Directors’ social networks and firm efficiency: A structural embeddedness perspective

Abstract

The performance of firms is usually influenced by their structural embeddedness in social networks. This paper investigates the effects of structural hole positions of directors on their firms’ operating and investing efficiency, from a corporate finance perspective. We build an interlocking network of the directors in Chinese listed companies, and compute the network constraint index to represent the richness of structural holes in this network. The empirical results show that firms with more structural holes are more efficient in both operating and investing activities (through the channel of reducing their firms’ under-investment problems), and these relations are more pronounced in competitive industries. Further tests find that firms with more structural holes perform better over time. The results suggest that a firm’s ‘structural hole position’ plays an important role in firm efficiency. These findings provide new evidence for the emerging literature of social networks and corporate finance.

Keywords:

• board network
• investing efficiency
• operating efficiency
• social tie
• structural hole

1. Introduction

Research shows that the heterogeneity of firms’ internal resources can lead to different levels of operating and investing efficiency (Liu, Fu, & Qiu, 2011). However, this view arises mainly from the perspective of static resource heterogeneity, and ignores the possibility of resource acquisition from the external environment, namely, a dynamic social network and its effects on firm efficiency. This paper focuses on directors’ social ties, and investigates the role of firms’ social networks in their operating and investing activities. In the social network field, the concept of ‘network’ involves two dimensions: network relation and network structure. Burt (1979) was the first to study the connections between firms’ directors, and to examine the effects of these social connections on firm efficiency from a structural perspective. In Structural holes: The social structure of competition (1992), Burt systematically introduces the concept of the ‘structural hole’. He explains that there are some individuals who cannot contact each other directly, and describes these network contacts as holding disconnected positions. These disconnections can be regarded as holes in the overall network structure. In this kind of network, individuals who are in the core positions of structural holes can connect with different people, and thus have advantages in both information and control. Such advantages are helpful for enhancing a firm’s power in market competition. In management studies, structural hole theory is used to explain various phenomena, especially strategic management (Liu et al., 2011; Qian, Yang, & Wu, 2010; Shipilov, Rowley, & Aharonson, 2006; Walker, Kogut, & Shan, 1997). From the perspective of resource dependence, a firm’s operating and investing activities can be significantly influenced by the acquisition of social capital from its social network (Liu et al., 2011; Cai & Sevilir, 2012). From a sociological perspective, social networks comprise two components: network relations and network structures (Granovetter, 1992). Analyses of these two components are called the ‘relation embeddedness view’ and the ‘network structural hole position view’, respectively. The corporate finance literature mainly discusses the existence and strength of network relations, that is, whether firm relations exist or how strong these relations are, as in the works of Engelberg et al. (2012), Fracassi and Tate (2012) and Larcker et al. (2013). However, the network structural hole position view focuses on the strategic position of individuals in a social network, and emphasises the roles of intermediates and bridges. Granovetter (2005) points out that under various conditions, the most important factor is not the network relation itself, but the structural position of bridges connecting different social networks. So according to the two dimensions of social network, related studies are divided into a ‘relation embeddedness view’ and ‘network structural hole position’ view. Prior research, such as that of Cai and Sevilir (2012), Larcker et al. (2013) and Chen and Xie (2011, 2012), finds that a director’s network relations can help a firm to gain greater social capital, while a director’s network structures, such as the structural hole position in a network, can also improve a firm’s efficiency. The structural hole position carries the advantages of both information and control (Burt, 1992, p. 34). To my knowledge, there are few studies on the role of social network structural positioning in corporate finance and accounting, so this paper attempts to fill this gap by investigating the relation between directors’ network hole positions and firms’ operating and investing efficiency in China.

In social networks, organisations are embedded in an environment that constitutes various relations, and their resource acquisition channels depend mainly on the networks of other actors. Therefore, a firm can develop a firm-level network through its director-level network, that is, the network created by the directors’ or executives’ personal networks. The purpose of this paper is to explore the differences in efficiency among firms with various structural hole positions in their directors’ interlocking networks. A secondary purpose of the paper is to compute the network constraint index that represents the value and richness of structural hole positions. Based on data from all Chinese A-share listed companies between 2001 and 2011, the empirical results show that firms with more structural holes operate and invest more efficiently, and this effect is more pronounced in competitive industries. Further tests find that firms with more structural holes are more likely to perform better over time, and that a firm’s structural hole position plays a key role in the firm’s operating and investing activities.

This paper contributes to the accounting and finance literature in the following ways. First, there are few studies on firms’ network structural positions in the field of corporate finance. In addition, existing studies on organisational and strategic management are usually based on small sample sizes, in which the real networks may be artificially severed. This paper is among the first to employ a large sample of Chinese firms, and finds that a firm’s network position disparity influences firm efficiency. Second, although there are a few emerging studies involving crossover investigations of social networks and corporate finance, most of these studies are based on the ‘relation embeddedness view’, which assumes that the directors’ power becomes stronger with more network relations. However, this assumption ignores the important role of network structural position. This paper adopts a ‘network structural hole position’ view, and extends social network analysis in the corporate finance literature.

The remainder of this paper is organised as follows. Section 2 presents a literature review and develops the hypotheses. Section 3 lays out the research design, and Section 4 follows up with supporting empirical evidence. Section 5 provides some conclusions.

2. Literature review and hypothesis development

2.1. Research on structural hole position and corporate finance

Several researchers focusing on international strategic management have found that network strategic positions among firms can influence their strategy and performance (Walker et al., 1997), market share (Baum, Rowley, Shipilov, & Chuang, 2005; Shipilov et al., 2006), patents (Ahuja, 2000), and knowledge transfer (Reagans and McEvily, 2003). Other scholars focus on the intra-firm structural hole position, and demonstrate that the CEO’s position in a firm affects its corporate governance efficiency (Mitchell, 2005). However, studies related to firms’ network positions remain very limited: Yao and Xi (2008) investigate the relations between the structural holes of executives’ consulting networks and their firms’ competition advantages, and find out that there is a positive relation. Qian et al. (2010) collect integrated circuit industry data from Shenzhen City, and argue that firms located in the centre of their networks are more innovative, and thus benefit more from innovation because of their network positions. Liu et al. (2011) illustrate that network resources gained from social networks are positively correlated with a firm’s diversification. They measure this correlation by adopting both centrality and structural hole measurement to represent firms’ network positions. Cai and Sevilir (2012), Chen and Xie (2011, 2012), Fracassi (2013) and Larcker et al. (2013) examine relationships between board network centrality and corporate governance activities such as investment, M&A, executive compensation and stock returns. It should be kept in mind that the measurement of network centrality is based only upon the strength of network relations, without distinguishing whether the relations are redundant. This kind of measurement also ignores network structural embeddedness, which is also the core component of a social network. In summary, studies that connect network structural positions and corporate activities are still lacking.

