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THE EVOLUTION OF THE BOARD INTERLOCK NETWORK FOLLOWING
SARBANES-OXLEY
Michael Withers
1
Department of Management
Mays Business School
Texas A&M University
College Station, Texas 77843.4221
Email: mwithers@mays.tamu.edu
Ji Youn (Rose) Kim
Department of Management
Gatton College of Business & Economics
University of Kentucky
Lexington, KY 40506
Email: rosejykim@uky.edu
Michael Howard
Department of Management
Mays Business School
Texas A&M University
College Station, Texas 77843.4221
Tel.: (503) 914-7130
Fax: (979) 845-9641
Email: mhoward@mays.tamu.edu
(Corresponding Author)
Keywords: social networks, board interlocks, network formation, institutional effects, corporate
governance
Acknowledgements: We are grateful to Raffaele Corrado, David Schaefer, and Tom Snijders for
their helpful comments and feedback.
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All authors contributed equally in developing this study.
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THE EVOLUTION OF THE BOARD INTERLOCK NETWORK FOLLOWING
SARBANES-OXLEY
ABSTRACT
We examine the impact of the passage of Sarbanes-Oxley (SOX) on the evolution of the board
interlock network for Fortune 300 firms during the 1998-2006 period using a stochastic actor-
oriented model. Placing particular emphasis on director accountability and board independence,
SOX created considerable disparity in demand and supply in the labor market for corporate
directors. We examine whether the regulatory change may have led firms to draw more on
socially embedded processes of board interlock partner selection such as reciprocity, transitivity,
and multiplexity after SOX. We find that after the passage of SOX, a firm’s tendency to
reciprocate board interlock ties has been reinforced. Similarly, firms appear to have relied more
on their existing alliance partners to fill their board seats in the post-SOX period.
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1. INTRODUCTION
Extensive research has argued that director ties among large, established firms result in
the creation and persistence of corporate elites in the U.S. economy (Mills, 1956; Palmer et al.,
1986). These powerful elites act not only to ensure the maintenance of their privileged position
in the economy but also to offer a platform for the diffusion of critical information and new,
valuable managerial practices (Davis, 1991; Haunschild, 1994; Haunschild and Beckman, 1998;
Hernandez et al., 2015). Thus, board interlock ties have important economic consequences for
managers, corporations and shareholders (Martin et al., 2015; Zona et al., in press).
While many outcomes of board interlocks have been established in prior research
(Mizruchi, 1996; Shropshire, 2010), far less attention has been paid to the dynamics of creation
and maintenance of such an important interorganizational network. Only a handful of studies
have examined interlock tie formation or dissolution (e.g., Beckman et al., 2004; Kim et al.,
2016; Koskinen and Edling, 2012; Yue, 2012). These studies show that the selection of a board
interlock partner is driven by a combination of director-, firm- and dyad-specific characteristics
as well as endogenous structural processes. However, other research suggests that exogenous
shocks such as institutional changes in the regulatory or legal environment may also generate
significant changes in firm behaviors (Edelman, 1990; Koka et al., 2006; Lang and Lockhart,
1990; Seierstad and Opsahl, 2011), which may in turn affect the dynamics of the network.
In the context of board interlocks, the Sarbanes-Oxley Act (SOX) represents a profound
regulatory change. Enacted as emergency law in the midst of high profile corporate scandals in
2002, this act is considered to be one of the most important pieces of legislation in the federal
securities laws (Donaldson, 2003). Because SOX was adopted in the context of serious concerns
regarding the actions of directors, auditors, and self-regulatory organizations, it not only imposed
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particular requirements on boards but also changed the expectations of how boards and directors
should behave. Consequently, SOX has been the source of substantive changes in board
composition and membership in individual firms (Linck et al., 2009).
Beyond the boards of individual firms, SOX may also have driven fundamental changes
to the processes of partner selection and, consequently, the evolution of the board interlock
network among firms. Specifically, SOX created specialized demand for directors to be equipped
with specific skills in financial oversight. Also, the mandate required greater responsibility and
effort of individual directors, coupled with nontrivial penalties if they fail to fulfill their duty. As
a result, despite the increase in demand for external board members, the supply has contracted as
firms become less permissive when their executives or directors consider additional board
membership in other firms (Linck et al., 2009). This broadly suggests that the partner selection
process in the board interlock network in the post-SOX era may differ substantially from
selection in the pre-SOX period; however, little is known regarding the details of how SOX
influences board interlock network dynamics.
The goal of our paper is to address this gap in the literature. We propose that the passage
of SOX may have led firms to draw from more socially embedded processes of partner selection
such as reciprocity, transitivity, and multiplexity in the post-SOX period. These network
mechanisms offer specific, unique types of information regarding potential partners - reciprocal
ties reinforce known, existing bonds in the interlock context; alliances provide knowledge of
external partnerships built on a different context of interaction; and transitive ties leverage
information from trusted common third parties – each allowing firms to better find interlock
partners in the reduced pool of corporate directors. We explore the evolutionary dynamics of the
board interlock network using longitudinal network data of Fortune 300 firms during the 1998-
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2006 period. We employ stochastic actor-oriented models (SAOMs) for empirical analysis,
which have been specifically developed for analyzing network change with longitudinal data
(Snijders, 2001, 2005). We find that after the passage of SOX, a firm’s tendency to reciprocate
board interlock ties has been reinforced. Similarly, firms appear to rely more on their existing
alliance partners to fill their board seats in the post-SOX period. While firms generally sought
partners through their indirect network ties during the study period, we find that such a tendency
of triad closure was not necessarily reinforced after SOX.
Our study contributes to research on board interlock networks (Davis et al., 2003; Martin
et al., 2015) by considering the effects of an important exogenous institutional change on the
evolution of interlock ties among firms. We also contribute to the growing research on the
passage of SOX by providing some evidence of the unintended consequences of the law, as firms
made substantial adjustments in response to this profound change in the legal environment
(Coates and Srinivasan, 2014; Linck et al., 2009). Finally, network evolution is an outcome of
complex processes that operate at multiple levels (Ahuja et al., 2012). Stochastic Actor-Oriented
Models (SAOMs) provide a powerful tool to analyze network evolution with longitudinal
network data (Snijders, 2001, 2005; Snijders et al., 2010). Joining a growing body of research
utilizing SAOMs, our work demonstrates the usefulness of this methodology to further advance
organizational network research (Corbo et al., 2016; Howard et al., in press).
