Board of Directors and Corporate Networks

Abstract

Social network analysis (SNA) is an emerging research field in finance. This chapter references SNA and knowledge of corporate governance, to deal with a similarly emerging topic in finance, board interlocking, and shall examine the validity of the small-world model in a relevant emerging market and the existence of associations between the firm’s worth and its network of corporate relationships. This study references official data relating to more than 400 listed companies. The main results suggest that the network configuration of the relationships between board members and companies reflects the small-world model. Furthermore, there seems to be a significant relationship between the firm’s worth and its network centrality, described according to an “inverted U” type curve, which suggests optimum values exist for social prominence in the corporate network.

Portions of this chapter appeared in the 2011 paper “Small Worlds and Board Interlocking in Brazil: A Longitudinal Study of Corporate Networks 1997–2007”, Brazilian Review of Finance, vol 9, pp521–548.

An element of finance literature has assumed that the frontier expansion of this field of knowledge is associated with research development characterized by connected domain approaches, which integrates various areas of knowledge. In this context, for example, works on behavioral finance and economic sociology stand out. Along this same line of thinking, the corporate governance area has proved to be a fertile field for connected domain research, because the topic has developed through contribution from various professionals from different disciplinary areas. It has to be emphasized that the corporate board is a central theme in the study of corporate governance and financial innovations (Yermack 2017). Since Mills (1956) published The Power Elite, critics have argued that the North American corporate environment can be seen as an insular, politically powerful network of “old boys.” According to this logic, attribute sharing enables the establishment of ties between board members of the major publicly quoted companies, which initiates a network configuration (a set of nodes linked by nodes). This network has frequently been seen as a small world of mutual knowledge, characterized by the sharing of activities on company boards (board interlocking).

Is corporate Brazil a small world? Do members of the boards of listed companies know each other? The replies to questions like these can offer insight to information flow, innovation, and management practices (Kang et al. 2018). A small world is understood to be an environment that is characterized by a network whose actors are close to one another (few degrees of separation), resulting in an environment in which the actors are strongly clustered. This suggests a simultaneous sharing of worldviews and standards of professional conduct on the part of the board members (Stafsudd 2009). According to financial literature, in the context of the roles the corporate board is tasked to undertake, the network formed by its members has shown itself to be a powerful means of propagating corporate management practices, from how to acquire a firm (Haunschild 1993) to how firms respond to takeovers (Davis and Greve 1997). And recently researchers have made contributions from technology to governance mechanisms, for instance, Yermack (2017) discusses interactions between Blockchains and corporate governance and indicates this field as a track for future research on financial innovations.

According to the arguments of Leitner (2005) and Davis et al. (2003:301), the contagion process (via the network) within individual boards is clear: members meet frequently (almost on a monthly basis), to share knowledge and ideas, possibly obtained from some other boards, based on member interactions with directors of other boards. Therefore, the topography of corporate social networks and the firm’s positioning in these networks are important, in view of this contagion dynamic and information flow (Coleman 1990; Martínez-Jaramillo et al. 2010). Therefore, if the network structure of relationships among board directors has an impact on the information flow between companies, it is expected that changes in network structures will have important consequences on strategies, including the financial strategies adopted by organizations.

In Brazil, studies into board interlocking, the central subject of this research, which are characterized by extensive longitudinal studies, are still unknown, especially with describing the small world of company boards of directors (Lazzarini 2007). The “neighborliness” of the corporate elite is assumed to be the network of interlocks created when boards share one or more common directors (Schonlau and Singh 2009; Bouwman 2011). In turn, board directors are connected by the common service they provide on one or more corporate boards. They also have attributes in common, e.g., courses and the universities where they were educated (Cohen et al. 2010). In the Brazilian experience, significant company changes might have been caused by events such as (i) internationalization processes; (ii) a more active stance by institutional investors; (iii) mergers and acquisitions; (iv) redefinition of government practices, seen as highly recommendable; (v) reclassification of the Brazilian economy regarding public security risk; and (vi) the supposed stability of the Brazilian economy (in a context of global crisis).

While it is rarely questioned that such factors drive changes in how top administrators, and by extension the companies, establish ties in the corporate environment, analysts have never documented a representative number of the net results of these transformations. The main contribution of this article is based on the attempt to develop a point of reference for future works, whose purpose is to expand the frontiers of knowledge in finance, using social network analysis (SNA).

This chapter presents highlights from this research and references this large data set of listed firms and describes research in the area of corporate governance using a connected domain approach, an aspect that is widely recognized in constructing and advancing scientific knowledge, particularly in the field of finance. In view of the above arguments, initiating a small-world approach, the purpose of this article is to analyze how the configuration of the global relationship network evolved between Brazilian listed companies and their board directors between 1997 and 2007, using SNA to do so. Furthermore, the study also observes the manner in which the firm’s position within the corporate relationships network impacts the firm’s worth.

The main results were obtained: (i) the network of relationships between board members (and also between companies) reflects a small-world model. In other words, the average distance between board directors (and the company) is sufficiently small. At the same time, the values for the clustering coefficient of the board members are high. In addition, evidence points to the existence of a relationship between the firm’s network centrality and its worth that may be described as an “inverted U” type curve. In other words, within the scope of the corporate relationships network, evidence points to the existence of companies’ centrality values that maximizes their worth. These research findings provide insight into how corporate networks can impact firm performance. At the end of this chapter, some recommendations are provided, including directions for future research.

