% confidence intervalsthat are drawn around it. The effect is significant whenever the upper and lower bounds ofthe confidence interval are both above (or below) the zero line.

Figure 1 shows that Degree Centrality has a statistically positive effect on a firm’sInnovation Performance in almost all feasible values of Network Density. Moreover,the positive effect declines as Network Density increases. In denser networks, a centralposition becomes a weaker contributor to innovation performance. Degree Centralitystops having a statistically significant positive effect on a firm’s Innovation Performanceonce Network Density is bigger than about 0.25. These findings support hypothesis 1.

Figure. 1

The Marginal Effect of a Firm’s Degree Centrality on Its Innovation

Performance

Figure 2

The Marginal Effect of a Firm’s Structural Hole on Its Innovation Performance


Figure 2 shows that, when Network Density is smaller than 0.05, Structural Hole hasa statistically positive impact on a firm’s Innovation Performance and this effect becomesweaker as network density increases. However, when Network Density is bigger than 0.1,Structural Hole has a statistically negative impact on a firm’s Innovation Performance andthe magnitude of the detrimental effect increases as Network Density increases. Thesefindings offer support to hypothesis 2.

Discussion and Conclusion

A literature review highlights an ongoing debate on whether social capital is morea function of network closure or structural hole, i.e., the bonding–bridging debate, andthat the conflicting empirical evidence as a result needs a theoretical reconciliation. Themore recent studies have identified a number of contingency factors of the social capitaladvantages, including industry context (Rowley et al., 2000), institutional environment(Batjargal, 2010; Martinez & Aldrich, 2011), network objectives (Ahuja, 2000a), andtiming (e.g., Slotte-Kock & Coviello, 2010). However, a consensus is still missing overwhat or how contingency factors condition the mechanisms through which social capitalcreates advantages. As such, a gap in the literature remains: if both the bonding andbridging arguments are valid, depending on context, then under which conditions shouldthey be complementary or otherwise?

In this study, we examine how collective social capital at the network level moderatesthe relationship between a firm’s individual social capital and its innovation performance.We argue that how individual social capital generates advantages, either in the bondingor the bridging view, is contingent upon collective social capital, which is a more funda-mental contingency factor. As such, we test a cross-level theoretical framework of therelationship between social capital and firm innovation performance. Using computersimulation based on data collected from multiple sources, we find that network density—which is often used to measure network-level social capital—negatively moderates theimpacts of firm-level social capital on a firm’s innovation performance. In particular, inlow-density networks, degree centrality and structural holes are complementary atenhancing innovation performance. In high-density networks, however, the positiveimpact of degree centrality is weakened and structural holes appear to have a negativeimpact. The findings suggest that: (1) in cooperation networks with too many alliances,most of the members are well connected and active, the ones with high centrality cannotget as much superiority as those in sparse networks; (2) dense networks have redundantinformation and resources among members, consequently the ones spanning structuralhole positions cannot receive diversified information as expected; (3) furthermore, struc-tural holes are detrimental to innovation performance in dense networks because thebroker’s control behaviors can be sanctioned.

Contributions

First, our study contributes to the bonding–bridging debate in the social capitalliterature, i.e., whether network closure or structural holes create social capital, by inject-ing collective social capital as a fundamental contingency factor. As we have mentioned,to reconcile the debate, researchers recently have argued that advantages from networkclosure and from structural holes can be complementary in nature (Capaldo, 2007; Greve& Salaff, 2003; Rothaermel & Deeds, 2006). Entrepreneurs therefore can benefit from


holding either a central network position or structural holes, or both, depending on thecontext. Given the cost of creating and maintaining social ties, however, it is critical tounderstand the contingencies. As found in this study, network centrality and structuralholes are indeed complementary to each other when network density is low. In otherwords, in a relatively sparsely connected network, ideally a firm should try to bothposition itself in a more central position in the network and to bridge structural holes. Thecombined benefits will help the firm achieve better innovation performance. In contrast, ina context with high network density, the positive impact of network centrality significantlydrops and structural holes become detrimental. In other words, if all members are verywell connected with each other in a dense network, a more central position does not leadto too much advantages and a broker can be sanctioned for controlling the manipulatinginformation flow. These findings demonstrate that social capital is a function of bothnetwork closure and structural holes in low-density networks, and a function of onlynetwork closure, albeit a weaker one, in high-density networks.