2.2. Structural hole position and firm behaviour

Burt (1992, p. 19) points out that social networks contain some individuals who cannot directly contact others. These people hold disconnected positions in their social networks, and such disconnections are called structural holes, as they are like holes in the entire network. Networks consist of various weak ties. Hence, they are full of structural holes. People in the core positions of structural holes, who do hold the connections, can obtain more information and resources, and those who build up connections with people who are formally disconnected enjoy both information and control advantages. The same situation applies within a firm’s network, in which various firms enjoy different advantages through holding different positions within their networks. As organisations are embedded in environments with diverse social networks, their specific resource access channels are obtained from the networks of individuals within those organisations. In other words, the network relations of a firm need some kinds of instrumentalities or intermediates. As Burt (1983) states, the structure of a director’s ties offers a non-market environment for a firm’s business transactions. Jackson (2008) refers to the analysis of such ties as ‘actor-based modelling’. Distinctions between individual-level network input (of board directors) and organisation-level network output (of the firm) are commonly made in social network research. For instance, Larcker et al. (2013) compute firms’ network centrality (in terms of degree, betweenness, closeness and eigenvector) based on the interlocking directors. The extant research also examines the influence of firm networks on stock returns. Fracassi (2013) takes the social ties of board directors (from current employment, former employment, education, and other relations) as a basis for generating a firm-level social network, and then analyses the influence of firms’ social networks on the convergence of corporate policies. It is necessary to note that there are different types of structural holes in different positions within the industrial chain. These ‘holes’ have distinctive roles in shaping corporate behaviour. However, as most firms act as suppliers, producers and customers at the same time, it becomes difficult to differentiate these types of networks in empirical studies. In addition, it is hard to determine whether a director’s social ties lie in the same areas of the industrial chain as those of the firm’s suppliers, producers and customers. Hence, in studying a firm’s structural hole position in terms of its directors’ network, this paper mainly focuses on the dimension of the producer role. So our paper mainly discusses networks of director-level relations among firms that are generated by interlocking. As shown in Figure 1, we assume that there are sub-networks A and B. In network A, firms A1, A2, A3, A4 and O1 do not directly contact each other. Instead, they build up relations indirectly through firm A5. That is to say, these five firms can only communicate with each other through firm A5, so that A5 occupies ten structural hole positions: A1-A2, A1-A3, A1-A4, A1-O1, A2-A3, A2-A4, A2-O1, A3-A4, A3-O1 and A4-O1. In this case, sub-network A is full of structural holes, and A5 can obtain resource advantages from its core position. However, in sub-network B, firms B1, B2, B3, B4 and O1 are connected with each other directly or can be connected through more than one firm’s help, which means without any firm in sub-network B, other firms can also contact, so they form a non-hole network. In this kind of network, information and resources are similar and redundant among different firms, and the firms cannot control each other’s communicating channels. In both sub-networks A and B, firm O1 functions as the ‘bridge’, and controls more structural holes than firm A5. According to the definition of a structural hole, firms O1 and A5 undoubtedly control other firms’ communications. In addition, firm O1 further links two sub-networks, and is classified as a weak tie. In this type of network, firms that hold a key structural hole position can easily obtain more resources (Qian et al., 2010; Yao et al., 2008).

Figure 1. A firm’s structural hole position generated by the directors’ social networks.

In corporate activities, competition is a key factor in improving firm efficiency, and information access is one of the most important channels for winning competitions. Members that do not directly contact others cannot access information-sharing channels due to the existence of structural holes, so their information is heterogeneous and redundant. Thus, they may rely on a third member, who connects them as a bridge, to obtain benefit from the third member’s information diversity and competitive advantages. Burt (1992, p. 38) classifies the benefits of structural holes into two types: information advantages and control advantages. Information advantages may be further classified by whether they relate to access, timing or referrals. An access advantage can help a firm get more valuable information, reduce its information collecting costs, and improve its efficiency in collecting and transferring information. A timing advantage allows firms to acquire information earlier. A referrals advantage can help firms gain more opportunities and resources through introductions, communications and referrals. Having a control advantage means that the broker who builds a bridge that links a number of firms can decide whose benefit should be taken care of first.

When a firm obtains a social network that is full of structural holes, it acts as a bridge in the firm-level network between directors who hold central positions in their networks. Such firms usually act as the mediators to contact other firms that used to be disconnected. Firms in the bridge position have more network centrality. They also hold more information transformation and business opportunities, or intermediary interests. We describe the benefits that such bridging firms obtain from their operating and investing activities in the following sections.

2.3. Structural hole positions and the improvement of a firm’s operating efficiency: A control advantage perspective

Firms’ operating activities usually face imperfect competition, mainly because different firms with various strategic network positions obtain their resources differently. If a firm wants to improve its operating efficiency, it must get benefits from holding different positions in the industrial chain (such as ‘supplier-producer-seller’) and then reduce transaction costs at every stage of the chain (Yao & Xi, 2008). These constraints, which most firms generally face, are determined by the transaction networks between suppliers and customers. In this situation, a firm’s social network can make those transactions easier. Firms in the centre of a structural hole can use the control power embedded in their network to reduce their transaction costs (Stevenson & Radin, 2009). For instance, in the material purchasing stage, the firm can take advantage of its network control power to reduce purchasing costs and shorten the time needed to make purchases, thereby accelerating its material turnover rate. In the goods selling stage, a firm holding a structural hole position is more powerful in bargaining with customers in the market, which is helpful for increasing sales and improving its operating income. More importantly, firms with dominant structural hole positions can withdraw cash from customers more quickly, thus reducing transaction costs. These firms can accelerate the operating cycle, and thereby further improve operating efficiency. In a firm’s operating activities, the most inefficient factor is the uncertainty of uncontrollable transactions (Yao & Xi, 2008). Firms with dominant structural hole positions can strengthen their control and reduce this uncertainty. However, a firm that is at the edge of the network typically faces a greater danger of being kicked out of the core network and lacking bargaining power over suppliers and customers (Burt, 1992). Therefore, these peripheral firms tend to suffer from greater uncertainty and larger transaction frictions, which ultimately lower their operating efficiency.