2. NETWORK EVOLUTION AND BOARD INTERLOCKS TIES
When a firm invites a director from another firm, a board interlock tie is formed between
the two firms (Mizruchi, 1996). A board interlock plays an important role in managing external
dependences (Pfeffer and Salancik, 1978) and obtaining critical resources, such as information
(Haunschild and Beckman, 1998; Shropshire, 2010) and legitimacy (Galaskiewicz, 1985). Firms
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also utilize board interlocks to help them influence and monitor the operations of their external
partners (Mizruchi, 1996). From this perspective, board interlocks serve as a potential
mechanism to reduce interfirm opportunism by increasing the flow of information between
organizations (Phan et al., 2003). More recently, research shows that board interlocks may also
be used to leak strategic information that firms want to protect (Hernandez et al., 2015).
While extensive research has examined the benefits of these interorganizational
relationships (e.g., Mizruchi, 1996), just a handful of studies have considered the determinants of
board interlock formation. For example, these studies have examined the effects of peer referral
in director selection (Koskinen and Edling, 2012), small world clustering effects in interlock
networks (Robins and Alexander, 2004), prior experience in external interorganizational
relationships (Beckman et al., 2004; Yue, 2012) and the role of common outside affiliations on
interlock network evolution (Gagliolo et al., 2014).
When considering board interlock formation, it is important to note that an interlock
represents an interorganizational tie between two firms (Pennings, 1980); however, the tie is
created by the appointment of an individual to one or both boards (Withers et al., 2012). With
this perspective in mind, the board interlock research traditionally treats the interlock formation
as a firm-level decision (Bazerman and Schoorman, 1983), whereas the director selection
literature has focused more on individual directors and considers the formal process by which
they are identified, screened, nominated, and elected (or appointed) to corporate boards (Withers
et al., 2012). Thus, the board interlock formation process occurs at both levels. For the selecting
firm, it is the board’s nominating committee, representing the firm, that makes the decision on
who to nominate to the board (note that individuals nominated are almost always appointed to
the board). For the individual nominated, they must be willing the serve on the board. However,
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an executive’s home firm would have considerable influence on the boards he or she decides to
join. For example, recently some firms have begun placing limits on the overall number of
boards an executive can serve on at one time (Spencer Staurt, 2016). More explicitly, firms could
decide to form an interlock by sharing board members. Thus, while we recognize the individual-
level drivers that might produce inadvertent interlock formation, our research follows the
tradition of treating board interlocks as a firm-level decision (Bazerman and Schoorman, 1983;
Beckman et al., 2004; Howard et al., 2016; Yue, 2012).
In the board interlock networks, exogenous institutional changes represent forces that
have the potential to explicitly and inadvertently reshape the structure and evolution of the
interfirm networks (Ahuja et al., 2012). For example, industry deregulation increased board
interlocks between competitors in the airline industry (Lang and Lockhart, 1990). In the broader
board composition context, Seierstad and Opsahl (2011) studied exogenous shocks from
legislation, examining how gender representation laws in Norway shaped board membership.
Broad environmental factors may influence firms to seek more board interlocks in order to
manage or shield them from different types of uncertainty (Beckman et al., 2004; Boyd, 1990;
Martin et al., 2015). On the other hand, the need of firms to protect strategic knowledge may also
lead them to dissolve existing ties to prevent involuntary spillovers (Hernandez et al., 2015).
While firm- or dyad-specific characteristics are important drivers of the board interlock network,
recent research finds that endogenous structural processes such as reciprocity and transitivity
play equally important roles in shaping the network structure (Kim et al., 2016). Though less
frequently studied, exogenous institutional change offers a strong impetus for changes in firm
behaviors, impacting the pattern of interorganizational networks (Koka et al., 2006). In the
corporate governance context of board interlocks, the Sarbanes-Oxley (SOX) Act represents a
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seismic change in the institutional environment that may have had a profound impact on the
evolution of board interlock networks (Green, 2005).
2.1 Sarbanes-Oxley and the corporate director labor market
The passage of SOX and the new requirements from the listing exchanges (e.g., NYSE,
NASDAQ) have created major institutional changes in corporate governance (Coates and
Srinivasan, 2014; Green, 2005; Monks and Minow, 2004). As Hoskisson, Castleton, and Withers
(2009, p. 61) explain, “Policies at the macro institution level (i.e., recent legislative and stock
exchange policies) have been enacted to increase board independence.” These changes have
placed more emphasis on director accountability by emphasizing audit committee independence
and overall board independence (Coates and Srinivasan, 2014).
As firms respond to these mandates, board composition has been directly impacted
(Marlin and Geiger, 2011; Valenti, 2008). Specifically, SOX has had a tremendous influence on
both the demand and supply of corporate directors (Dalton and Dalton, 2010; Linck et al., 2009).
On the demand side, the requirement for greater board independence in addition to demands for
specific skills in financial literacy has increased the need for more board interlock ties with other
firms (Linck et al., 2009). On the supply side, however, the potential candidate pool of corporate
directors has contracted. In general, executives have much to gain by sitting on the boards of
other companies, such as prestige and increased social capital (Fahlenbrach et al., 2010; Fich,
2005). However, as the workload and responsibilities for outside directors increase along with
litigation risks of being a director, executives are limited in their availability to take on this
additional work outside their organization (Boivie et al., 2012). Companies are also likely to
limit the number of board seats on which their executives may serve (Green, 2005; Linck et al.,
2009). As a result, the overall supply of potential directors available to serve on boards has
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declined (Dalton and Dalton, 2010) despite the increased demand. Thus, the institutional changes
derived from SOX have impacted the labor market for corporate directors, presenting a particular
challenge for firms in their partner selection process (Withers et al., 2012).
3. DYNAMICS OF THE BOARD INTERLOCK NETWORK AFTER SOX
Given the reduced supply of corporate directors (Linck et al., 2009), firms may look to
their current networks in their efforts to fill board vacancies or to expand the board (Bazerman
and Schoorman, 1983). More directly, as the supply of potential interlocking partners declined
(Dalton and Dalton, 2010; Linck et al., 2009), the uncertainty surrounding interlock partner
selection has increased. To address this challenge, organizations may draw on socially embedded
ties, benefiting from greater knowledge of potential directors and interlock partners (Granovetter,
1985). Established relationships may lead to referrals or other information that help minimize
partner uncertainty and risk in forging new ties (Burt and Knez, 1995). We examine a series of
socially embedded processes that may have helped firms overcome the difficulties of partner
selection in the post-SOX period.