The Composition of Boards and Interlocking

Significant interest in the topic of board interlocking, both by academia and the business community, is not a recent phenomenon (Bearden et al. 1975). However, definition of the term “board interlocking” has not been unanimous. Among the various opinions that exist on the topic, the most frequent argument found in the literature posits that board interlocking exist if at least one company board member simultaneously occupies a place on another company’s board of directors (Mizruchi 1996). However, it was not until the end of 2009 that this topic was included in the discussion agenda about best practices in Brazil’scorporate governance environment (IBGC 2015). In this research, it is assumed that the occurrence of board interlocking leads to the rise of personal and corporate networks. Figure 14.1 shows a basic scheme in which four companies (nodes) are linked by ties that reflect the sharing of attributes, in this case sharing company board members as nodes linked by ties that form a network.

Fig. 14.1

Schematic representation of corporate networks. Note: This figure represents a typical scheme for a nondirectional network of 4 companies (nodes/vertices 1–4), linked by 11 board directors (nodes/vertices A to K). The top part of the figure illustrates the two-mode projection of companies with shared board members. In the lower left, the set of X nodes = {1,2,3,4} represents the one-mode network of companies (network of companies). On the lower right, the Y node = {A,B,……,J,K} shows the network of board directors (linked by companies in common). In this research the one-mode analysis structure was adopted, or rather, it was either assumed that the network was formed by board directors or merely by companies. However, literature already offers discussion of two-mode approaches (Robins and Alexander 2004). (Source: Prepared by the author, Adapted from Newman et al. 2001)

The Small-World Model

Recent advances in mathematics and computing and, specifically, developments in graph theory (based on knowledge of SNA) have resulted in a widespread increase of research regarding social networks. In particular, the small-world model is a powerful tool to scrutinize the phenomenon of network formation (Conyon and Muldoon 2006). The small-world phenomenon was initially analyzed in the work of Milgram (1967), which consisted of an experiment that involved sending letters to various people who forwarded them, via a network of people they knew.

The study concluded that apparently distant people may be in actual fact connected by a very short chain of known intermediaries. Milgram (1967) found this close chain was essentially limited to a critical path of 6 (six) steps. In other words, according to this author, there is a great tendency that an individual known by one person will also form part of the circle of relationships of a second known individual or mutual acquaintance. The theoretical small-world model is described in detail by Newman et al. (2001). Two global characteristics of this theoretical network model, which has profound consequences for the social phenomenon, must be observed with particular attention in the characterization of a small world: (i) the distance between actors (L) and (ii) the clustering coefficient (C_Δ).

In social networks such as corporate networks (i.e., companies or board directors), locally grouped and globally connected actors are expected; or rather, many less prestigious companies are linked to others that have greater social prominence. So, Baum et al. (2004) emphasize the relevance of studying network properties, as well as their evolution over time, in view of their impacts on small-world consequences, since this type of configuration can significantly affect the speed of interaction between the component companies of a network of corporate relationships, for example Davis et al. (2003).

The first property of the small-world model is that pairs of randomly chosen nodes may be unexpectedly close to each other. A graph/network with N nodes contains N (N−1)/2 pairs of nodes. If they are numbered 1, 2…, N and d_i,j is the distance between nodes i and j, then someone can calculate the typical distance between the component nodes of the network, using the following Eq. (14.1):

$$ L=\frac{2}{N\left(N-1\right)}\sum \limits_{i<j}{d}_{i,j} $$

(14.1)

In the context of corporate boards (and in accordance with the analysis unit, firms or board members), the term L measures the (typical) number of steps necessary to move from one actor to another within the context of the network. Put another way, in a network of corporate relationships, information will reach a director after being passed on by L intermediary members, since typically there are L directors separating director i from director j. The second property of the small-world model is the high clustering coefficient, a measure of the density of the network. According to Newman et al. (2001), the clustering coefficient for the (global) network is calculated as follows (14.2):

$$ {C}_{\varDelta}=\frac{3\times \mathrm{number}\ \mathrm{of}\ \mathrm{triangles}\ \mathrm{in}\ \mathrm{the}\ \mathrm{graph}}{\mathrm{number}\ \mathrm{of}\ \mathrm{connected}\ \mathrm{links}} $$

(14.2)

where a triangle is a set of three different nodes, j, k, and l, in which each node (or actor) is connected to two others. A connected link consists in a set of three nodes, j, k, and l, in which j is connected to k and k is connected to l (l need not be connected to j); the factor 3 in the numerator is necessary to ensure that 0 ≤ C_Δ ≤ 1, as each triangle contributes to the increase in the three connected links. Figure 14.2 illustrates this notion. To the right of the figure, there are 2 complete triangles (6–8–9) and (4–6–9), but 13 connected links (6–4–7; 6–4–9; 7–4–9; 4–6–8; 4–6–9; 8–6–9; 4–7–8; 6–8–9; 6–8–7; 7–8–9; 4–9–6; 4–9–8; 6–9–8), so ${C}_{\varDelta}=3\times \frac{2}{13}=\frac{6}{13}$. The distance (L) between node 6 and node 9 is 2 (2° of separation).

