Interlocking directorates and dynamic corporate performance: the roles of centrality, structural holes and number of connections in social networks

Abstract

This study investigates how interlocking directorates affect dynamic corporate performance among 187 Taiwanese electronics companies during a 3 year sampling period (2013–2015). This study consists of two stages. First, this study measures the operational efficiency of electronics companies using the dynamic slacks-based measure model of data envelopment analysis. Second, this study adopts a truncated-regression model with bootstrap to examine the impacts of interlocking directorates on dynamic corporate performance. The empirical findings of this study indicate that centrality (direct connections), structural holes (indirect connections), and the number of connections (total connections) related to interlocking directorates have significant positive influences on the dynamic corporate performance of Taiwanese electronics companies. The results suggest that more interlocks at the board level leads to better corporate performance over a long-term period. Overall, this study uses social network analysis to shed light on the role of interlocking directorates and its importance to dynamic corporate performance from the resource dependence perspective.

Appendix

1.1 Dynamic slacks-based measure of efficiency in DEA model approach

Assume that the dynamic process presented in Fig. 1 deals with $n$ companies ($j = 1, \ldots ,n$) over $T$ times ($t = 1, \ldots ,T$). During each time, companies have common $m$ inputs ($i = 1, \ldots ,m$), $s$ outputs ($r = 1, \ldots ,s$), and $g$ carry-over items ($h = 1, \ldots ,g$). Let $x_{ij}^{t} , \, y_{rj}^{t} ,$ and $z_{hj}^{t}$ denote the input, output, and carry-over values of the jth company at time t, respectively. The DSBM model under variable returns to scale (VRS) evaluates the efficiency of the observed company by solving the following non-oriented fractional program:

$$\begin{aligned} & \left[ {\text{DSBM}} \right] \\ & ATE_{0}^{{}} = MIN \, \frac{{\frac{1}{T}\sum_{t = 1}^{T} \left[ { 1- \frac{ 1}{m}\left( {\sum_{i = 1}^{m} {{s_{it}^{ - } } \mathord{\left/ {\vphantom {{s_{it}^{ - } } {x_{io}^{t} }}} \right. \kern-0pt} {x_{io}^{t} }}} \right)} \right]}}{{\frac{1}{T}\sum_{t = 1}^{T} \left[ { 1 { + }\frac{ 1}{{\left( {s + g} \right)}}\left( {\sum_{r = 1}^{s} {{s_{rt}^{ + } } \mathord{\left/ {\vphantom {{s_{rt}^{ + } } {y_{ro}^{t} }}} \right. \kern-0pt} {y_{ro}^{t} }} + \sum_{h = 1}^{g} {{s_{ht}^{c} } \mathord{\left/ {\vphantom {{s_{ht}^{c} } {z_{ho}^{t} }}} \right. \kern-0pt} {z_{ho}^{t} }}} \right)} \right] \, }} \\ \end{aligned}$$

(1)

$$\begin{aligned} & {\text{subject}}\;{\text{to}} \\ & x_{io}^{t} = \sum\limits_{j = 1}^{n} {x_{ij}^{t} \lambda_{j}^{t} + s_{it}^{ - } } ,\quad i = 1, \ldots ,m;\quad t = 1, \ldots ,T, \, \\ \end{aligned}$$

(2)

$$y_{ro}^{t} = \sum\limits_{j = 1}^{n} {y_{rj}^{t} \lambda_{j}^{t} - s_{rt}^{ + } ,\quad r = 1, \ldots ,s;\quad t = 1, \ldots ,T,}$$

(3)

$$z_{ho}^{t} = \sum\limits_{j = 1}^{n} {z_{hj}^{t} \lambda_{j}^{t} - s_{ht}^{c} ,\quad h = 1, \ldots ,g;\quad \, t = 1, \ldots ,T,}$$

(4)

$$\sum\limits_{j = 1}^{n} {z_{hj}^{t} \lambda_{j}^{t} } = \sum\limits_{j = 1}^{n} {z_{hj}^{t} \lambda_{j}^{t + 1} } ,\quad \forall h;\quad t = 1, \ldots ,T - 1,$$