3.1 Reciprocal board interlocks
A reciprocal board interlock occurs when “an employee of firm A sits on firm B's board
and at the same time an employee of firm B sits on firm A's board” (Hallock, 1999, p. 55).
Following this definition, a firm may form a reciprocal board interlock tie when one of its
executives is appointed to the board of its outside director’s home firm. Alternatively, the focal
firm may also create a reciprocal tie by appointing an outside executive to its board from a
company where one of the focal firm’s executives is currently serving as a director.
Reciprocal ties are often suggested to benefit managers, in terms of higher compensation
and other benefits, rather than their shareholders (Fich and White, 2005; Hallock, 1997).
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Moreover, given that information may flow through the single board tie without the need for
reciprocity, reciprocated ties are less desirable in terms of information sharing advantages often
associated with board interlocks (Haunschild and Beckman, 1998). Indeed, research suggests,
“Because it is costly to use up a board slot on a firm to which one is already linked, firms should
refrain from establishing reciprocal board linkages and terminate reciprocal linkages where they
do exist” (Galaskiewicz and Wasserman, 1981, p. 476).
However, reciprocal ties may be an important way for firms to overcome the reduced
pool of potential directors driven by SOX. The contraction in the corporate director labor market
following SOX reduced the availability of potential interlock partners (Linck et al., 2009). Thus,
when seeking to form new board interlock ties, firms may perceive current interlock partners as
viable sources of directors to fill board seats. Existing ties offer clear information regarding the
suitability of the external partner, in the directly relevant context of an established interlock.
Such reciprocal ties strengthen the existing interorganizational relationship (Fich and White,
2005) and may reduce the uncertainty around the selection of an interlock partner (Bazerman and
Schoorman, 1983). From a managerial perspective, such reciprocal ties may not only address the
need for the appointment of an outside director following SOX, but may also allow a focal firm
to avoid the intense monitoring from increased board independence (Hoskisson et al., 2009).
Such reciprocal ties serve as a means of “achieving greater loyalty” between the two firms (Fich
and White, 2005, p. 179), which may help reduce any uncertainty derived from the institutional
change. In this regard, the changes in the institutional context may provide firms with a
particular motivation to form reciprocal ties (Beckman et al., 2004; Gulati, 1995; Podolny,
1994). In sum, in the post-SOX context, firms may be more likely to reciprocate board interlock
ties given the reduced pool of potential new interlock partners and the interorganizational
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advantages that may derive from such partnerships in the changing institutional context.
Following these arguments, we posit:
Hypothesis 1: After the passage of SOX, the tendency of firms to reciprocate board
interlock ties is reinforced.
3.2 Board interlocks from indirect networks
Board interlocks formed from a firm’s indirect network represent “ties between two firms
resulting from a common tie to a third party” (Westphal et al., 2001, p. 728). Unlike
reciprocating ties, selecting partners from indirect ties represents an opportunity for firms to
create linkages to new resources and external contingencies (Haunschild, 1993; Mizruchi, 1996;
Pfeffer and Salancik, 1978). While research has long recognized the use of indirect network ties
in seeking new interlock partners, the linkages to new resources and information may be
particularly important following the institutional and governance changes that accompanied the
passage of SOX. Similar to direct ties, indirect ties generally provide intelligence about potential
board interlock opportunities and decrease uncertainty surrounding the reliability of potential
partners (Coleman, 1988; Van De Ven, 1976). The cost of an optimal search and managers'
bounded rationality also lead firms to choose their board interlock partners within the bounds of
existing social networks (Bazerman and Schoorman, 1983; Simon, 1972).
As previously noted, Sarbanes-Oxley created scarcity in the pool of corporate directors
by formalizing their oversight role and specifying the required skills and qualifications of board
members. Firms face greater challenges in 1) identifying suitable directors, and 2) obtaining
information to ensure their qualifications for occupying this increasingly critical role. When
information through direct ties is not available, firms could leverage information from trusted
common third parties. Thus, a focal firm may perceive the common third party partners of firms
with which it currently has ties as promising potential candidates for new interlocks. Relying on
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indirect network ties may be a particularly salient means to obtain viable interlock partners after
SOX. Thus, we suggest the following:
Hypothesis 2: After the passage of SOX, the tendency of firms to invite directors from
their indirect network is reinforced.
3.3 Board interlocks with alliance partners
Firms may also seek to reinforce other existing interorganizational relationships by
forming board interlock ties with existing alliance partners (Beckman et al., 2004; Gulati and
Westphal, 1999). Beckman and colleagues (2004, p. 263) discuss such reinforcing linkages in
terms of multiplex network ties and suggest that “firms may add relationships of a different type
with an existing partner, e.g., adding an alliance when an officer of that firm is already on the
board.” As another type of direct network, such pre-existing ties provide information on potential
partnership opportunities and breed familiarity between the organizations.
Research finds that firms are more likely to form multiplex ties when there are higher
levels of market-level uncertainty as they tend to choose past exchange partners to deal with the
uncertainty by reinforcing their existing relationships (Beckman et al., 2004). However, research
also finds that the drivers of multiplex ties may have particular temporal boundary conditions
(Howard et al., 2016). The institutional change following the passage of SOX created unique
uncertainty in the environment with the reduced pool of potential directors. To cope with this
uncertainty, firms may perceive their current alliance partners as particularly attractive interlock
partners. Forming an interlock tie with an existing alliance partner reduces the uncertainty
around interlock partner selection as the firms are familiar with one another through their prior
relationships. While the information regarding the potential interlock partner comes from an
entirely different exchange context, it may have considerable value and application to the
interlock decision, compared to the task of firms assessing candidates with whom they are
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completely unfamiliar. In this regard, selecting partners for board interlock ties from existing
alliance partners may be another mechanism to address the challenges of making new board
interlock ties in the reduced pool of potential partners following the passage of the SOX Act.
Therefore, we hypothesize:
Hypothesis 3: After the passage of SOX, the tendency of firms to prefer prior alliance
partners in selecting board interlock partners is reinforced.
4. METHODS
We investigate the influence of SOX on the evolution of board interlock networks using a
sample of the largest service and industrial firms in the U.S. economy listed in the Fortune 300 in
1997. We eliminated 39 privately held and non-US based organizations. We also eliminated 41
firms that went bankrupt, went private or ceased operation as public firms during the study
period to ensure the consistency of financial information in our analysis. This leaves us with a
final sample of 220 firms.