In addition, firms in dominant structural hole positions can aggregate diversified information and generate collaborating opportunities (Lin, 2002, p. 61). Their multiple links for collaboration result in their interdependence among other firms, which increases trust while decreasing information asymmetry, and therefore improves the quality of collaboration. Hoskisson, Hitt, and Hill (1993) point out that intra-firm knowledge or information transformation can help diversified enterprises to reduce their operating costs. In summary, we have the first hypothesis as follows.

H1:

The operating efficiency of firms occupying a dominant structural hole position in their directors’ network is greater than that of firms without such a position.

2.4. Structural hole positions and the improvement of a firm’s investing efficiency: An information advantage perspective

The influence of a firm’s structural hole position on its investment activities is mainly effected through an information gathering advantage. Investment inefficiency can involve either over-investment or under-investment, which are mainly caused by managers’ opportunistic incentives (Jensen, 1986; Stulz, 1990) or information asymmetry (Fazzari, Hubbard, & Petersen, 1988; Xu & Zhang, 2009) respectively. The flow of information within the social network can significantly change a firm’s investment activity. Larcker et al. (2013) find that a central position in a board’s network can help directors get more relevant information, but members at the network’s edge positions can only rely on others to transfer information (Freeman, 1979). When it comes to investment decision-making, the learning effect causes information and academic knowledge from different firms to disseminate among social network members (Westphal & Seidel, 2001; Zaheer & Bell, 2005). If a firm is in the key position within its network, it plays the role of ‘intermediary’ and ‘bridge’, and can therefore get more accurate and timely information related to investment activities (Granovetter, 1985). Specifically, the directors of firms in a dominant structural hole position may serve as directors in other firms at the same time. This interlocking relationship helps these directors to observe the decision-making processes of other firms as they conduct similar investing activities. These directors may communicate with other directors about similar investing experiences (Cai & Sevilir, 2012). Sometimes a director with few direct connections can still earn an information advantage through good communications with other directors who have more network relations (Bonacich, 1972). As a result, they can better understand the merits, growth prospects and risks related to their investment efficiency.

More importantly, a firm has to command more heterogeneous information to obtain an excess profit. Bridge firms always hold weak ties with other firms through which they can get more heterogeneous information from their networks (Granovetter, 1985) and avoid convergent investment. The reason for a high value on weak ties is that these ties play the key role in connecting groups, organisations, and society, so that they can transfer non-redundant information and knowledge; while the strong ties in a group exist mainly to protect the inter-organisation relationship. Moreover, the access and referral benefits of a structural hole position give an information advantage in the ‘timing’ of competition, that is a ‘one-step ahead’ competitive advantage, to use the term proposed by Burt (1992, p. 115). In a competitive environment, good investment opportunities fade away so quickly that if a firm cannot respond rapidly enough, it lags behind other firms in seizing the opportunities, and the return on its investment declines (Chen & Xie, 2011). In this sense, speed in gathering information about good investment projects is critical. If a firm’s directors occupy more structural hole positions, those directors can control more channels of information about good investment opportunities, and can give timely advice to their boards and managers, thereby obtaining the ‘one-step ahead advantage’ in investment activities (Burt, 1992). This timing benefit is the direct result of an information advantage in investment decision making. From this perspective, the second hypothesis emerges as follows.

H2:

Firms occupying a dominant structural hole position within the directors’ network outperform other firms in investing efficiency.

The network effect is also influenced by each actor’s characteristics (Burt, 1992, p. 71), and the degree of industry competition is another core factor in a firm’s operating and investing efficiency (Wang, 2011). Therefore, the effect of a structural hole depends partly on the industry competition that the firm confronts. In monopoly industries, a firm can rely on its monopoly status to obtain advantages in operating and investing activities (Wang, 2011). In this circumstance, the influence of information acquisition and control advantage through the director’s network is less significant. The firm would therefore take advantage of its monopoly position instead of its structural hole position during the negotiation process. However, in competitive industries, a strategic network position can result in stronger structural autonomy, as most firms cannot gain excess profits easily through the advantage of a direct monopoly position (Zaheer & Bell, 2005). This means that a firm in a strategic network position can obtain a larger market share and make more efficient investments. Compared with monopoly industries, firms in competitive industries rely more on structural hole positions to gain favourable resources. Hence, the third hypothesis is as follows.

H3:

The positive relation between a structural hole position and operating/investing efficiency is more pronounced for firms in more competitive industries than for firms in monopoly industries.

Although most evidence from analytical and empirical studies supports the positive effect of a structural hole, some studies indicate negative effects. For example, Shipilov and Li (2008) find that although a network can facilitate the gathering of information, the network may also restrict information for business partners if a lack of trust and poor resource-sharing prevents the firms in key network positions from concentrating on collaboration and performance improvement. The results of our empirical tests (e.g., Chen & Xie, 2011, 2012) indicate that at least within the Chinese context, the structural hole has a mainly positive effect. However, as the structural hole may bring about negative effects due to the firm’s outside-network environment, we distinguish market competition based on H1 from that based on H2. We are aware of the negative effect that a structural hole can cause, and hope to provide more in-depth evidence on this potential of structural holes in the future.

3. Research design

3.1. Measurement of structural hole position

Having social capital can be redefined from the structural hole perspective as having a position to act as a ‘bridge’ between network members, and therefore enjoying advantages in both information and control through connecting those who cannot directly connect each other. In studying such social capital, the key question is how to measure the structural hole position of a member in a social network, as the presence or absence of structural holes determines the potential availability of information and control advantages. Before measuring a structural hole, we must define a direct link between two firms (Freeman, 1979). By ‘direct link’, we mean a tie in which one or more directors/managers of a firm serve on the board of another firm in the same year. In that case, we assume that the two firms communicate with each other directly, and a network based on this direct link is referred to as the firm’s social network, which is generated from the directors’ interlocking ties. We compute structural hole positions based on the directors’ interlocking networks in Chinese listed companies. In these companies, most of the CEOs also serve on the boards, so the directors’ networks usually include the corporate executives. This method of measuring individual-level networks (of board directors) to represent the organisation-level networks (of firms) is common in social network studies (Jackson, 2008; Larcker et al., 2013).