Fig. 14.2

Examples of simple graphs. Note: The left-hand side of the figure shows a complete graph (all the nodes are interconnected), illustrating a component/cluster. On the right-hand side of this figure, two connected components/clusters are shown. By way of illustration, in any network, if three nodes, j, k, and l, form a connected link, then j is connected to k and k is connected to l, and, if “is connected to” were a strictly transitive relationship, then the conclusion is that node j is connected to node l. Therefore, in the network shown in this figure, node 9 is linked to node 8, and node 8, in turn, is linked to node 7. So, by transitivity, node 9 is linked to node 7. Therefore, the clustering coefficient C_Δ, computed according to the expression (2), represents the proportion of links for which the transitive conclusion is verified. It needs to be emphasized that there is a local clustering coefficient measure (for each component node in the network), as proposed by Watts and Strogatz (1998). (Source: Prepared by the author)

Small-world validity can be checked by comparing the values obtained for these two measures relative to the networks being analyzed, starting from the values for these two parameters in random networks (simulated) with a same number of actors, n, and ties, k. For random networks, L_expected ∼ ln(n)/ln(k) and C_Δexpected ∼ k/n, where n is the number of nodes (or actors) in the network and k is the average degree centrality (average number of adjacent ties) of each component actor in the network (Watts and Strogatz 1998). So in the light of the measures found, the strictly typical finding of small world will be seen if L_observed ∼ L_expected, while C_Δobserved ≫ C_Δexpected. However, like the procedure assumed by Baum et al. (2004) and Davis et al. (2003), in this research verification of the existence of a small world in the context of personal and corporate networks will be satisfied when Q_sw = (C_Δ observed/L_observed) × (L_expected/C_Δexpected) ≫ 1.

The Small-World Model in the Corporate Environment

The board of directors is an important social network, especially in the fields of economics, finance, and management. Some (few) recent studies have documented that, even in Brazil, directors frequently hold more than one position on corporate boards. Fama and Jensen (1983) emphasize that, at least in the North American economy, outside board members (outsiders) act as executives in other companies or are important decision-making agents in other organizations. However, in the Brazilian experience, there seems, as yet, to be no research to inform this phenomenon within the national context.

In this sense it is expected that the connectivity of companies leads to consequences, such as dissemination of executive remuneration practices (Subrahmanyam 2008) and the adoption of anti-takeover measures, poison pills, and the spread of golden parachutes (Davis and Greve 1997). Over the last few years, both the capital markets specialist media (including in Brazil) and academic publications have discussed the supposition that certain corporate boards are configured like a type of “closed club.” Concerning the application of the small-world approach to the study of the board interlocking phenomenon, the clustering coefficient measure is a way of investigating the “clique” or “clubby” aspects of boards (Conyon and Muldoon 2006; Yermack, 2006).

A limited number of studies examine the small-world properties of social networks within the context of corporate governance. These works typically compare small-world characteristics (the L and C_Δ measures) with those that are expected from a family of random graphs, originally introduced in the work done by Erdös and Rényi (1959). Only one study (Mendes-Da-Silva and Vidal 2010) was found that considers the Brazilian market in this regard.

Among the works that deal with small-world properties in the context of company boards, Davis et al. (2003) examine a sample of US corporate boards at three points in time; the results obtained by these authors suggest that the North American corporate environment can truly be understood as a “small world.” Conyon and Muldoon (2006) found that the small-world concept applies to the United States, Germany, and the United Kingdom.

The small-world approach has also been used in other studies on networks comprising ties and actors, which go beyond board interlocking. The link between companies resulting from sharing controlling shareholders in Brazil was studied by Lazzarini (2007), who recommends research of corporate boards such as this study has undertaken. The small-world concept within the corporate environment was also used by Baum et al. (2004) to study the network formed by banks that underwrite operations for raising funds in the Canadian capital market.

Positioning in the Corporate Network and the Firm Value

There are two basic classes of measures for understanding social networks: the positioning of each node/actor in the network and the topography of the network (Wasserman and Faust 1994). The first category illustrates the measures of social prominence (centrality), which describe how influential a node/actor may be within the context of its/his/her network. It was decided to use two of these measures: degree centrality (degree), the number of adjacent ties to each actor, and betweenness centrality (betweenness), the capacity to intermediate contacts between various actors in the network.

Pfeffer and Salancik (1978) start from the assumption that firms create ties to obtain desired resources and manage uncertainties in the corporate environment. Therefore, networks are seen as a way for firms to access organizations with the required resources and the capacity to help the firms support the restrictions imposed by the external environment. Bunderson (2003) also notes that groups seem to achieve higher performance levels (take better decisions) when board members share an accurate understanding of the others’ expertise. Pirson and Turnbull (2011) present a structured analysis of the gains that networked boards enjoy relative to isolated boards, e.g., a reduction in the judgment bias in decisions, better risk control, and a greater capacity to react to crisis. It is therefore expected that the greater a company’s influence in a corporate network, the greater its access to resources will be, whether they are negotiated in the market or not. Given these findings, it is reasonable to test the following hypothesis:

H_1a:

There is a significant association between degree centrality and the firm value.