The Sarbanes-Oxley legislation was passed on July 30, 2002. Thus, using 2002 as a
reference point and a three-year window preceding and following the legislation, we constructed
longitudinal board interlock network data during the period of 1998 through 2006. Firms
typically appoint their board members every three years, and a three-year window has been used
in prior research to examine director exit (Boivie et al., 2012). Research also suggests that the
empirical design with a sliding time window is useful in capturing evolutionary dynamics of
networks (Doreian, 1986). Specifically, we constructed the following three matrices to capture
the networks that existed before, during and after the passage of SOX with equal length time
periods: 1) the pre-SOX board interlock network observed during 1998-2000; 2) the board
interlock network observed during 2001-2003; 3) the post-SOX board interlock network during
2004-2006. However, it is important to note that SOX was rapidly adopted in year 2002
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following a series of unexpected corporate scandals, and there is no established rule for the
choice of time window. Thus, in order to test the effects of the exogenous shock represented by
SOX, the board interlock structure at the time of the SOX (i.e. wave 2) may be better captured by
looking at only the year 2002 instead of the period during 2001-2003 that includes the adjacent
years because the latter approach may add unnecessary noise. Thus, we also constructed the
following three networks: 1) the pre-SOX board interlock network observed during 1998-2000;
2) the board interlock network observed at 2002, with the preceding and succeeding years
omitted to closely isolate network structure at the time of treatment; 3) the post-SOX board
interlock network during 2004-2006 (i.e., the pre- and post-SOX networks retain the three year
length, whereas the second network is captured at the event year of 2002). This is essentially a
quasi-experimental design. As will be shown in the Results section, we empirically examine and
find that our results are consistent regardless of the use of specific time window, suggesting that
the network change is likely to be attributed to the passage of SOX. Thus, we discuss our
analysis using the network observed in the year 2002 for the second wave in the remainder of the
paper. Figure 1 captures the time structure we use to construct the three waves of the networks in
our analysis.
Figure 1. SAOM analysis time structure.
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Our observational panels are constructed as binary sociomatrices whose entry on row i
and column j equals 1 if a focal firm i initiates a tie by inviting a director from another firm j to
serve on its board, and 0 otherwise
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. This is a directed graph (Xij ≠Xji).
We rely on the GMI Ratings corporate governance database (formerly the Corporate
Library) to collect data on the board interlocks. This database tracks board membership of
publicly traded US firms. We collect financial data from COMPUSTAT.
4.1 Statistical model
We model the evolution of the network of board interlocks between companies using
stochastic actor-oriented models of network change (SAOMs), implemented through the use of
the Siena package in R (Ripley et al., 2015; Snijders, 2001, 2005; Snijders et al., 2010). This
network methodology is well suited for our analysis of network evolution for several reasons
(Snijders et al., 2010). First, this modeling approach accommodates an interdependent process of
tie formation that is influenced by both actor- and dyad-specific characteristics as well as other
ties in the rest of the network. Second, it allows us to properly account for endogenous structural
effects (e.g., reciprocity, transitivity), which have been shown to be particularly important
drivers of partner selection in board interlocks (Kim et al., 2016). Finally, by taking an actor-
oriented perspective, this methodology is appropriate to examine the effect of an exogenous
shock such as SOX at the broader, aggregate network level as firms adjust their partner selection
behavior while subject to structural constraints. Although it is not possible to directly test
2
While we created firm-by-firm networks, an alternative approach is to create bipartite firm-to-director networks.
By capturing the duality of firms and individual directors, bipartite networks show the number of directors that two
firms share. However, there are challenges associated with creating bipartite director-to-firm networks with stable
membership over time. Some individual directors leave for reasons (e.g. retirement or death) that are irrelevant to a
firm’s motivation to keep them. Other directors may join over time but they may not have firm affiliations. Although
a firm-to-firm network may also experience composition change in terms of joiners or leavers due to acquisition or
bankruptcy, it is more stable than the network involving individual directors. Because we are less interested in
individual directors but more on the change of interorganizational network structure after SOX, we focus on the one
mode network. Research also suggests that conversion of the two mode into one mode is not necessarily less
desirable and structural features of the network can be retained (Everett and Borgatti, 2013).
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causality in SAOMs
3
, they have particular strengths, such as the use of longitudinal network data
and the capability to explicitly model a variety of factors that might have also caused the network
change at different levels (including endogenous structural processes such as reciprocity and
transitivity). These attributes of SAOMs do allow us to rule out other alternative explanations
and improve our capability to infer that the passage of SOX may have triggered firms’ behaviors
and subsequent network change after the event, compared to the pre-SOX period. Below we
provide a brief account of the model; for full description of SAOM techniques, see Snijders
(2001) or Snijders et al. (2010).
While network data are observed at discrete time points, SAOM analysis assumes that the
underlying process of network evolution is an outcome of continuous, gradual changes that
actors make. Using the network first observed as given, the model seeks to capture the change of
the network from the first state to the second observation (i.e., period 1) and similarly from the
second to the third observation (i.e., period 2). Thus, if there are M waves (i.e., observation
moments) of network data, this covers M-1 periods. As shown in Figure 1, there are two periods
to be modeled, as we have three observed networks (pre-SOX, event year and post-SOX). The
model takes an actor-oriented perspective, and tie changes are assumed to have occurred
sequentially. Specifically, at each moment, a focal actor may get a chance to change its outgoing
tie (either creating or terminating a tie) or do nothing (maintain the current status quo). The rate
function in the model is concerned with choosing an actor from the network who makes a
change. Once an actor is chosen, the objective function models how likely it is for the focal actor
to change his or her network in a particular way that will be beneficial for achieving key
3
In general, randomization and good experimental design is required to make solid causal claim. Thus, when
experimentation is not possible, as is the case for most network studies, causality can only be inferred. This
limitation is not unique to SAOMs but rather general with many other statistical methods (Ripley et al., 2015;
Robins, 2015).
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objectives (hence, the name ‘objective function’). The objective function depends on the focal
actor’s personal network as well as those to whom there are direct or indirect ties, and covariates
of all actors in the personal network.
The objective function is described as a linear combination of terms called effects.