We assume (as Figure 2 illustrates) that firm A has four directors: I11, I12, I13 and O1. Firm B also has four directors: I21, I22, I23 and O2. Firm C has five directors: I31, I32, I33, O1 and O2. Director O1 serves in both firm A and firm C, and also links firms A and C directly through the path of 1 which means two actors connect to each other directly whereas path of 2 means two actors are linked indirectly through the help of a third actor. Similarly, director O2 serves in both firm B and firm C, and also links firms B and C directly through the path of 1. However, O2’s position is different from that of O1; firm A and firm B do not contact with each other directly without the communication of O2, so there is a ‘hole’ in the social network among the three firms. In this case, firm C acts as a bridge, due to the interlocking status of directors O1 and O2.¹

Figure 2. Generation of firms’ network and structural hole positions, based on director-level networks.

Like Burt (1992, p. 54) and Zaheer and Bell (2005), we measure the structural hole using the following model:(1)

where i means the firm being studied in the social network, j means the other firms in the network, excluding firm i, and q means a firm other than i or j, namely . If firm i and firm j share a director, then they have a direct relationship through the path of 1. Thus, P_ij represents the strength of the paths from firm i to firm j, which indicates direct relations between firm i and firm j. However, ∑P_iqP_qj represents the summed strength of the indirect network relations between firm i and firm j that pass through firm q, which indicates that firm i indirectly relates to firm j. The variable C_ij represents constraints on firm i’s effort to communicate with firm j, namely the ‘network constraint index’.

There are two indices used in measuring structural holes: the structural hole index (including factors of efficient size, efficiency, constraints and rank), and the betweenness index. Both measures have their own advantages, but the network constraint index is more widely used (Liu et al., 2011). It is a comprehensive index that efficiently measures the deficiency of structural holes. An increase in the value of the network constraint index indicates a decrease of structural holes, which indicates that the firm concerned is at the edge of its network. A firm’s performance is usually negatively correlated to its network constraint index (Burt, 2004). The largest value of this index is one, so researchers always use the difference between one and the constraint index to represent the richness of structural holes (Burt, 1992; Zaheer & Bell, 2005), calculated as follows:(2)

Using the new index, there is a positive relation between CI_i and the richness of structural holes.

3.2. Research model and the definition of main variables

After constructing the measurement of structural holes, the relation between a firm’s network position and its operating and investing efficiency is reflected in the following models:(3) (4)

Here, model (3) is used to test Hypothesis 1, that is, the relation between structural hole position and operating efficiency. The speed of asset turnover represents the efficiency in converting assets into sales and cash through the ‘supplying-producing-selling’ operating chain. In particular, the relative differences between particular peer firms can be captured by the heterogeneity of control power that each firm has in the operating chain (Li, 2007). We use both the raw value (turnover) and the industry-adjusted value (turnover_adj) of asset turnover to capture firm operating efficiency (Li, 2007). Our classification of industries follows the CSRC’s 2001 standard of listed firms. This standard divides the manufacturing sector into ten groups using the 2-digit-SIC code, and other firms into 11 groups using the 1-digit -SIC code.

Model (4) is used to test Hypothesis 2, that is, the relation between structural hole position and investing efficiency, which is estimated using the model in Richardson (2006):(5)

We use the residual of Model (5) to represent investing efficiency, where INV_t is the amount of investment of a firm in year t, defined as the change in fixed assets, construction in progress, intangible assets and long-term investments, scaled by the average total assets; the construction of INV_t is based on balance sheet data, and we use data from cash flow statements to construct INV in the robustness tests. The variable Q_t-1 represents a firm’s growth opportunity at the end of year t–1, defined as the sum of the year-end market value of its equity and the book value of its liabilities, scaled by total assets. Cash_t-1 is a firm’s cash holdings, defined as cash and cash equivalents, scaled by total assets at the end of year t–1. ListY_t-1 is the listing age of the firm at the end of year t–1. Size_t-1 and Lev_t-1 are the logarithm of total assets and the leverage at the end of year t–1, respectively. RET_t-1 is the cumulative monthly return, adjusted by the market return from May in year t–1 to April in year t. INV_t-1 is the total investment in year t–1. To eliminate the industry and year effect, we regress the model for each industry-year separately. If the residual of the model is positive, it indicates over-investment (overINV). If the residual of the model is negative, it indicates under-investment (underINV). Note that in the following analysis we multiply underINV by –1, which means that the larger the value of underINV, the more severe the under-investment. We use the absolute value of underINV and overINV to represent the magnitude of investment efficiency. Following Biddle, Hilary, and Verdi (2009), Chen, Hope, Li, and Wang (2011), Chen (2011b), Chen and Xie (2011), and Li (2007), as firm’s corporate governance can affect firm efficiency, we control for board size (number of board directors at the end of year t), the proportion of independent directors on the board at the end of year t (OUT), the natural log of the total compensation of the top three executives (COMP) and duality (DUAL – a dummy variable that equals 1 if the chairman and CEO are the same person, and 0 otherwise); firms’ ownership also affect firms’ performance, so we control for SOE (a dummy variable that equals 1 if the state controls the firm, and 0 otherwise), SHR1 (the percentage of shares held by the largest stockholder at the end of year t) and SEP (the separation of cash flow rights and control rights at the end of year t); we also control for firms’ other characteristics, namely SIZE (the natural log of total assets at the end of year t), LEV (the ratio of total liabilities to total assets at the end of year t), ROA (return on assets in year t) and CATA (ratio of current assets to total assets at the end of year t). The definitions of these variables are shown in Table 1. The control variables used in various previous studies are different. One reason might be the differences in the targets of each study. To make our results robust, we add each of the corporate governance and firm characteristic variables into one or more of our models. For example, in Model (3) we add long-term investment ratio, accounts receivable turnover, and inventory turnover. In Model (4) we add operating cash flow, management fee ratio and other receivables. These further analyses do not influence our main results. In Model (3) and Model (4), we expect CI to be positive, which means that the operating and investing efficiency of firms with a dominant structural hole position in their directors’ network is greater than that of firms not in such a position.

Table 1. Variable definitions.