H_1b:

There is a significant association between centrality and the firm value.

Literature offers arguments and evidence, however, that point to the existence of trade-offs with regard to the firm’s centrality. In this line of thinking Harris and Shimizu (2004) underline the idea that boards may be so occupied (an increased number of connections may result in directors overaccumulating functions) that they compromise their role within the company environment, i.e., monitoring executive activities and considering the adequacy of the management decisions relative to shareholder expectations, ultimately reducing the firm’s value. Fich and Shivdasani (2006) found results that point to the idea that firms with boards who keep “busy” (busy boards) which, according to these authors, means essentially outsiders who hold three or more places on boards, have poor corporate governance. Labianca and Brass (2006) also highlight the negative role of relationships within the context of social networks, which may reduce the firm value.¹ Given these arguments that suggest there are value limits for the firm’s centrality, the following hypothesis is tested:

H₂:

There are values associated with the firm’s centrality that maximize its worth.

Over and above centrality in the network, there are other interesting measures, including the efficiency of the links (structural holes). According to the arguments from Burt (1992) and Noyes (2007), we examined the relationships between the firm’s structural holes and the identification of investment alternatives, as well as Yang et al. (2010). In constructing nonredundant ties (coming from positioning itself in the corporate relationships network in such a way as to optimize structural holes, a procedure shown in Fig. 14.3), the company can benefit from its access to information that enables it to identify new investment opportunities (whose proxy adopted here is Tobin’s Q). The right-hand side of Fig. 14.3 shows the expectation of value creation due to the greater efficiency of the firm’s ties. In order to consider whether the efficiency of the firm’s ties is a consequence of the firm’s greater inclination to invest, it is expected that the market will judge the firm’s investment opportunities in a better light, as reflected in its market worth, which motivates a test of the following hypothesis:

Fig. 14.3

Structural holes and the firm value. Note: The left-hand side of this figure illustrates a procedure to optimize the firm’s structural holes (redefine its position in the network in such a way as to reduce the inefficiency of the ties that are constituted). On the right-hand side of the figure is an illustration of the expected association between the firm’s structural holes and the return for shareholders. (Source: Adapted from Burt 1992, p. 22 and p. 37)

H₃:

There is a significant association between the firm’s structural holes and its value.

According to Scott (2001), informal social networks between board members can resolve problems associated with a lack of team spirit, coordination, and cooperation. Such informal networks may result from various types of relationship. For example, ties formed at academic institutions may facilitate an approximation between directors, thus increasing their linking capacity in various network types. A similar educational background may also facilitate dialogue, since professions serve as approximation mechanisms between executives, given the cultural cognitive affinity attributed to a shared identity.

With regard to the relevance of personal characteristics to strategy and corporate performance, Labianca and Brass (2006:606) emphasize that social networks research, especially if company-focused, has ignored the relevance of individual personality and personal characteristics on corporate performance. In this regard, Cohen et al. (2008) presented an in-depth discussion on how the firm’s performance relates to the ties constituted by executives sharing courses and schools, a thinking that is also shared by Kilduff (1992) and Mehra et al. (2001). In these terms, the prevalence of the board directors in sharing personal characteristics, e.g., the company in which they serve as director (corporate ties), their graduate school (university ties), and/or their professional qualifications (similarity in educational background), would be a source of competitive advantage on some occasions, in view of the increase in mutual trust, integration of behavior, and cooperation between board directors.

Using these arguments, the owning of share capital by board directors also supplies elements that might increase an organization’s legitimacy in terms of their actions (Scott 2001; Westlund and Adam 2010), since it starts from the assumption that influential directors tend to have more access to information as well as enjoying a greater reputation with financing mechanisms and market regulators (Lin 2001). These arguments lead us to test the following hypotheses:

H_4a:

There is a significant association between the centrality of the board that comes from corporate ties and the firm value.

H_4b:

There is a significant association between the centrality of the board that comes from university ties and the firm value.

H_4c:

There is a significant association between the centrality of the board that comes from a similar educationa l background and the firm value.

In addition, Coleman (1990) and Pirson and Turnbull (2011) argue that by acquiring competences, improving information access, minimizing redundant efforts, and identifying investment opportunities and by leveraging the social capital that comes from greater cohesion, the company can be expected to enhance its worth through its greater density/local clustering position, which leads to the following hypothesis:

H₅:

There is a significant and positive association between the local clustering coefficient of the firm and its value.

Data Collection and Variables

Official annual data was made available by the Brazilian Securities Commission (CVM) and by consultancy company, Economatica®. The unit of analysis used here was either the boards of directors of companies listed on the stock exchange or board directors themselves within the Brazilian context between 1997 and 2007. Information was collected about the actual board directors from 415 companies (forming an unbalanced panel), resulting in a group of thousands of board directors. The collection and database preparation phase included extensive manual and computer procedures to ensure date quality as it related to the boards, aimed to ensure accuracy in identifying the ties between individuals/firms. This included reading and standardizing each individual’s name across companies while at the same time eliminating any ambiguities. For example, one board director was found with different renderings of his name: (i) Antonio Carlos Augusto R. Bonchistiano, (ii) Antonio Carlos A. R. Bonchistiano, and (iii) Antonio Carlos Augusto R. Boncristiano. For the panel data regression, the Tobin’s Q index was used as a dependent variable for the firm’s proxy value, which was estimated in accordance with a procedure proposed by Chung and Pruitt (1994). The independent variables used in the panel data regression were organized in three groups, namely, measures relating to the positioning of the firm in the corporate network, structure of the firm’s board of directors, and control variables.

