Do female directors will have impact on corporate performance?

Abstract

The purpose of this study is to explore the influence of female directors on the corporate performance of Chinese banks and Taiwanese financial holding companies. The sample consists of 14 Chinese banks and 15 Taiwanese financial holding companies in 2010–2014. The empirical results show that the proportion of non-executive female directors and independent female directors have significant positive influence on corporate performance. The result shows that the higher the proportion of female directors is, the better off the corporate performance would be. There is robust evidence in the data to conclude that female directors in specific posts can influence a firm’s corporate performance.

Appendix I

1.1 Epsilon-based measure of efficiency in DEA model approach

Epsilon-based measure of efficiency in DEA model is illustrated as follow.

Step 1 We used SBM model for finding slacks and projected DMUs to efficient frontiers. They are all projected to the unique efficient DMU. Throughout this paper, we deal with n DMUs $\left( {j = 1, \ldots ,n} \right)$ having m inputs $\left( {i = 1, \ldots ,m} \right)$ and s outputs $\left( {r = 1, \ldots ,s} \right)$. The input and output matrices are denoted by $X = \left\{ {x_{ij} } \right\} \in R^{mxn}$ and $Y = \left\{ {y_{ij} } \right\} \in R^{sxn}$ respectively. We assume X > 0 and Y > 0.SBM

$$\hbox{min} \frac{{1 - \frac{1}{m}\sum\nolimits_{i = 1}^{m} {\frac{{s_{i}^{ - } }}{{x_{io} }}} }}{{1 - \frac{1}{s}\sum\nolimits_{r = 1}^{m} {\frac{{s_{r}^{ + } }}{{y_{ro} }}} }}$$

$$\begin{array}{*{20}l} {Subject\;to} \hfill & {} \hfill \\ {x_{io} = \sum {_{j = 1}^{n} x_{ij} \lambda_{j} + s_{j}^{ - } = 0} } \hfill & {i = 1, \ldots ,m.} \hfill \\ {y_{ro} = \sum {_{j = 1}^{n} y_{rj} \lambda_{j} - s_{r}^{ + } = 0} } \hfill & {i = 1, \ldots ,s.} \hfill \\ {\sum {_{j = 1}^{n} } \lambda_{j} = 1} \hfill & {} \hfill \\ {\lambda_{j} (\forall j),s_{i}^{ - } \ge 0(\forall i),s_{r}^{ + } \ge (\forall r).} \hfill & {} \hfill \\ \end{array}$$

(5)

Using the optimal slacks $s^{ - *}$ and $s^{ + *}$ we define the projected input and output for DMUo by

$$\begin{array}{*{20}l} {\overline{{X_{io} }} = x_{io} - s_{i}^{ - *} (i = 1, \ldots ,m)} \hfill \\ {\overline{{Y_{ro} }} = y_{ro} + s_{r}^{ + *} (r = 1, \ldots ,s)} \hfill \\ \end{array}$$

(6)

We notice that SBM model may produce different projections but they are on the efficient frontiers of the production possibility set. Thus, we have n VRS-efficient DMUs denoted by

$$\left[ {\begin{array}{*{20}c} {\overline{X} } \\ {\overline{Y} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {\bar{X}_{11} } & \cdots & {\bar{X}_{1} } \\ {} & \cdots & {} \\ {\bar{X}_{m1} } & \cdots & {\bar{X}_{mn} } \\ {\bar{Y}_{11} } & \cdots & {\bar{Y}_{1n} } \\ {} & \cdots & {} \\ {\bar{Y}_{s1} } & \cdots & {\bar{Y}_{sn} } \\ \end{array} } \right] = \left[ \begin{aligned} \bar{X}_{1} \hfill \\ \cdots \hfill \\ \bar{X}_{m} \hfill \\ \bar{Y}_{1} \hfill \\ \cdots \hfill \\ \bar{Y}_{s} \hfill \\ \end{aligned} \right]$$

(7)

All CRS (constant-returns-to-scale) efficient DMUs are included in this set along with VRS-efficient DMUs.