𝑓𝑖 (𝛽,𝑥)= ∑ 𝛽𝑘𝑠𝑘𝑖 (𝑥)
𝑘
In the equation above, i refers to a focal firm. The value of the objective function,
𝑓𝑖 (𝛽,𝑥), depends on the state x of the network, and 𝑠𝑘𝑖 (𝑥) are the effects. Each of these effects
describes a factor that may drive the evolution of the network. Some factors are endogenous
structural factors (e.g., reciprocity and transitivity) whereas others are exogenous covariates that
describe the characteristics of the actors in the network (e.g., firm size, performance). The
weights of these effects, 𝛽𝑘, are the parameters to be estimated from the data by a generalized
method of moments.
4.2 Independent variables
Reciprocity effect accounts for the tendency for a firm to send a board interlock tie with
those firms whose executives already occupy a board seat in the focal firm. It is measured by the
number of reciprocated ties of focal firm i. Transitive triplet effect represents triadic closure. It
refers to a firm’s propensity to form a board interlock tie with another firm which shares a
common 3rd party tie. It is defined as the number of transitive patterns in firm i's relations, i.e.
ordered pairs of firms (j,h) to both of which i is tied, while j is also tied to h. Alliance
relationship has been consistently shown as an important form of interorganizational relationship
(e.g., Ahuja, 2000). We create this variable by examining whether sampled firms have alliance
relationships with each other during the time periods of our study. In the Siena model, if there are
M waves (i.e., observation moments) of network data, there are M-1 periods. Thus, for
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specifying a single changing dyadic covariate, an n x n x (M-1) array is needed when n is a
number of actor in a given network. Changing dyadic covariates are assumed to have constant
values from one observation moment to the next. Thus, we created two alliance networks to
capture this changing dyadic covariate; the first one is the alliance network over the pre-SOX
period of 1998-2000
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, aligned with our defined structure for the pre-SOX board interlock
networks. The second network reflects the alliance matrix captured at year 2002. Finally, to
examine the effect of SOX on the three mechanisms of interest (i.e. reciprocity, transitive ties,
and prior alliance relationship), we included the main effect of a post SOX dummy
5
, and the three
interactions of this variable with each of the social process we proposed: post SOX dummy X
reciprocity, post SOX dummy X transitivity, and post SOX dummy X alliance. We use the
approach developed by Lospinoso et al. (2011) in assessing time heterogeneity (i.e. the effect of
SOX in our context).
4.3 Control variables
We address a number of factors influencing interlock formation through controls at the
firm and dyad level. We control for firm size by measuring the number of employees in each
firm. We take the log transformation of this variable to reduce its skewness. We include ROA to
control for firm performance, given that directors of successful firms may be more likely to be
invited for a director seat. We account for the firm’s stock volatility by measuring the
standardized monthly volatility of the focal firm’s stock in the year prior to the network change
(Beckman et al., 2004). We also account for the level of board independence (measured by the
number of outside directors divided by the total number of board members) and CEO duality
4
We conducted a robustness check by using the alliance network captured only in the year 1998 instead of the
aggregated network over 1998-2000, and the results are consistent with our main analysis.
5
By convention, the first period is considered as a base period (Lospinoso et al., 2011). Because we have two
periods, the pre-SOX period is considered as a baseline and a time dummy for the post-SOX period is included.
Note also that in Siena, the main effect of the time dummy variable is the same as the interaction “time dummy X
outdegree”, and the outdegree is the intercept of the model. We do include the outdegree effect in the model as well.
19
(measured as 1 if the CEO is also the chair of the board and 0 otherwise) as they may influence a
firm’s tendency to seek external directors or attractiveness as a board interlock partner (Krause et
al., 2014). Finally, while we created a board interlock network among Fortune 300 firms, our
sample firms may also have board interlock ties with firms outside the network. We include an
actor-level control for the ties outside the network by first counting the total number of other ties
for each firm's set of directors and subtracting out the number of ties that we observe within our
sample. All firm-specific characteristics above are captured in the years 1998
6
and 2002.
Geographic closeness has shown to be another important determinant of board interlock tie
formation (Kono et al., 1998). Thus, we include the dyadic control variable of colocation in the
same state. We also control for whether firms operate in the same industry based on their 2-digit
SIC code.
A growing body of research stresses the importance of properly accounting for
endogenous structural effects (i.e. the effect of local substructures) in conducting network
research (e.g., Ahuja et al., 2012; Kim et al., 2016; Lazega et al., 2012; Snijders et al., 2010).
Thus, although we focus on the influence of the two primary local structures – reciprocity and
transitivity, we additionally control for the influence of in-degree, out-degree, and other potential
endogenous effects. Outdegree is the most basic effect, representing the tendency to have any
ties with other network actors while controlling for other effects included in a model. The
outdegree effect is analogous to an intercept in conventional statistical models and is included in
all models as a default in model estimation. Three cycle effect accounts for a firm’s tendency for
the formation of short cycles of generalized reciprocity. In-degree popularity (sqrt) effect
accounts for the well-known ‘Matthew effect’ (Barabási and Albert, 1999; Merton, 1968). A
6
We conducted a robustness check in which we use the mean values for firm-level covariates during the period of
1998-2000, instead of year 1998. The results are consistent with the main result.
20
positive popularity effect suggests that a firm which is being invited by many other firms is more
likely to attract additional ties
7
. Out-degree activity (sqrt) effect accounts for actor i’s tendency
to simply be very active in forming or maintaining new ties. Out-degree popularity (sqrt) effect
reflects the tendencies of those firms with high out-degrees to attract additional incoming board
interlock ties. This effect is an important substructure to be included when testing a transitivity
effect (Robins et al., 2009). Finally, to capture firms with no ties in our observed network, we
include terms to account for isolates with regard to outdegree and indegree respectively
8
.
5. RESULTS
The main descriptive statistics of the three waves of board interlocks are presented in
Table 1.
Table 1. Descriptive statistics of the board interlock networks
Pre-SOX (1998-
2000)
SOX (2002)
Post-SOX
(2004-2006)
Number of firms
220
220
220
Density
0.013
0.012
0.015
Number of edges
649
575
707
Mean of indegree
2.95
2.66
3.21
Std.dev of indegree
2.34
2.40
2.76
Mean of outdegree
2.95
2.61
3.21
Std.dev of outdegree
3.30
2.37
2.58
Both average indegree and outdegree increased in the post-SOX network relative to the pre-SOX
network. The probability that any pair of firms has a board interlock tie at some point (i.e.
network density) was generally 1% during the pre-SOX and SOX (i.e. 2002) network, and it
increased to 1.5% in post-SOX periods. Figure 2-4 shows the plots of the three observed
networks.