Measures relating to the positioning of the firm in the corporate network: A specific SNA software application, Ucinet 6.0 for Windows, was used to obtain the variables relating to the positioning of the firm in the corporate network. Degreecentrality (degree) in absolute terms, an actor included in a network comprising g actors, can achieve g − 1 ties, at most. Degree considers only adjacent relationships or, rather, the local centrality of the players. According to Freeman (1979), the degree centrality index, defined by C_D (n_i) of an actor n_i participating in a network, is given by (14.3):

$$ {C}_D\left({n}_i\right)=d\left({n}_i\right)={x}_{i+}=\sum \limits_j{x}_{ij}=\sum \limits_j{x}_{ji} $$

(14.3)

In this work the normalized form of degree centrality was used, expressed in a percentage form (degree divided by the maximum number of ties possible, expressed as a %). In Fig. 14.1, for example, board director G has degree centrality = 5 and normalized degree centrality = 50%.

However, interaction between two nonadjacent actors may depend on a group of other actors, who may exercise some control over the interactions between two nonadjacent actors. Therefore, in order to put two actors, n₂ and n₃, in contact with each other, the shortest path is n₂ → n₁ → n₄ → n₃, then it can be said that actors n₁and n₄ control interactions between actors n₂ and n₃. This is, therefore, the concept of betweenness centrality (betweenness), which considers the interaction between nonadjacent actors. If all distance communications d(n_j, n_k), which go through actor k, are counted, this provides a measure of “stress.” When there is more than one possible path between j and k, all paths that pass through actor i are considered equiprobable. Therefore, the betweennesscentrality for n_i is the sum of the estimated probabilities for all pairs of actors, not including the i-th actor. This is given by the Eq. (14.4):

$$ {C}_B\left({n}_i\right)=\sum \limits_{j<k}\frac{g_{jk}\left({n}_i\right)}{g_{jk}} $$

(14.4)

where g_jk is the number of paths that link two actors. Therefore, if all these paths are equiprobable in terms of choice for establishing communication, the probability of a path being chosen is simply $\frac{1}{g_{jk}}$. In short, this measure indicates the number of pairs of nodes that an actor is capable of linking. In this research the normalized form (expressed as a %) was used. For example, in Fig. 14.1, board director G has betweennesscentrality = 12.5 and normalized betweenness centrality = 27.77%.

The third variable of the positioning of the firm is structural holes, which are types of nonredundant relationship between two contacts (Burt 1992). Therefore, the smaller the number of redundant ties, the greater the number of structural gaps, there being less information redundancy. We specifically use the efficiency measure of the ties (Burt 1992:53), which measures the number of nonredundant contacts, EffSize, relative to the total number of contacts n of an actor i.

The fourth positioning variable of the firm is the local clustering coefficient: C_i to the i-th node is given by the proportion of ties between the vertices in its neighborhood, divided by the number of ties that could exist between them. By way of illustration, in Fig.14.1 the node G has C_i = 0.40. According to a procedure by Watts and Strogatz (1998), a graph G = (V, E) formally consists in a set of nodes Vand the ties E between them. A tie, e_ij, connects node i to node j. Neighborhood N to the vertex v_iis defined as those immediately connected neighbors. Therefore, if node v_i has k_i neighbors, $\frac{k_i\left({k}_i-1\right)}{2}$ ties would exist between the neighborhood nodes. So C_i is formally defined in (14.5):

$$ {C}_i=\frac{2\left|\left\{{e}_{jk}\right\}\right|}{k_i\left({k}_i-1\right)}:{v}_j,{v}_k\in {N}_i,{e}_{jk}\in E. $$

(14.5)

The three other independent variables, corporate degree centrality, universitycentrality, and knowledge centrality, consist in the average degree centrality of board directors in the networks of directors formed by these three ways of establishing ties, which led to H_4a, H_4b, and H_4c.

Structure of the firm’s board of directors: (i) Size of the board, expressed by the ln of the number of directors of the firm in each year studied; (ii) outsiders, expressed by the percentage of board members that are external to the firm (Yermack 1996).

Control variables: selected on the basis of the possible influence they exercise over the dependent variable (the firm value) and the independent variables. If the control variables have a correlation with some of these variables and are not considered in the model, the relationship between the variables of interest cannot be shown in an adequate manner: age of the firm (ln of the number of months between registering the firm with the CVM until the end of the financial year t), superior performance (difference between the Ebit index/total sales of the i-th firm and the Ebit index/total sales of the economic sector to which the firm belongs), ln of quick ratio of the i-th firm in the t-th year, and ln of total assets of the i-th firm in the t-th year.