Variable name	Definition
Dependent variables
Operating efficiency	Operating efficiency, both the raw value (turnover) and industry-adjusted value (turnover_adj) of asset turnover of year t, defined as sales divided by total assets.
Investing efficiency	Investment efficiency. For details regarding the computing process, please see Richardson (2006). As described before, we divide this variable into overINV and underINV as well.
Independent and control variables
CI	Network constraint index. For detailed definition, please see 3.1, Computed using Pajek software.
IHHI	The Herfindahl index of industry concentration at the end of year t, calculated as the sum of squared sales, divided by the square of the sum of sales.
BOARD	The number of directors on a board at the end of year t.
OUT	The proportion of independent directors to all board directors at the end of year t.
COMP	The natural log of the total compensation of the three executives with the highest compensation.
DUAL	Equals 1 if the chairman and CEO are the same person, and 0 otherwise.
SOE	Equals 1 if the state controls the firm, and 0 otherwise.
SHR1	The proportion of the shares held by the largest stockholders among all shares outstanding at the end of year t.
SEP	The separation of cash flow rights and control rights at the end of year t.
SIZE	The natural log of total assets at the end of year t.
LEV	The ratio of total liabilities to total assets at the end of year t.
ROA	Return on assets in year t.
ROE	Return on equity in year t.
CATA	Ratio of current assets to total assets at the end of year t.
IND/YEAR	Industry and year dummy. The classification of industries follows the CSRC’s 2001 standard of listed firms. This standard divides the manufacturing sector into 10 groups using the 2-digit-SIC code, and other firms into 11 groups using the 1-digit -SIC code

3.3. Data

We collect data from 2001 to 2011 on Chinese A-share listed firms. After removing the financial industries and the observations with missing data, the final sample contains 10,415 firm-year observations.

To maintain the integrity of the network, we include all A-share listed firms when computing the network constraint index of structural holes.² Information on directors is manually collected (to determine whether directors with the same name are actually the same person), and the other data are from the CSMAR database (http://www.gtarsc.com), a financial and stock trading database widely used in Chinese studies. The process of computing the networks generated by directors is as follows. First, we calculate the number of board seats of directors for each year, and also identify which directors have direct relations through sitting on the same board. If directors have such a relation, then their connecting path is marked as 1, that is, they have a direct network relationship. Second, we identify the indirect relations stemming from the direct network relations. Third, we integrate both the direct and indirect network relations for the whole board network. Next, we compute the network constraint index in the following way. First of all, we give every director a unique ID, and convert the data into a ‘firm-director’ one-mode matrix. After that, we import the matrix into Pajek using the ‘txt2pajek’ software (Fracassi, 2013; Fracassi & Tate, 2012),³ and compute the network constraint index. To eliminate the effect of extreme values, we winsorise all continuous variables at the 1% and 99% levels and build a cluster for the model at the firm level.

4. Main results

4.1. Descriptive analysis⁴

The statistical analyses of the main variables are shown in Table 2. The mean value of CI is 0.26, and the difference between the maximum and minimum value of CI is 0.789, which means that the disparity is large. This disparity facilitates our study. The means of turnover and turnover_adj are 0.676 and 0.102, respectively, and the mean value of investing efficiency is 0.063.

Table 2. Descriptive statistics.

Variables	Obs.	Mean	Median	Max.	Min.	Std.
CI	10415	0.262	0.000	0.789	0.000	0.295
turnover	10415	0.676	0.557	2.246	0.054	0.485
turnover_adj	10415	0.102	0.000	2.027	-0.730	0.462
absINV	10415	0.063	0.045	0.278	0.001	0.061
overINV	4952	0.059	0.046	0.148	0.000	0.047
underINV	5463	-0.059	-0.044	0.000	-0.208	0.053
BOARD	10415	9.306	9.000	15.000	5.000	2.017
OUT	10415	0.310	0.333	0.556	0.000	0.121
COMP	10415	13.277	13.356	15.283	10.913	0.951
DUAL	10415	0.163	0.000	1.000	0.000	0.369
SOE	10415	0.553	1.000	1.000	0.000	0.497
SHR1	10415	38.516	36.550	100.000	0.160	16.148
SEP	10415	5.539	0.000	53.424	0.000	8.064
SIZE	10415	21.333	21.198	24.196	19.126	1.105
LEV	10415	0.488	0.485	1.172	0.074	0.227
ROA	10415	0.030	0.035	0.169	-0.243	0.069
CATA	10415	0.548	0.558	0.971	0.078	0.216

4.2. Results of multivariate regressions

To better understand the issue, we multiply underINV by –1, so that the larger the underINV, the more severe the underinvestment. The results of Models (3) and (4) are shown in Table 3.

Table 3. Relation of structural hole position and operating/investing efficiency.

	turnover	turnover_adj		absINV	(–1)^*underINV	overINV
CI	0.059^**	0.062^**		0.002	–0.005^**	0.007
	(2.17)	(2.15)		(0.67)	(–2.17)	(1.40)
BOARD	0.004	0.003		–0.001	–0.001^**	–0.000
	(0.73)	(0.54)		(–1.33)	(–2.14)	(–0.46)
OUT	–0.110	–0.141		0.026	0.007	0.017
	(–0.74)	(–0.91)		(1.49)	(0.52)	(1.19)
COMP	0.096^***	0.094^***		–0.003^**	–0.003^***	–0.001
	(7.27)	(6.44)		(–2.51)	(–3.33)	(–0.71)
DUAL	–0.011	–0.016		–0.000	0.001	–0.001
	(–0.46)	(–0.68)		(–0.08)	(0.20)	(–0.52)
SOE	0.091^***	0.088^***		–0.006^***	–0.007^***	–0.003^*
	(4.13)	(3.68)		(–2.78)	(–3.13)	(–1.91)
SHR1	0.002^***	0.002^***		0.000^***	0.000^***	0.000^*
	(3.37)	(3.40)		(2.68)	(2.82)	(1.68)
SEP	0.001	0.001		–0.000	–0.000	–0.000
	(1.13)	(0.97)		(–0.59)	(–0.32)	(–0.94)
SIZE	0.015	0.020		–0.004^***	–0.003^***	–0.003
	(1.31)	(1.61)		(–3.33)	(–2.95)	(–1.57)
LEV	0.249^***	0.257^***		0.001	0.009^**	–0.002
	(5.09)	(4.81)		(0.17)	(2.46)	(–0.51)
ROA	1.286^***	1.308^***		–0.024	0.022^**	–0.031^*
	(11.07)	(10.65)		(–1.62)	(2.11)	(–1.72)
CATA	0.535^***	0.581^***		–0.045^***	–0.068^***	–0.024^***
	(9.40)	(9.29)		(–8.23)	(–15.85)	(–5.81)
Cons	–1.678^***	–2.159^***		0.211^***	0.209^***	0.135^**
	(–6.67)	(–8.01)		(8.38)	(9.57)	(2.04)
Ind/Year	yes	yes		yes	yes	yes
R^2_adj	0.319	0.177		0.063	0.106	0.038
F-Value	30.94	13.89		8.81	27.34	3.24
Obs.	10415	10415		10415	4952	5463

Note:

^*** ,

^** , and

^* indicate 0.01, 0.05, and 0.10 significance levels, respectively. The results are clustered at the firm level.