7
We used the square root versions for all degree-related effects because they are empirically shown to be better
measures than raw degrees (Snijders et al., 2010).
8
For the isolate effect in terms of outdegree, we used outTrunc effect with parameter c=1. For isolates in terms of
indegree, we used antiInIso effect. See Ripley et al. (2015) for more details.
21
[insert Figure 2, 3 and 4 about here]
The general impression from a visual inspection of pre- and post-SOX networks is one of
greater interconnectedness. Consistent with the density, activity, and popularity increases shown
in Table 1, firms appear to have more transitive connections and closed loops than in the prior
period. At the same time, the post-SOX graph shows more isolates, suggesting a more densely
connected network among relatively fewer actively linked organizations. This could be due to a
downgrading effect – perhaps isolates shown in the post-SOX graph create new ties to firms
outside (and thus less profitable than) the Fortune 300. Finally, we include alliance ties in the
network plots, shown as red lines (contrasting with the blue lines reflecting interlocks). Visual
inspection suggests that alliance activity between sample firms decreased following the passage
of SOX. While our focus is the evolution of board interlock networks, future research may
examine whether SOX also influenced the evolution of alliance networks.
In our theoretical framework, we suggested that the passage of SOX contracted the
director pool as firms became more restrictive in the number of boards on which their executives
may serve, due to increased workload and associated risks. The broad trends support this notion
– the number of unique directors sitting on the boards of the companies in our network decreased
from 2,155 unique directors in 1998 to 1,803 unique directors in 2006. However, these are
merely descriptive statistics; in order to understand the underlying mechanisms of the network
evolution, we need a more rigorous statistical analysis.
Table 2 shows the results of the Siena models. We computed the Jaccard index to
examine the degree of change in the network (Snijders et al., 2010see ). During our study period,
this index remains within an acceptable range suggested in prior literature, with 0.4 for period 1
(from pre-SOX network to the network observed in the SOX year, 2002) and 0.41 for period 2
22
(from the network in the SOX year to the post-SOX network). The convergence of the estimation
algorithm was successful in all models with the t statistics for all parameters below 0.1. The
overall maximum convergence ratio for each model is also within the accepted range, below
0.25. In Siena model results, all parameters are coefficients of the utility function that actors try
to maximize by choosing to create new ties, to maintain existing ties, or to terminate them. A
positive, significant coefficient of a variable indicates that there is a higher probability of moving
towards a network configuration where the variable drives network evolution. The rate
parameters represent the amount of change between two subsequent networks, in other words,
the speed at which the network changes. It is calculated separately for each of the two periods –
before and after SOX.
23
Table 2. SIENA models for the evolution of board interlock networks
Model 1
Model 2
Model 3
Model 4
(wave 2:2001-2003)
Model 5
(robustness)
β
s.e.
β
s.e.
β
s.e.
β
s.e.
β
s.e.
Rate parameters
Rate parameter period 1
3.57
0.19
5.20
0.34
5.49
0.38
5.00
0.31
5.31
0.35
Rate parameter period 2
3.56
0.19
5.30
0.36
4.84
0.31
4.66
0.28
4.68
0.29
Evaluation function
parameters
outdegree (density)
-2.45
0.04
-2.16
0.29
-1.98
0.30
-2.23
0.27
-1.94
0.29
reciprocity
3.48
0.12
3.49
0.13
3.30
0.11
3.55
0.14
transitivity
0.89
0.07
0.90
0.06
0.83
0.06
0.92
0.07
three cycles
-1.41
0.16
-1.41
0.14
-1.25
0.14
-1.43
0.16
popularity
0.08
0.09
0.02
0.08
0.05
0.08
0.02
0.08
activity
-0.38
0.07
-0.40
0.08
-0.33
0.07
-0.41
0.08
two path
-0.08
0.08
-0.10
0.09
-0.06
0.07
-0.10
0.09
isolate in terms of outdegree
-2.52
0.32
-2.46
0.33
-1.98
0.36
-2.50
0.36
isolate in terms of indegree
-1.29
0.22
-1.33
0.21
-1.23
0.21
-1.32
0.21
Interaction terms
post SOX dummy X
reciprocity
0.43
0.19
0.37
0.16
0.43
0.18
post SOX dummy X
transitivity
-0.03
0.10
0.07
0.08
-0.03
0.09
post SOX dummy X alliance
2.38
0.91
1.66
0.60
2.42
1.00
Dyadic covariates
alliance
0.19
0.40
-0.42
0.49
0.71
0.45
0.26
0.30
0.72
0.49
same industry
-0.40
0.19
-0.31
0.18
-0.31
0.19
-0.28
0.19
-0.31
0.20
same state
0.48
0.08
0.38
0.07
0.37
0.08
0.33
0.08
0.37
0.08
average weighting of ties
-
-
-
-
-
-
-
-
-0.12
0.19
Firm-specific covariates
post SOX dummy
0.33
0.10
-0.22
0.09
0.34
0.10
firm size alter
0.24
0.07
0.02
0.08
-0.02
0.08
-0.02
0.08
-0.02
0.08
firm size ego
0.43
0.08
0.39
0.09
0.32
0.09
0.30
0.08
0.34
0.09
financial performance alter
0.63
0.36
0.88
0.41
1.31
0.43
1.17
0.40
1.33
0.44
financial performance ego
-0.14
0.34
-0.31
0.33
0.05
0.38
0.31
0.43
0.05
0.39
firm specific uncertainty alter
-0.23
0.23
0.00
0.24
0.07
0.25
-0.08
0.23
0.07
0.25
firm specific uncertainty ego
-0.79
0.29
-0.67
0.30
-0.66
0.30
-0.73
0.30
-0.69
0.31
board independence alter
0.66
0.18
0.22
0.21
0.00
0.20
-0.05
0.19
0.00
0.20
board independence ego
0.89
0.21
0.47
0.22
0.19
0.21
0.03
0.22
0.20
0.23
CEO duality alter
0.06
0.08
0.02
0.09
0.00
0.09
0.09
0.09
0.00
0.08
CEO duality ego
-0.04
0.09
-0.06
0.09
-0.05
0.09
-0.03
0.09
-0.05
0.10
ties with firms outside the
network alter
0.009
0.004
-0.001
0.004
0.006
0.004
0.01
0.00
0.01
0.00
24
ties with firms outside the
network ego
0.002
0.004
-0.002
0.005
0.006
0.005
0.01
0.00
0.01
0.00
Model 1 includes only exogenous variables. In model 2, we include endogenous
structural effects as well as the exogenous covariates. In model 3, we add the post-SOX dummy
and the three interaction terms of interest, post SOX dummy X reciprocity, post SOX dummy X
transitivity, and post SOX dummy X alliance. Subsequent goodness of fit analysis of the
outdegree and indegree distribution suggests that model 3 reflects the observed data and shows
better fit than model 1 and model 2, which ignore endogenous structural effects and time
heterogeneity. In Figures 5 and 6, we examine violin plots created based on the results of the
sienaGOF function (Hintze and Nelson, 1998; Ripley et al., 2015). Compared to the plots based
on model 1 and model 2, the plots for outdegree and indegree based on model 3 show that the
observed values stay closely within the simulated values. The Monte Carlo Mahalanobis
Distance Test of Lospinoso and Snijders (2011)
9
also suggests that the simulated values based on
our model are not significantly different from the observed values, suggesting that model 3
reasonably fits the observed network (Ripley et al., 2015; Snijders and Steglich, 2013).