(5)

$$\begin{aligned} & \sum\limits_{j = 1}^{n} {\lambda_{j}^{t} = 1,\quad t = 1, \ldots ,T,} \\ & \lambda_{j}^{t} \ge 0,\quad s_{it}^{ - } \ge 0,\quad s_{rt}^{ + } \ge 0,\quad s_{ht}^{c} \ge 0. \\ \end{aligned}$$

(6)

where $x_{io}^{t} , \, y_{ro}^{t} ,$ and $z_{ho}^{t}$ are linked to $x_{ij}^{t} , \, y_{rj}^{t} ,$ and $\, z_{hj}^{t}$ by the intensity variable $\lambda_{j}^{t}$. The restrictions of (2)–(6) make up the production possibility set, whereby (5) ensures that carry-over variables continue from t to t + 1, while (6) suggests the assumption of variable returns to scale. $s_{it}^{ - } , \, s_{rt}^{ + } ,$ and $s_{ht}^{c}$ are slack variables of input surplus, output gap, and carry-over gap, respectively. While the dividend is mean input efficiency, the divisor is the reversed mean output efficiency.

In line with Charnes et al. (1978), this study puts a scalar $\delta \left( { > 0} \right)$ into the restrictions (1)–(6) to transform $\left[ {\text{DSBM}} \right]$ into $\left[ {\text{DSBMt}} \right]$, a nonlinear programming problem. Thus, we have the following equations:

$$\begin{aligned} & \left[ {\text{DSBMt}} \right] \\ & \tau_{0}^{{}} = MIN \, \frac{1}{T}\sum_{t = 1}^{T} \left[ {\delta - \frac{ 1}{m}\left( {\sum_{i = 1}^{m} {{\delta s_{it}^{ - } } \mathord{\left/ {\vphantom {{\delta s_{it}^{ - } } {x_{io}^{t} }}} \right. \kern-0pt} {x_{io}^{t} }}} \right)} \right] \, \\ \end{aligned}$$

(7)

$$\begin{aligned} & {\text{subject}}\;{\text{to}} \\ & 1 = \frac{1}{T}\sum_{t = 1}^{T} \left[ {\delta { + }\frac{ 1}{{\left( {s + g} \right)}}\left( {\sum_{r = 1}^{s} {{\delta s_{rt}^{ + } } \mathord{\left/ {\vphantom {{\delta s_{rt}^{ + } } {y_{ro}^{t} }}} \right. \kern-0pt} {y_{ro}^{t} }} + \sum_{h = 1}^{g} {{\delta s_{ht}^{c} } \mathord{\left/ {\vphantom {{\delta s_{ht}^{c} } {z_{ho}^{t} }}} \right. \kern-0pt} {z_{ho}^{t} }}} \right)} \right] \, \\ \end{aligned}$$

(8)

$$\delta x_{io}^{t} = \sum\limits_{j = 1}^{n} {x_{ij}^{t} \delta \lambda_{j}^{t} + \delta s_{it}^{ - } } ,\quad i = 1, \ldots ,m;\quad t = 1, \ldots ,T,$$

(9)

$$\delta y_{ro}^{t} = \sum\limits_{j = 1}^{n} {y_{rj}^{t} \delta \lambda_{j}^{t} - \delta s_{rt}^{ + } ,\quad r = 1, \ldots ,s;\quad t = 1, \ldots ,T,} \,$$

(10)

$$\delta z_{ho}^{t} = \sum\limits_{j = 1}^{n} {z_{hj}^{t} \delta \lambda_{j}^{t} - \delta s_{ht}^{c} ,\quad h = 1, \ldots ,g;\quad t = 1, \ldots ,T,} \,$$

(11)

$$\sum\limits_{j = 1}^{n} {z_{hj}^{t} \delta \lambda_{j}^{t} } = \sum\limits_{j = 1}^{n} {z_{hj}^{t} \delta \lambda_{j}^{t + 1} } ,\quad \forall h;\quad \, t = 1, \ldots ,T - 1,$$