Empirical Model

In view of the purpose of this research, the data analysis is organized into two main blocks: (i) verification of the validity of small worlds to the Brazilian market (using a procedure suggested by Davis et al. (2003) and by Stafsudd 2009) and (ii) verification of the existence of associations between the positioning (of the company) in the corporate relationships network and the firm value, using panel data regression (unbalanced statistic). From the set of variables detailed on previous section of this chapter, the model to be tested is (14.6), with N = 415 and T = 11.

$$ {\mathrm{Value}}_{it}={\beta}_0+\sum \limits_{k=1}^K{\beta}_k{x}_{kit}+{u}_{it},{\kern1.5em}_{t=1,\dots, T,}^{i=1,\dots, N,} $$

(14.6)

in which the value of the i-th firm in the t-th year, Value_it, depends on K exogenous variables, (x_1it, ⋯, x_Kit), which differ between the firms at two given moments in time and also vary over time. The error term, u_it, which is assumed as an IID random variable, with an average of zero and variance${\sigma}_u^2$, independent of (x_1i, ⋯, x_iT), represents the effects of the omitted variables that are specific to both the firms and to the period studied.

Verification of the Small-World Phenomenon in Board Director Networks

According to Davis et al. (2003), the results obtained (summarized in Tables 14.1 and 14.2) are indicative of the existence of the small-world phenomenon between listed companies and between board members, respectively. It has to be emphasized that the strength of this configuration, Q_SW, grew over the period and maintained values that were considerably greater than 1 (Q_SW ≫ 1), whether for the network of directors or the network of companies.

Table 14.1 Small-world statistics of the network of relationships between listed companies in Brazil (1997–2007)

Table 14.2 Small-world statistics for the network of relationships between board members of listed companies in Brazil (1997–2007)

The results in Table 14.2 suggest that board directors are highly grouped from the local point of view, but maintain their distance (between each other) in the network, which does not impede the finding that their world is considered to be “as small as” could be expected. This indicator illustrates the structural consistency of the conditions of the small-world phenomenon. These results comprise empirical evidence of the cooperation between board directors in terms of companies’ links, rather than a deliberate effort on the part of the directors to constitute this network configuration. Therefore, one can understand that the Brazilian corporate environment has operated within the described parameters of a small world. In other words, it seems that the Brazilian capital market has grown in such a way that demand for directors from outside the firm has led to choice mechanisms of board members being selected in such a way as to establish a network in which distances between people are smaller (consequently the companies will be closer).

Obviously, this does not provide sufficient elements to imply, with any degree of certainty, that there is a development of relationships between board directors within the environment of the Brazilian capital market. However, it does lead to an important reflection about the corporate environment: while relationships between board directors have not been very close globally, the high clustering coefficients (C_Δ) revealed in the data indicate the formation of “neighborhoods” and, therefore, the possibility of forming social capital via cohesion (Coleman 1990). To calculate small-world statistics, it is necessary to assume the existence of a totally connected network. Therefore, the main component of the complete network was adopted. By way of illustration, Fig. 14.4 shows the segregation of a main component.²

Fig. 14.4

Segregation of the main component of the network of board directors in 2007. Source: Prepared by the author, based on official data collected from the IAN/CVM. Notes: (i) This figure illustrates the segregation of the main component of the network of relationships between board directors in 2007; (ii) on the left-hand side is the complete network arrangement of directors (1941 professionals grouped in 134 components/clusters); (iii) on the right is the main component of the network (a component that brings together the greatest number of interconnected nodes), in which 1191 directors participate; (iv) each node represents a director belonging to the network of corporate relationships, and the size of each node indicates the degreecentrality of each director; and (v) it is worth emphasizing that this research considered the board directors and executives (those who are also board directors in other companies) of the companies participating in the research. The intention was not to fail to compute a tie between two companies when an executive simultaneously performs director functions in at least one other company (to do so a function was developed in Visual Basic that can be obtained on request from the author of this study)

In Table 14.1 it can be seen that the Q_SW index for the network of companies is considerably greater than 1 throughout the whole period, highlighting that in addition to being bigger than the unit value, it has been growing. In other words, in 1997 it assumed the value ∼6.54, and by 2007 it had tripled this value to ∼17.30. In light of the measures found for the corporate relationships network and considering the small-world checking procedures suggested by Watts and Strogatz (1998) and the experiences applied to capital markets by Baum et al. (2004:312) and Davis et al. (2003), it seems that the Brazilian market, even though it grew between 1997 and 2007, behaved in the manner of a small-world environment. This characteristic has been particularly strong in recent years.³

This type of finding suggests that contagion power may have increased as a result of the speed of communication, which is the function of the power of dissemination of management practices, driven by board interlocking. Put another way, the Brazilian corporate environment, while it has grown significantly, as shown in Tables 14.1 and 14.2 (Δ%# of companies and Δ%# of board directors), is a cohesive network, in which contact between companies is ever closer, thus increasing the relevance of the reputation of the firm in its access to resources that are judged to be essential to its operation. In this sense, and according to the thinking of Subrahmanyam (2008), it is to be expected that the companies’ connectivity results in consequences, such as the dissemination of executive remuneration practices. It has to be emphasized that management practices will depend on the firm’s performance level and, by extension, its value in the perception of market agents.