9
The null hypothesis for this test is that the auxiliary statistics for the observed data are distributed according to the
statistics shown in the plot. The larger the p-value, the more confident we are that the observed network is more
likely to come from our estimated model. On the other hand, if the p-value is low (for example, below the
conventional level of significance, 0.05), the differences between the observed network and simulated networks are
significant, suggesting poor fit.
25
Figure 5. Goodness of fit of outdegree distribution for three models.
Figure 6. Goodness of fit of indegree distribution for three models.
We interpret the results based on model 3. A positive coefficient on the post-SOX
dummy suggests that compared to the pre-SOX period, there was a particular increase in a firm's
tendency to form and maintain a board interlock tie during the post-SOX period, while
controlling for a firm's general tendency to form a tie. Our particular interest, however, is on the
interaction terms to see whether there has been time heterogeneity for the three social processes:
reciprocity, transitivity and alliance. Consistent with Hypothesis 1, a positive coefficient of the
interaction between post SOX and reciprocity suggests that after the passage of SOX, firms’
26
tendency to reciprocate board interlock ties has been reinforced (β=0.43, SE=0.19). However, we
find little evidence for our hypothesis 2 that the transitivity has been reinforced in the post SOX
period (β=-0.03, SE=0.10). Finally, a positive coefficient of the interaction between post SOX
and alliance relationships shows support for our hypothesis 3, suggesting that after the passage of
SOX, a firm’s tendency to form or maintain a tie with existing alliance partners has been
reinforced (β=2.38, SE=0.91).
Several endogenous structural processes are found to be important drivers of network
change. A negative outdegree (density) parameter suggests that while accounting for other
effects included in the model, a firm is less likely to form or maintain a tie with other firms. This
is understandable because costs of managing a social relationship generally outweigh its benefit.
A positive coefficient on reciprocity suggests that a firm’s tendency to reciprocate a tie is an
important driver of network change. A positive transitivity effect, together with a negative three
cycle
10
effect, suggests that open triads are likely to close. A negative activity effect suggests that
a firm with more incoming ties is less likely to invite a director from other firms. A negative
isolate effect in terms of outdegree and indegree, respectively, suggests that a firm is less likely
to connect with those who otherwise would have no board interlock ties with others in the
network. These results of the endogenous effects are consistent with prior research (Kim et al.,
2016; Koskinen and Edling, 2012; Robins and Alexander, 2004), and suggest that in network
evolution research, it is imperative to properly account for the effects of endogenous structural
processes. In terms of firm characteristics, a firm is more likely to create or maintain a tie with
another firm in the same state. A firm with higher levels of stock volatility is less likely to seek a
10
Block (2015) suggests that transitive reciprocated triplets effect could be used included as an alternative of three
cycle effect. We conducted a robustness check by replacing three cycle with the transitive reciprocated triplets, and
our main results remain essentially the same.
27
tie. A larger firm is more likely to seek a tie whereas a financially successful firm is more likely
to be selected as a board interlock partner.
We tested the robustness of our model in multiple ways. First, as we discussed earlier in
the Method section, there is no theoretical underpinning for the validity of the time window we
choose from the viewpoint of SAOMs. Thus, we empirically examine whether our results are
sensitive to the specific time window we use to construct the second wave. Specifically, we use
the following three networks with equal length time period: 1) the pre-SOX board interlock
network observed during 1998-2000; 2) the board interlock network observed during the SOX
period of 2001-2003; 3) the post-SOX board interlock network during 2004-2006. The results of
this model
11
(Model 4 in Table 2) are consistent with our main analysis.
Second, in constructing our sociomatrices, we consider whether firm i invites any
individual from firm j. This is consistent with prior research on board interlocks suggesting that
major reasons for board interlocks include coopting the alter firm to reduce a firm's dependence
on the alter firm (Hillman, Withers, & Collins, 2009) and gaining legitimacy (Mizruchi, 1996).
Inviting multiple individuals from the alter firm may also enhance the risk of being controlled by
the alter firm (Pfeffer & Salancik, 1978). However, it is possible that firm i invites multiple
individuals from firm j. Thus, although the board interlock literature offers these reasons that
multiple interlocks in the same dyad may not occur frequently, we examined our data to
determine how frequently firms share multiple directors. Despite the theoretical redundancy and
inefficiency of multiple concurrent interlocks, we find that 248 of the 649 tied firm pairs in the
pre-SOX period and 128 firm of the 707 tied pairs in the post-SOX period shared two or more
common directors. The highest number of shared directors is 4 in the pre-SOX period and 5 in
the post-SOX period. We conducted a robustness test to evaluate whether this strength of tie
11
For this model, we use the covariates captured in year 1998 and 2001.
28
effect is significantly influencing our analysis of interlock network evolution. In Model 5 in
Table 2, we have included a dyadic variable in our analysis that reflects the weighting of ties (i.e.
number of shared directors) in each of the pre-SOX, and SOX to test its influence on subsequent
network change. The result of the model with this variable, average weighting of ties (under the
Dyadic covariates in Table 2) shows that the variable is not significant, and our results are not
biased by the strength of tie effect.