Step 2 We calculated the diversity matrix by the formula (8)

Definition 1

(Diversity index). We define the “diversity index” of vectors a and b as the deviation of $\left\{ {c_{j} } \right\}$ from the average $\bar{c}$ in the following way:

$$\begin{aligned} D\left( {a,b} \right) & = \frac{{\mathop \sum \nolimits_{j = 1}^{n} \left| {c_{j} - \bar{c}} \right|}}{{n\left( {c_{max} - c_{min} } \right)}},\;(if\;c_{max} > c_{min} ) \\ & = 0 \, (ifc_{\hbox{max} } > c_{\hbox{min} } ) \\ \end{aligned}$$

(8)

Step 3 The affinity matrix is calculated by the formula (9).

In the input-oriented case, we calculate the affinity matrix $s = \left[ {s_{ij} } \right] \in R^{m*n}$ with the elements

$$s_{ij} = s\left( {\overline{{x_{i} }} ,\overline{{x_{j} }} } \right)\left( {i,j = 1, \ldots ,m} \right)$$

(9)

All elements of the matrix S satisfy the bounds: $1 \ge s_{ij} \ge 0\left( {\forall \left( {ij} \right)} \right)$

Step 4 The largest eigenvalue and eigenvector of the affinity matrix are calculated.

We define $\varepsilon_{x}$ and $w^{ - }$ in the EBM as follows:

$$\begin{aligned} \varepsilon_{x} & = \frac{{m - \rho_{x} }}{m - 1}\;\left( {if\;m > 1} \right) \\ & = 0\left( {if\;m = 1} \right) \\ w^{ - } & = \frac{{w_{x} }}{{\sum\nolimits_{i = 1}^{m} {w_{xi} } }} \\ \end{aligned}$$

(10)

The thus defined $\varepsilon_{x}$ and $w^{ - }$ satisfy the relationship $0 \le \varepsilon_{x} \le 1$ and $ew^{ - } = 1$

Step 5 Use of $\varepsilon_{x}$ and $w^{ - }$ in the EBM of efficiency.

[EBM-I–V]

$$r^{*} = \mathop {\hbox{min} }\limits_{\theta ,\lambda ,s} \theta - \varepsilon_{x} \sum\limits_{i = 1}^{m} {\frac{{w_{i}^{ - } s_{i}^{ - } }}{{x_{io} }}}$$

(11)

$$\begin{array}{*{20}l} {Subject\;to} \hfill & {} \hfill \\ {\theta x_{io} - \sum\limits_{j = 1}^{n} {x_{ij} \lambda_{j} - s_{i}^{ - } } = 0} \hfill & {i = 1, \ldots ,m.} \hfill \\ {\mathop \sum \limits_{j = 1}^{n} y_{rj} \lambda_{j} \ge y_{r0} } \hfill & {r = 1, \ldots ,s.} \hfill \\ {\mathop \sum \limits_{j = 1}^{n} \lambda_{j} = 1} \hfill & {} \hfill \\ {\lambda_{j} \ge 0} \hfill & {} \hfill \\ {s_{i}^{ - } \ge 0} \hfill & {} \hfill \\ \end{array}$$

(12)

where $w_{i}^{ - }$ is the weight (relative importance) of input ${\text{i}}$ and satisfies $\sum\nolimits_{i = 1}^{m} {w_{i}^{ - } } = 1(w_{i}^{ - } \ge 0\forall i)$ and $\varepsilon_{x}$ is a key parameter which combines the radial $\theta$ from BCC model and the non-radial slacks term. Parameters $\varepsilon_{x}$ and $w^{ - } = (w_{1}^{ - } , \ldots ,w_{m}^{ - } )$ must be supplied prior to the efficiency measurements. As can be seen from the term $\frac{{w_{i}^{ - } s_{i}^{ - } }}{{x_{io} }}$ in the objective function (5) of, $\frac{{s_{i}^{ - } }}{{x_{io} }}$ is units-invariant and so $w_{i}^{ - }$ should be a units-invariant value reflecting the relative importance of resource “i”.