Regressions

The results of the impact of the chosen independent variables on the company’s value were estimated using three different procedures: OLS, random effects (RE), and fixed effects (FE), as presented in Table 14.3; FE with a robust standard error was found to be adequate (Hsiao 2005; Petersen 2009)⁴. Since (i) the Breusch-Pagan test (p < 0.001) rejected the adequacy of the pooled OLS, suggesting the use of RE; (ii) the F test (p < 0.001) suggested that the coefficients generated by the pooled OLS are not consistent (suggesting greater consistency when controlling for FE); (iii) the White test indicated problems of heteroscedasticity (p < 0.001); and (iv) the Hausman test (p < 0.001) contradicted the null hypothesis that the parameters’ model controlling for RE was consistent.

Table 14.3 Estimated parameters for the worth of the firm

So, as Yermack (1996) assumed, and following the recommendations of Hsiao (2005), in this research, the regression model controlling for Feb (as a result of the existence of non-observed variables that probably affect the firm value) was more consistent in terms of its parameters. In situations like this, the FE model controls the variables omitted from the regression. In addition, the FE model allows a single intercept for each firm, being thus indicated for modeling panel data when the intercept α_i is dealt with as a fixed parameter. It is equally desirable to use FE when observations are obtained from the whole population (SNA does not admit use of samples) and it is wished to make inferences for the individuals (firms) for which data are available. All these conditions apply to this work.⁵

Assuming the fixed effects model as being the most suitable, discussion of the results using panel data regression diagnosis revolves around the estimated parameters in Model 3, although all the simulated models are reported in this particular table. With regard to the nine position regressors of the firm in the corporate network, the results obtained in the FE model indicate that there are signs of the existence of values for the degree centrality of the firm⁶ that maximize its value. In other words, if the linear coefficient, β₁ ≈ 0.1798 (p < 0.01), is positive and the quadratic coefficient β₁’ ≈ −0.0496 (p < 0.05) is negative, it is understood that there may be an association between degree centrality in the corporate network and the firm value, described as an “inverted U” type curve (existence of the point of maximum curvature).

It seems that the value of both those companies with lower centrality values and with higher centrality values reduces, probably for different but similar worth-reducing reasons. This result is in line with the arguments of Bunderson (2003) and Labianca and Brass (2006) and supports not rejecting the H_1a and H₂ hypotheses. It is understood, therefore, that there will be a combined effect between the linear and quadratic terms of the independent variable. The optimum point will therefore be seen when ∂E(γ)/∂(x) = 0.

According to the estimated parameters for degree centrality (normalized degree), the point of maximum curvature for degree centrality is around 1.8125; in other words, provided the other estimated coefficients in Model 3 are respected, with the dependent variable being Tobin’s Q, it seems that a value for normalized degree centrality ≈ 1.8125% indicates a maximum for Tobin’s Q index vis-à-vis the estimated parameters in the regression obtained in Model 3, all things being equal. Put another way, according to the estimated coefficients for normalized degree centrality, a firm can maximize its value if it establishes, on average, a value close to 1.8% of the possible adjacent ties with other companies. Therefore, in 2007, when 385 companies were found to be in the corporate network, the degree (via interlocking) that maximizes the firm value is around seven companies, i.e., [0.018125 × (385–1)], all things being equal.

On the other hand, with regard to betweenness centrality, no results were found that support the idea that this positioning measure of the firm in the network exercises a significant influence on its worth (β₂ ≈ 0.0121; p > 0.1), which leads to rejection of hypothesis H_1b, thus contradicting the arguments of Bunderson (2003) and Labianca and Brass (2006).

In line with the defense of Burt (1992) and Yang et al. (2010), the structural holes of the firm are positive and significantly associated with its value (β₃ ≈ 0.1198; p < 0.1). This suggests that those companies whose board interlocking ties are less redundant achieved greater worth. In other words, it seems that the companies that optimized structural holes increased their worth. This supports non-rejection of H₃. A result along these same lines is that the firm’s clustering coefficient proved to be negatively associated with its worth (β₄ ≈ −0.1643; p < 0.05) and this suggests that companies with a greater degree of local alignment tend to be worth less. A reasonable understanding is that there are value limits to the firm’s centrality and the level of local alignment. This was demonstrated by the significance of the quadratic term of the firm’s centrality degree (β₁’ ≈ −0.0496; p < 0.05). Hypotheses H_4a, H_4b, and H_4c were rejected, indicating the nonsignificance of the association of the firm’s worth with the relative densities of the ties of the board directors which result from sharing boards, universities, and areas of knowledge, respectively, thus contradicting the arguments of Lin (2001) and Cohen et al. (2008).

Put another way, based on the arguments of Burt (1992), the information flow in personal relationships and social groups presumes that the probability of a piece of information being propagated in a network grows with the strength of its ties, which from the empirical point of view is estimated by two independent dimensions: (i) the frequency of the ties and (ii) emotional closeness (Burt 1992). But the results obtained did not support this argument. In the view of Labianca and Brass (2006), the existence of ties (e.g., having attended the same university and/or having done the same course), despite the asymmetry of values and preferences of the network actors, would produce negative results for the firm (negative externalities), vis-a-vis the difficulty of maintaining common objectives.