Third, in Siena, it is generally considered as a good practice to specify all of the three
effects for actor-level covariates (ego, alter, and similarity/same effects for dummies). While our
main model does not include the similarity effects, we ran a model including the similarity/same
effects. The results of our variables of interest are qualitatively similar in terms of the coefficient
and significance, while two similarity/same effect parameters were found significant (firm size
and financial performance). However, subsequent analysis on the goodness of fit (both the plot
and the Mahalanobis test statistics comparing the differences between the observed values and
simulated values) for this more complex model shows poorer fit than our proposed model
without the “same” effect. This indicates that the complex model with the same effects does not
reflect the observed network well, perhaps due to over-specification. Thus, we decide to go with
a simpler model without the similarity effects in our main analysis.
6. DISCUSSION
Institutional changes can have a profound effect on the strategies and practices of
organizations (Edelman, 1990). In this study, we observe how changes in the legal environment
stemming from the passage of the Sarbanes-Oxley legislation of 2002 impacted the market for
directors and consequently the evolution of the board interlock network consisting of the large,
prominent firms in the U.S. economy. In part, our work underscores the importance of
29
continuing to consider critical questions, such as “How and Why Do Interlocks form?”
(Mizruchi, 1996: 272), but also considering questions regarding the structural processes that
underlie those interlock networks. In addressing why firms form interlocks, Mizruchi (1996)
suggests that firms form interlocks for a variety of reasons (i.e., collusion, cooptation and
monitoring, legitimacy, executive career advancement, social cohesion). While our study does
not suggest that these previously identified reasons for interlock formation have changed as a
result of the institutional shifts brought about by SOX, it does provide evidence that SOX may
have impacted the influence of some structural processes by which firms form and dissolve
interlocks.
We examine a number of network structural effects that influence the evolution of board
interlocks in the period following the environmental change. Despite the inefficiencies and
informational redundancies associated with reciprocal interlock ties (Haunschild and Beckman,
1998), we provide evidence that the SOX implementation strengthened the tendency of firms to
pursue this type of interorganizational tie. Consistent with our theoretical framework, our results
support the notion that the reduced supply of willing directors coupled with the increased
demand for specialized skills in financial oversight led firms to rely more on socially embedded
routes for seeking or maintaining interlock ties. Reciprocal ties fit nicely into this category –
doubling ties with established interlock partners avoids much of the uncertainty that would
accompany the recruitment of directors from previously non-interlocked firms.
A tendency to create multiplex ties, a qualitatively different type of tie between nodes,
has also increased after SOX. Within our sample, firms showed a greater post-SOX tendency to
create or maintain interlocks to firms with which they conducted strategic alliances in the prior
period. Similar to reciprocity, alliances between firms are likely to increase the available
30
information regarding a potential partner firm. Alliances often involve high-level exchanges and
negotiations between executive teams, offering partner firms a chance to become more familiar
with each other’s strategies and capabilities (e.g., Gulati and Gargiulo, 1999). Gagliolo, Lenaerts,
and Jacobs (2014) found an analogous effect on interlock formation in the context of directors’
shared ties to voluntary associations. This importance of pre-existing connections in general and
information flow through those ties are also consistent with prior research showing the effect of
small world on interlocks (Robins and Alexander, 2004).
We hypothesized that the effects of transitive closure, another socially-embedded process
of partner selection, would also be reinforced as a result of the institutional changes brought forth
by SOX. Consistent with prior research (Kim et al., 2016), we find that a firm is more likely to
partner with another firm that is indirectly connected to the focal firm. However, we did not find
evidence of a heightened effect of transitive closure in the post SOX context. One possible
explanation is that the shock to the director labor market led firms to favor the most direct
socially embedded processes, those that provide first-order knowledge of their potential interlock
partners such as previously established relationships in the form of direct interlocks or alliances.
While indirect ties reduce the information gap in seeking new partners, they may be a less
effective mechanism for this purpose to overcome the challenge during the post-SOX period.
We note certain limitations in our study. Research on the formation and evolution of
corporate interlocks is at an early stage, with relatively few published studies in management
research (Kim et al., 2016; Yue, 2012). There has been limited research on the dynamics of the
board interlock network using longitudinal network methods. As a result, there may be other
factors driving board interlock selection that we do not fully understand. While the network of
interorganzational ties among Fortune 300 firms arguably represents an important domain of
31
study driving significant economic consequences, we recognize that the social processes of board
interlock partner selection among smaller organizations may be different and may react
differently to institutional change. Future work in different contexts may lend greater insights
into these variations.
Our study contributes to research on the evolution of organizational networks, in
particular board interlock networks. Prior research examines the effect of governmental
regulations, technology shock or exogenous event on the dynamics of alliance or ownership
networks (Corbo et al., 2016; Corrado and Zollo, 2006; Madhavan et al., 1998), yet relatively
little is known regarding the drivers of board interlock network change. More recently, Seierstad
and Opsahl (2011) have examined exogenous shocks of changing legislation on board
composition within an individual firm. By extending these ideas to the context of board interlock
networks, we examine the influence of SOX and how this legal change interacts with other micro
mechanisms of partner selection. In doing so, our study provides a greater understanding of the
evolution of this important organizational network. At the same time, building on the literature
on SOX (Coates and Srinivasan, 2014; Linck et al., 2009), our results provide some evidence of
the unintended effects of the regulatory change. Finally, despite much interest in organizational
networks, there has been limited empirical work on network evolution, partly due to prior
limitations in methodologies to account for endogenous structural effects in examining complex
underlying processes (Ahuja et al., 2012). Siena stochastic actor-oriented models (SAOMs)
provide a powerful statistical tool specifically developed for this purpose (Snijders et al., 2010).
SAOMs have been used in various domains to examine knowledge and innovation networks
(Balland et al., 2016; Conaldi et al., 2012), syndication networks in venture capital industry
(Checkley et al., 2014), regional clusters (Giuliani, 2013), and interaction between intro- and
33
FIGURE 2. NETWORK VISUALIZATION – PRE-SOX
Interlock ties are shown in blue, alliances in red
34
FIGURE 3. NETWORK VISUALIZATION – SOX IMPLEMENTATION, 2002
Interlock ties are shown in blue, alliances in red
35
FIGURE 4. NETWORK VISUALIZATION – POST-SOX
Interlock ties are shown in blue, alliances in red
36
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