The first two columns illustrate the relation between structural hole position and firm’s operating efficiency. CI is positively correlated with both turnover and turnover_adj at the 5% level, which also supports hypothesis 1. Columns 3 to 5 illustrate the relation between structural hole position and firm’s investing efficiency. This relation is not significant when the dependent variable is absINV, which means that there is no obvious correlation between a firm’s structural hole position and its overall investment efficiency. However, if we divide the investing inefficiency into over-investment and under-investment, the coefficient on CI is negatively significant when the dependent variable is underINV, and insignificant when the dependent variable is overINV. This finding shows that the firm’ structural hole position can help gain information and opportunities, which further helps reduce under-investment. A core network structural position endows a firm with an information advantage, especially for investing activities. When dependent variable is turnover or turnover_adj, the coefficients on SOE, ROA and LEV are significantly positive, and the coefficients on BOARD, DUAL and OUT are insignificant; when dependent variable is absINV, the coefficient on SIZE is significantly negative, and the coefficients on BOARD, DUAL and OUT are also insignificant. The results show that firms’ corporate governance are not related to firm efficiency. The reason may be the convergence of firms’ corporate governance mechanisms (Chen, 2011a).

Table 4 shows the results from the subsamples of monopoly and competitive industries. As in Table 2, IHHI is the Herfindahl index of industry concentration at the end of year t, calculated as the sum of squared sales, divided by the square of the sum of sales. In order to generate a partition variable, we define HHI as a dummy variable, which equals 1 if the value of IHHI is greater than the median value of all industries, and 0 if otherwise. Hence HHI with the value of 1 represents the monopoly industries. The first two columns illustrate the relation between a structural hole position and operating efficiency in various industries (the dependent value is turnover_adj). We can see that the coefficient on structural hole position is significantly positive in competitive industries, but is insignificant in monopoly industries. This finding suggests that in competitive industries, having a structural hole position enhances operating efficiency. The last two columns describe the relations between a structural hole position and investing efficiency in different industries (the dependent value is underINV). Similarly, in competitive industries the coefficient of CI is significant, and there is no obvious relation in monopoly industries. These results support Hypothesis 3, that the positive relation between a structural hole position and operating efficiency (or investing efficiency) is more pronounced for firms in competitive industries.

Table 4. Product market competition, structural hole position and operating/investing efficiency.

	HHI=0	HHI=1		HHI=0	HHI=1
	turnover_adj	turnover_adj		underINV	underINV
CI	0.071^***	0.020		–0.004^*	–0.006
	(3.42)	(0.67)		(–1.74)	(–1.31)
BOARD	0.005	0.000		–0.000	–0.001
	(1.64)	(0.10)		(–0.64)	(–1.60)
OUT	–0.201^*	–0.038		0.009	0.002
	(–1.77)	(–0.24)		(0.66)	(0.09)
COMP	0.082^***	0.111^***		–0.000	0.001
	(9.85)	(8.84)		(–0.25)	(0.47)
DUAL	–0.023	–0.017		–0.003	0.000
	(–1.33)	(–0.68)		(–1.53)	(0.11)
SOE	0.090^***	0.088^***		–0.006^***	–0.000
	(6.88)	(4.30)		(–3.55)	(–0.09)
SHR1	0.002^***	0.002^***		–0.000	0.000^**
	(6.09)	(3.67)		(–0.47)	(1.96)
SEP	0.001^**	0.001		0.000	–0.000^**
	(2.04)	(1.10)		(1.32)	(–2.53)
SIZE	0.029^***	0.003		–0.003^***	–0.003^**
	(4.45)	(0.32)		(–2.99)	(–2.44)
LEV	0.249^***	0.151^***		0.011^***	0.014^**
	(8.46)	(3.76)		(2.72)	(2.16)
ROA	1.450^***	0.963^***		0.058^***	0.058^***
	(15.14)	(7.16)		(4.78)	(2.82)
CATA	0.400^***	0.488^***		–0.035^***	–0.036^***
	(14.07)	(13.45)		(–9.70)	(–6.59)
Cons	–2.174^***	–1.928^***		0.108^***	0.112^***
	(–15.29)	(–9.66)		(6.22)	(3.87)
Ind/Year	yes	yes		yes	yes
R^2_adj	0.161	0.154		0.033	0.044
F-Value	66.89	22.91		10.05	4.69
Obs.	7634	2781		3675	1277

Note:

^*** ,

^** , and

^* indicate 0.01, 0.05, and 0.10 significance levels, respectively. The results are clustered at the firm level.

4.3. Additional analysis

Burt (1992, p. 34) argues that the information and control advantages obtained from a structural hole position can further improve a firm’s performance over time. To test whether this is true in the network of firm directors, we investigate whether firms located centrally in a structural hole position improve their performance in years t+1 and t+2. We use both ROA and ROE as our proxies for performance. As shown in Table 5, the relation between CI and performance in year t+1 and year t+2 are both positive at the 5% and 10% levels. Moreover, in untabulated analysis we use the change in ROA and ROE to measure a firm’s performance, and find that ROA changes and CI are positively correlated at the 5% level in year t+1. In addition, ROE changes and CI are positively correlated at the 10% level in year t+1. However, these correlations are not significant in year t+2. These additional tests strongly support our main results.

Table 5. Structural hole position and future performance.