Second, the study sheds light on the dark side of social relationships. While mostexisting studies support the alleged benefits of social capital, it has also been found thatparticular network configurations and networking may have negative consequences.2 Forexample, innovation performance may be dampened due to overembeddedness (Uzzi,1996), the lack of flexibility as a result of being caught in cohesive networks (Gargiulo &Benassi, 2000; Maurer & Ebers, 2006), or the networking overload when too much timeis spent on networking (Steier & Greenwood, 2000). The combination of positive andnegative impacts may result in curvilinear effects (Lechner, Frankenberger, & Floyd,2010). In line with these studies, our study finds that the effects of structural holes oninnovation performance will change from positive to negative when network density risesto too high. The implication is that in the contexts with a high level of collective socialcapital, the bridging social capital at the individual level can be detrimental. This findingis consistent with Xiao and Tsui’s (2007) finding that structural holes have negative effectsin China’s collectivistic culture. As they argued, this is because the collectivistic cultureis likely embedded in a dense network, where network closure rather than structural holesis more likely to create social capital (Xiao & Tsui). Our findings further suggest that thedetrimental effects of structural holes can be positive in low-density networks, and that thebenefits of network centrality are also contingent on network density.

Third and more importantly, our study contributes to the understanding of socialcapital as both an individual and collective property, by applying its central premisesto network-level social capital in addition to firm-level social capital. Although muchresearch has studied the relationship between firms’ social capital and innovation per-formance, most of them tended to focus on one level of analysis (Rothaermel & Hess,2007), mainly on firm-level characteristics, and overlooking factors at and across differentlevels (Yang et al., 2010). As a result, little is known about how social capital at and acrossdifferent levels works in determining firms’ innovation performance. A multilevel theoryis ultimately aimed at providing us with a better understanding of how phenomena at onelevel are linked to those at another and, in so doing, provides us with a richer and morecomplete perspective of innovation (Klein et al., 1994; Rousseau, 1985). Our cross-levelanalysis of social capital and firms’ innovation performance contributes to the literature byadvancing the theory of social capital beyond the traditional single-level studies. Thefindings reveal that simultaneous and explicit consideration of multiple levels of analysis,and “dialogue” between research on different levels, can enrich our explanations of

2. We thank the reviewer for suggesting this issue.


intrinsically cross-level inter-organizational phenomena, with innovation as the dependentvariable. As an important attempt, our study provides support for a multilevel frameworkof social capital and firms’ innovation performance. We hope that future research willcontinue to utilize an integrative multilevel approach in seeking to develop a morecomprehensive understanding of the motivational complexities underlying knowledgesharing, utilization, and ultimately, performance (Quigley, Tesluk, Locke, & Bartol,2007).

Limitation and Future Research

As in many studies of this magnitude, there are a number of limitations in our study.While we extend theories on social capital and innovation with a cross-level theoreticalframework, there are also boundary conditions that can be further studied in futureresearch. For example, our study generally assumes away the dynamics in the externalenvironment (e.g., macroeconomy, etc.) and how these dynamics may shape the evolutionof an inter-firm network. Future research can advance the theory by incorporating the“external” dimension—variables such as environment uncertainty—in similar simulationstudies.

Second, the design of a two-level interaction, i.e., the firm and the network, might beoverly simplistic, as the issue of level of analysis is more complicated than just the twolevels. In particular, a large number of studies have focused on the team or unit level. It isworth investigating how the dynamics found in this study may be complicated by otherlevels.

Our study uses a custom-designed simulation program to generate a longitudinal andcross-level dataset to examine the cross-level interaction. The insights we have generated,however, need to be examined and validated through different research design. We hopeour exploratory effort will inspire future research and provoke future debate, and wepresent this set of evidence from simulation for future verification and falsification.

Appendix: General Algorithm of the Simulation Model

Parameter Descriptions

(1) Parameters of Firm Level

know: The knowledge capital that each firm has.Oknow: Knowledge capital that a firm can get from other directly connected organi-zations.

Oknowknow know conn

knowi i i

i

n

= × ×=∑λ1

1

(λ1 is a constant, n is the number of firms that have built alliances with the focal firm)KnowRes: The total knowledge resources of a firm, including the sum of its ownknowledge capital and those the firm can access from directly connected other firms.