The interaction term between the firm’s degree centrality and structural holes (degree vs. SH) received a positive and significant coefficient (β₈ ≈ 0.0332; p < 0.1), strengthening the idea that companies with a larger number of ties, and better ones, tend to achieve higher levels of worth in the view of market agents. This indication supports the assumptions of Burt (1992) that a larger and less redundant number of ties enable identification of new investment opportunities, which lead to an increase in the firm’s worth.

In observing the results obtained for the two variables relative to the composition of the board, it is found that board size did not prove to be significantly associated with the firm’s worth (β₉ ≈ 0.0081; p > 0.1), which contradicts the results obtained by Yermack (1996). In addition, the number of outside directors, even though it obtained a significant coefficient, has a small marginal effect on the firm’s Tobin’s Q (β₁₀ ≈ −0.0031; p < 0.05). Therefore, an innovative result and one that may merit greater attention from the academic community is that, rather than the size of the board, the way in which this board is linked by board interlocking to other companies may have a greater influence on the firm’s worth. Among the four control variables, both the firm’s age (β₁₁ ≈ 0.04781; p < 0.01) and the quick ratio (β₁₃ ≈ −0.1741; p < 0.01) were significant.

The results obtained in the panel data regressions support the idea that the firm’s degree centrality and structural holes are resources the company can and must manage with a view to achieving its corporate objectives. Therefore, the way in which the firm configures its board will determine its positioning in the network and consequently will have an impact on its access to market resources, whether formally negotiated or not, through board interlocking.

Concluding Remarks

Based on the graph theory, this research has attempted to check the validity of the small-world model for the capital market and to verify the existence of associations between the firm’s worth and its position in the corporate relationships network, by means of board interlocking. This study is most relevant in the context of the roles of corporate boards and their impact on the flow of resources (whether negotiated or otherwise in the markets), such as capital, status, prestige, and legitimacy within the corporate environment.

In the light of these results supported by a data set relating to 415 nonfinancial companies listed on the BM&FBovespa [São Paulo Stock Exchange] in the 1997–2007 period, it can be supposed that the top administration of hundreds of publicly quoted companies listed in Brazil essentially consists of people who know one another very well. According to the findings of Milgram (1967), over the 11 years studied, the board directors belonging to the main component of the network of relationships (∼50%) proved to be separated by a number of personal ties close to 6° of separation, meaning that the small-world properties were seen as being valid in the relationship networks that comprised both board directors and companies.

This supports the argument that in collaboration networks, individuals with an outstanding reputation, or who represent access to resources, experience, or knowledge, for example, tend to be more sought after. Consequently, they increase their prestige while at the same time exercising an influence on the governance practices of other companies via articulation and the sharing of prospects (Merton 1996; Moody 2004). Further, because of their career paths in different institutions over time and their peers in these institutions, they can promote a stratified connection between corporate boards, especially across companies that seek independent board members.

Such aspects raise questions as to the role exercised by certain companies in corporate governance via the activities of their board directors. Some companies may be more attractive in terms of establishing new relationships, thus increasing their influence in regard to their power to participate more actively in the flow of resources (financial and nonfinancial, whether formally negotiated in the markets, or otherwise) in the corporate relationships network; they act as key links between those companies that are around them.

Regarding company’s worth, results indicate the existence of optimum levels of centrality, and optimum social prominence levels of the firm (in terms of its degree centrality), which maximize the company’s worth. In line with the relevance of the firm’s position in the network to the firm’s worth, a positive association was found between structural holes and Tobin’s Q index. This reaffirms the arguments of Burt (1992), which defend the opinion that a reduction in redundant ties can improve access to new investments and new ways of mobilizing resources (not only financial ones) through board interlocking.

The results obtained with the firm’s position in the network, in comparison with the parameters estimated for the variables related to the corporate board composition, particularly the board’s size and the number of outside directors, support the idea that establishing parameters for ways in which a firm’s corporate power establishes ties with other boards is just as important as managing the board’s characteristics.

Directions for Future Research

The current discussion does not bring this topical debate to an end. Rather, the growth in the area of social network analysis and financial networks suggests an innovative field of research, with valuable insight to explain the phenomena that intervene in corporate governance questions. While the present study contributes expansion of the field of corporate governance, recently published works in the finance area have pointed to the contribution that such research describing the informal mechanisms of governance (as corporate networks are) can lead to a better understanding of governance models around the world, based on the complexity of corporate networks (Rossoni et al., 2018).

In addition, the dynamics of those networks shows an explicit growth across the time; this can be observed in Figs. 14.4 (2007) and 14.5 (2015). For an elucidatory discussion of this view, it is recommended that the texts of Fracassi and Tate (2012), Cohen et al. (2010), and Stafsudd (2009) be reviewed. Among aspects that might contribute to a better understanding of interlocking phenomenon, one can mention the presence of board directors who represent the interests of investors and economic groups (this was not dealt with in this research).

Fig. 14.5

Board members network in the Brazilian capital market (2015). Note: Each node represents one of the 1992 board members on listed firms in Brazil in 2015, and each tie implies at least a board shared between the board members