	Year t+1			Year t+2
	ROA	ROE		ROA	ROE
CI	0.0054^**	0.0158^**		0.0046^*	0.0148^*
	(2.30)	(1.99)		(1.82)	(1.80)
BOARD	0.0002	0.0005		0.0000	0.0005
	(0.66)	(0.43)		(0.03)	(0.41)
OUT	0.0095	0.0736		–0.0250	0.0375
	(0.73)	(1.64)		(–1.39)	(0.78)
COMP	0.0117^***	0.0360^***		0.0127^***	0.0347^***
	(11.88)	(10.78)		(11.14)	(9.95)
DUAL	–0.0040^**	–0.0130^*		–0.0044^*	–0.0139^**
	(–2.05)	(–1.95)		(–1.78)	(–2.00)
SOE	–0.0061^***	–0.0185^***		–0.0068^***	–0.0163^***
	(–3.91)	(–3.51)		(–3.89)	(–2.94)
SHR1	0.0004^***	0.0010^***		0.0004^***	0.0009^***
	(8.19)	(6.91)		(7.90)	(5.90)
SEP	–0.0002^***	–0.0008^***		–0.0001	–0.0002
	(–2.78)	(–2.89)		(–0.74)	(–0.80)
SIZE	–0.0023^***	0.0056^**		–0.0032^***	0.0034
	(–3.01)	(2.05)		(–3.38)	(1.17)
LEV	–0.0240^***	–0.0899^***		–0.0278^***	–0.0797^***
	(–7.01)	(–6.71)		(–5.09)	(–5.60)
CATA	0.0031	0.0623^***		–0.0016	0.0492^***
	(0.83)	(4.81)		(–0.43)	(3.59)
ROA	0.3756^***			0.2042^***
	(33.95)			(10.83)
ROE		0.2364^***			0.1011^***
		(19.32)			(7.92)
Cons	–0.0945^***	–0.6084^***		–0.0573^***	–0.5881^***
	(–5.62)	(–10.32)		(–2.75)	(–9.79)
Ind/Year	yes	yes		yes	yes
R^2_adj	0.2659	0.1359		0.1535	0.0877
F-Value	85.23	35.39		39.83	19.92
Obs.	8978	8586		8093	7702

Note:

^*** ,

^** , and

^* indicate 0.01, 0.05, and 0.10 significance levels, respectively. The results are clustered at the firm level.

4.4. Robustness tests

The following tests are performed to corroborate our results.

First, we use both the industry-adjusted ROA/ROE and market-adjusted yearly return (RET) as performance measures to examine the relationship between structural hole and future performance. Table 6 shows that the coefficients are all positively significant, whether using ROA_adj, ROE_adj, or RET as the performance measures in year t+1. However in year t+2, the relation between CI and ROA_adj is no longer significant. The significance levels when using ROE_adj or RET decrease, consistent with the main test results.

Table 6. Robustness test (1).

	Year t+1				Year t+2
	ROA_adj	ROE_adj	RET		ROA_adj	ROE_adj	RET
CI	0.005^**	0.015^**	0.485^***		0.004	0.014^*	0.084^***
	(2.27)	(1.96)	(19.04)		(1.54)	(1.70)	(3.76)
BOARD	0.000	0.001	0.004		0.000	0.000	0.005
	(0.59)	(0.42)	(0.91)		(0.35)	(0.33)	(1.33)
OUT	0.007	0.067	–0.313^**		–0.023	0.034	–0.125
	(0.53)	(1.51)	(–2.07)		(–1.56)	(0.73)	(–0.94)
COMP	0.012^***	0.036^***	–0.037^***		0.012^***	0.035^***	–0.012
	(11.98)	(10.99)	(–3.33)		(11.93)	(10.18)	(–1.25)
DUAL	–0.004^**	–0.013^**	0.044^*		–0.006^***	–0.015^**	0.022
	(–2.27)	(–2.05)	(1.94)		(–2.86)	(–2.12)	(1.12)
SOE	–0.006^***	–0.018^***	–0.068^***		–0.007^***	–0.016^***	–0.029^*
	(–3.96)	(–3.46)	(–3.83)		(–4.25)	(–2.87)	(–1.87)
SHR1	0.000^***	0.001^***	0.002^***		0.000^***	0.001^***	0.001
	(8.23)	(6.87)	(3.41)		(8.11)	(5.86)	(1.20)
SEP	–0.000^**	–0.001^***	–0.002^**		–0.000	–0.000	–0.000
	(–2.42)	(–2.71)	(–2.26)		(–0.60)	(–0.69)	(–0.37)
SIZE	–0.002^***	0.005^**	–0.070^***		–0.002^***	0.003	–0.041^***
	(–2.77)	(2.04)	(–7.59)		(–2.69)	(1.19)	(–5.02)
LEV	–0.024^***	–0.088^***	0.092^**		–0.023^***	–0.077^***	0.086^**
	(–7.02)	(–6.68)	(2.03)		(–6.11)	(–5.51)	(2.16)
CATA	0.004	0.059^***	–0.081^*		–0.002	0.047^***	–0.007
	(0.94)	(4.66)	(–1.87)		(–0.51)	(3.46)	(–0.19)
ROA	0.371^***				0.195^***
	(33.47)				(16.06)
ROE		0.231^***	0.017			0.099^***	0.042
		(19.14)	(0.45)			(7.89)	(1.29)
Cons	–0.134^***	–0.670^***	2.512^***		–0.118^***	–0.621^***	0.939^***
	(–7.97)	(–11.53)	(12.89)		(–6.93)	(–10.48)	(5.43)
Ind/Year	yes	yes	yes		yes	yes	yes
R^2_adj	0.237	0.120	0.553		0.110	0.067	0.697
F-Value	73.01	30.74	295.24		83.30	14.96	499.02
Obs.	8978	8586	8630		8093	7702	7842

Note:

^*** ,

^** , and,

^* indicate 0.01, 0.05, and 0.10 significance levels, respectively. The results are clustered at the firm level.

Second, we use the models developed by Biddle et al. (2009) and Chen and Xie (2011) to measure the investment efficiency. Biddle et al. (2009) argue that researchers can regress investment on a firm’s growth directly to compute the investment efficiency. The model for this is , where is measured as the sales growth in year t-1. Chen and Xie (2011) further investigate the nonlinear effect of sales growth, and change the model into , where is the dummy variable, to determine whether the sales growth is negative or positive. The variable absINV_B is the absolute value of investment efficiency generated from the residual of the Biddle et al. (2009) model, and absINV_C refers to the residual of the Chen and Xie (2011) model. Both results are demonstrated in Table 7. The relations between CI and absINV_B or absINV_C are both negatively significant at the 5% level, which means that our results for the network’s role on investment efficiency are stable.