KnowR know Oknowes = × + ×λ λ2 3

(λ2 and λ3 are distinct constants, representing the weighing of each factor)Conn: The strength of inter-firm alliances (integer valued from 1 to 9).Connsum: The sum of strength of a firm’s direct alliances.

Connsum Conni

i

n

==∑

1

(n is the number of alliances that a firm has)FirmRole: The role that a firm plays in the industrial chain, there is total of five differenttypes of organizations in the inter-firm network.Sta: The industrial status of a firm, mainly determined by the strength of a firm’salliances with other firms.

StaConnsum

Connsumj

j

m=

=∑

1

(Connsum is the sum of strength of the focal firm’s direct alliances, m is the number offirms that are of the same FirmRole with the focal firm.)

Pro: The total performance that the firm can get.

P o P e KnowR Sta KnowR PStar ( r , , )es e ( es re)= × × + ×μ λ λ1 4 5

(μ1, λ4, λ5 are constants, and Pre will be explained in “Parameters of Network Level”)Action: R&D investment, building new alliances, strengthening an existing alliance,weakening an existing alliance, relieving an existing alliance, and exiting the network.

(2) Parameters of Network Level

Num: The number of firms in the inter-firm network.Tknow: The total amount of knowledge capital owned by all the firms in the inter-firmnetwork.

Tknow knowi

i

n

==∑

1

Tconnsum: The sum of strength of all the inter-organizational alliances in the inter-firmnetwork.

Tconnsum Connsumi

i

n

==∑

1

(n is the number of alliances in the inter-firm network)Equ: The equilibrium of the industrial chain refers to the extent to which the inter-firmnetwork covers all five different types of firms on the value chain. It is a constant


number if we do not have a complete industrial chain (do not have all five types offirms); if we have a complete industrial chain, it is calculated as follows.

Equtknow i

tknowi

i

=−⎛

⎝⎞⎠ +

=∑

1

11

2

2

5 [ ]

[ ]δ

(δ2, δ3, δ4, and δ5 are constants, tknow is the total amount of knowledge capital owned byfirms of the same type, type i, in the industrial chain.)

Pre: The prospects of the technological standard refers to the extent to which membersvalued the future of technological standardization of the inter-firm network; it wascalculated as follows:

Pre Num Tconnsum Tknow Equ= × × + × ×( )λ λ6 7

(λ6, λ7 are constants)

Experiment Initialization

1. Set the initial conditions of an inter-firm network, including firms, their FirmRole andknow, together with their alliances and Conn of each alliance, and the development ofthe whole inter-firm network (such as the Num, Tknow, and Tconnsum of the inter-firm network).

2. Set the maximum number of rounds for the simulation model: N = 30.

Simulation Process

3. Start round i.4. Determine the number of firms entering into the inter-firm network: six firms each

round.5. Randomly set the FirmRole and know for each new firm.6. Sort the firms according to the amount of know they have.7. The firm with top priority in the queue makes decisions about whether to take actions.

If so, which action to take.8. According to the action taken by the firm, update firms’ knowledge capital (know),

alliances among them, and their status in the network (Sta), and most importantly,prospects of the technological standard (Pre).

9. If all firms have made decisions and taken actions, then go to 10, otherwise, go to 7.

Simulation Output and mechanism

10. At the end of each round, record the know, FirmRole, and exact alliances for eachfirm.

11. If round i is less than N, go to 4, otherwise stop and obtain results.


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Justin Tan is a Professor of Management and the Newmont Chair in Business Strategy in the Schulich Schoolof Business at York University in Canada.

Hongjuan Zhang is an Assistant Professor in the College of Management and Economics at Tianjin Universityin China.

Liang Wang is an Assistant Professor in the School of Management at University of San Francisco in the USA.

This research was in part supported by grants from Social Science and Humanities Research Council ofCanada, the National Natural Science Foundation of China (Grant No.71302097), and Guanghua-CiscoGlobal Leadership Institute. The research was initiated while the first author was the U.S. Fulbright Distin-guished Professor in China. Support from the Fulbright Foundation, the U.S. State Department, and the U.S.Embassy in China are gratefully acknowledged. Comments and suggestions from ETP reviewers are gratefullyacknowledged. We also thank Runhui Lin, John Lin, Kathleen Eisenhardt, and Yin Bai for valuable commentsand assistance. Please send inquiries to Hongjuan Zhang at [email protected].


network closure or structural hole? the conditioning

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