(12)

$$\begin{aligned} & \sum\limits_{j = 1}^{n} {\delta \lambda_{j}^{t} = 1,\quad t = 1, \ldots ,T,} \\ & \lambda_{j}^{t} \ge 0,\quad s_{it}^{ - } \ge 0,\quad s_{rt}^{ + } \ge 0,\quad s_{ht}^{c} \ge 0. \\ \end{aligned}$$

(13)

where $\delta s_{it}^{ - } , \, \delta s_{rt}^{ + } , { }\delta s_{ht}^{ + }$ and $\delta \lambda_{j} \,$ are nonlinear, and $\delta$ in the constraint (8) is adjusted to be 1. After defining $S_{it}^{ - } = \delta s_{it}^{ - } , \, S_{rt}^{ + } = \delta s_{rt}^{ + } , \, S_{ht}^{c} = \delta s_{ht}^{c} \;{\text{and}}\;\Lambda _{j}^{t} = \delta \lambda_{j}^{t}$, $\left[ {\text{DSBMt}} \right]$ becomes a linear program (LP) in $\delta , \, S_{it}^{ - } , \, S_{rt}^{ + } , \, S_{ht}^{c} ,{\text{ and }}\varLambda_{j}^{t}$ as follows:

$$\begin{aligned} & \left[ {{\text{DSBMt}}\_{\text{LP}}} \right] \\ & \tau_{0}^{{}} = MIN \, \frac{1}{T}\sum_{t = 1}^{T} \left[ {\delta { - }\frac{ 1}{m}\left( {\sum_{i = 1}^{m} {{S_{it}^{ - } } \mathord{\left/ {\vphantom {{S_{it}^{ - } } {x_{io}^{t} }}} \right. \kern-0pt} {x_{io}^{t} }}} \right)} \right] \\ \end{aligned}$$

(14)

$$\begin{aligned} & {\text{subject}}\;{\text{to}} \\ & 1 = \frac{1}{T}\sum_{t = 1}^{T} \left[ {\delta { + }\frac{ 1}{{\left( {s + g} \right)}}\left( {\sum_{r = 1}^{s} {{S_{rt}^{ + } } \mathord{\left/ {\vphantom {{S_{rt}^{ + } } {y_{ro}^{t} }}} \right. \kern-0pt} {y_{ro}^{t} }} + \sum_{h = 1}^{g} {{S_{ht}^{c} } \mathord{\left/ {\vphantom {{S_{ht}^{c} } {z_{ho}^{t} }}} \right. \kern-0pt} {z_{ho}^{t} }}} \right)} \right] \\ \end{aligned}$$

(15)

$$\delta x_{io}^{t} = \sum\limits_{j = 1}^{n} {x_{ij}^{t} \varLambda_{j}^{t} + S_{it}^{ - } } ,\quad i = 1, \ldots ,m;\quad t = 1, \ldots ,T,$$

(16)

$$\delta y_{ro}^{t} = \sum\limits_{j = 1}^{n} {y_{rj}^{t} \varLambda_{j}^{t} - S_{rt}^{ + } ,\quad r = 1, \ldots ,s;\quad t = 1, \ldots ,T,}$$

(17)

$$\delta z_{ho}^{t} = \sum\limits_{j = 1}^{n} {z_{hj}^{t} \varLambda_{j}^{t} - S_{ht}^{c} ,\quad h = 1, \ldots ,g;\quad t = 1, \ldots ,T,} \,$$

(18)

$$\sum\limits_{j = 1}^{n} {z_{hj}^{t} \varLambda_{j}^{t} } = \sum\limits_{j = 1}^{n} {z_{hj}^{t} \varLambda_{j}^{t + 1} } ,\quad \forall h;\quad t = 1, \ldots ,T - 1, \,$$

(19)

$$\begin{aligned} & \sum\limits_{j = 1}^{n} {\Lambda _{j}^{t} = 1,\quad t = 1, \ldots ,T,} \\ &\Lambda _{j}^{t} \ge 0,\quad \, S_{it}^{ - } \ge 0,\quad \, S_{rt}^{ + } \ge 0,\quad \, S_{ht}^{c} \ge 0. \\ \end{aligned}$$