Table 7. Robustness test (2).

	Investment inefficiency
	absINV_B	absINV_C
CI	–0.008^**	–0.008**
	(–2.19)	(–2.17)
BOARD	–0.002^***	–0.001
	(–3.64)	(–1.59)
OUT	–0.002	0.017
	(–0.11)	(0.84)
COMP	0.001	–0.001
	(0.56)	(–0.47)
DUAL	0.004	0.004
	(1.16)	(1.36)
SOE	–0.009^***	–0.009^***
	(–3.56)	(–3.85)
SHR1	–0.000*	–0.000
	(–1.83)	(–0.82)
SEP	–0.000	–0.000
	(–0.71)	(–0.42)
SIZE	–0.005^***	–0.005^***
	(–4.53)	(–4.02)
LEV	0.048^***	0.043^***
	(8.20)	(8.33)
ROA	0.044^**	0.070^***
	(2.33)	(4.14)
CATA	–0.028^***	–0.033^***
	(–4.54)	(–5.70)
Cons	0.267^***	0.278^***
	(11.30)	(11.94)
Ind/Year	yes	yes
R^2_adj	0.042	0.061
F-Value	16.82	17.46
Obs.	9120	9120

Note:

^*** ,

^** , and

^* indicate 0.01, 0.05, and 0.10 significance levels, respectively. The results are clustered at the firm level.

Our paper faces a potential endogeneity problem that must be dealt with. The firms with core structural hole positions are systematically different from firms without a core structural hole, which could cause these firms to select directors with more network relations and therefore achieve higher operating and investing efficiency. Under these conditions, a positive correlation between the structural hole position and firm efficiency might not be the result of the network structure. First of all, we regress the firm-level fixed effects for Models (2) and (3). The main results remain the same; in addition, like Larcker et al. (2013), we run the regression using two subsamples: the first sub-sample in which the firm directors do not change, and the second sub-sample in which the firm’s independent directors do not change. This regression ensures that the results are caused by network structure rather than changes in directors. The untabulated results show that the positive relation between CI and operating efficiency is more significant than that in Table 3. Also, the negative relation between CI and under-investment is close to but not significant. As Larcker et al. (2013) claim, researchers cannot remove all of the endogeneity problems. We can only use the limited methods available to alleviate these problems.

5. Conclusion

A growing literature is focusing on the relation between social networks and corporate finance (e.g., Cai and Sevilir, 2012; Fracassi and Tate, 2012; Larcker et al., 2013). According to the social network theory, there are two components of networks: network relations and network structures. The existing literature mainly investigates the network relations of firms, but the structural embeddedness view argues that it is the structural position of networks rather than simply the network relations themselves that enable actors to acquire resource advantages. As firms are embedded in various social networks, these networks are important aspects of economic organisations, so the networks specifically generated by interlocking relations between directors need to be measured and analysed. The structural hole, as first analysed by Burt (1992) is a highly crucial network structure. The different structural hole positions generated by firm directors’ networks can bring both control and information advantages to a firm. Such network positions can influence a firms’ operating and investing activities, and its future performance.

To investigate directors’ social networks, this paper first constructs the network of directors for Chinese A-share listed firms between 2001 and 2011. We then compute the firms’ structural hole positions using Pajek, which is one of the most widely used software tools in social network studies. Finally, we investigate the effects of firms’ structural hole positions on their operating and investment efficiency. Our results indicate that firms with more structural holes operate and invest more efficiently, and these effects seem even more pronounced in competitive industries. Further tests show that firms with more structural holes also perform better over time.

Our results show that the main activities of firms, such as operations and investments, can be profoundly influenced by the structural hole positions of their directors’ interlocking networks. Therefore, we suggest that network structure should be taken into consideration when analysing firms’ investment decisions, which would effectively expand the existing interdisciplinary research on ‘social network and corporate finance’. In addition, as one type of social network of China, namely Chinese ‘Guanxi’, structural holes is not paid enough attention. While there is widespread confirmation of the importance of structural holes in generating power and productivity in Western economies, evidence is weak and disconfirming for East Asia especially China (Chai & Rhee, 2009). As the study of structural holes in Chinese firms can relate to Confucian capitalism and the ‘East Asian Model’ of the firm, we expect more and more related studies in this field.

Acknowledgements

I am grateful for the helpful comments and suggestions from Professors Jason Xiao, Kangtao Ye, Xi Wu, Huilong Liu, Oliver Li, Wei Luo and participants at the 2012 Annual Conference of China Journal of Accounting Studies and the 11th International Symposium on Empirical Accounting Research in China. I would also like to thank two anonymous referees and the editors for their insightful comments. This work was supported by the National Natural Science Foundation of China (71202126), the Research Fund for the Doctoral Program of Higher Education (20120016120003), grants from the Beijing Municipal Commission of Education ‘Pilot Reform of Accounting Discipline Clustering’, grants from the Beijing Municipal Commission of Education ‘Joint Construction Project’ and the ‘Project 211’ Fund from Central University of Finance and Economics.

Notes

1. If one director serves on more than one board, then all of the firms on which that director serves can obtain network advantages from the director’s joint position, which is described in social network theory as an undirected graph. This paper only studies the directors’ positions in the current year, so that if one director serves on two different boards in different years, it would not show as a direct link according to our definition. Generally, interdisciplinary research on social networks and corporate finance identifies networks based on the directors’ serving behaviour in the current year’s position (Larcker et al., 2013). However, for research into the learning effect or contagion effect of interlocking director relations, the directors’ positions in different years are often included to test the spread of corporate policies (Bizjak, Lemmon, & Whitby, 2009; Fracassi & Tate, 2012).

2. We do not include the non-listed firms, because data for non-listed firms are hard to obtain. Compared with studies of strategic management or corporate finance, which usually use S&P 500 or S&P 1500 data, our sample is more comprehensive. Our sample also avoids the problem of severing networks artificially.

3. Pajek is a widely used software for large network analysis of social networks (http://pajek.imfm.si/).

4. Due to space constraints, the correlation matrix is not listed here, but is available upon request.