(20)

Let an optimal solution of $\left[ {{\text{DSBMt}}\_{\text{LP}}} \right]$ be $\left( {\tau_{o}^{*} , \, \delta^{*} , \, \varLambda_{j}^{t*} , \, S_{it}^{ - *} , \, S_{rt}^{ + *} , \, S_{ht}^{c*} } \right)$. Then, we have an optimal solution of $\left[ {\text{DSBM}} \right]$ as defined by:

$$ATE_{o}^{*} = \tau_{o}^{*} , \, s_{it}^{ - *} = {{S_{it}^{ - *} } \mathord{\left/ {\vphantom {{S_{it}^{ - *} } {\delta^{*} }}} \right. \kern-0pt} {\delta^{*} }}, \, s_{rt}^{ - *} = {{S_{rt}^{ + *} } \mathord{\left/ {\vphantom {{S_{rt}^{ + *} } {\delta^{*} }}} \right. \kern-0pt} {\delta^{*} }}, \, s_{ht}^{ - *} = {{S_{ht}^{c*} } \mathord{\left/ {\vphantom {{S_{ht}^{c*} } {\delta^{*} }}} \right. \kern-0pt} {\delta^{*} }}, \, \lambda_{j}^{t*} = {{\varLambda_{j}^{t} } \mathord{\left/ {\vphantom {{\varLambda_{j}^{t} } {\delta^{*} }}} \right. \kern-0pt} {\delta^{*} }}.$$

If the optimal solution for $\left[ {\text{DSBMt}} \right]$ satisfies $ATE_{o}^{*} = 1$ when there are no slacks, then the observed company is considered non-oriented overall efficient or, briefly, overall efficient:

$$TE_{o}^{t*} = {{\left[ { 1- \frac{ 1}{m}\left( {\sum_{i = 1}^{m} {{s_{it}^{ - *} } \mathord{\left/ {\vphantom {{s_{it}^{ - *} } {x_{io}^{t} }}} \right. \kern-0pt} {x_{io}^{t} }}} \right)} \right]} \mathord{\left/ {\vphantom {{\left[ { 1- \frac{ 1}{m}\left( {\sum_{i = 1}^{m} {{s_{it}^{ - *} } \mathord{\left/ {\vphantom {{s_{it}^{ - *} } {x_{io}^{t} }}} \right. \kern-0pt} {x_{io}^{t} }}} \right)} \right]} {\left[ { 1 { + }\frac{ 1}{{\left( {s + g} \right)}}\left( {\sum_{r = 1}^{s} {{s_{rt}^{ + *} } \mathord{\left/ {\vphantom {{s_{rt}^{ + *} } {y_{ro}^{t} }}} \right. \kern-0pt} {y_{ro}^{t} }} + \sum_{h = 1}^{g} {{s_{ht}^{c*} } \mathord{\left/ {\vphantom {{s_{ht}^{c*} } {z_{ho}^{t} }}} \right. \kern-0pt} {z_{ho}^{t} }}} \right)} \right] \, }}} \right. \kern-0pt} {\left[ { 1 { + }\frac{ 1}{{\left( {s + g} \right)}}\left( {\sum_{r = 1}^{s} {{s_{rt}^{ + *} } \mathord{\left/ {\vphantom {{s_{rt}^{ + *} } {y_{ro}^{t} }}} \right. \kern-0pt} {y_{ro}^{t} }} + \sum_{h = 1}^{g} {{s_{ht}^{c*} } \mathord{\left/ {\vphantom {{s_{ht}^{c*} } {z_{ho}^{t} }}} \right. \kern-0pt} {z_{ho}^{t} }}} \right)} \right] \, }}$$

(21)

If all optimal solutions of equation (21) satisfy $TE_{o}^{t*} = 1$ when there are no slacks in term $t$, then the observed company is considered non-oriented time efficient or, briefly, time efficient for time $t$.