Board Diversity and Corporate Social Disclosure: Evidence from Vietnam

Abstract

Debates around sound corporate governance propose board diversity as a key attribute to sufficiently challenge executive management for stakeholder engagement. This study contributes to this debate by empirically investigating the effect of board diversity on corporate social disclosure (CSD) of Vietnamese listed firms. The study finds a significantly positive effect of diversity-in-boards (dissimilarities among directors within a board, i.e., demographic attributes of board members) on CSD while diversity-of-boards (dissimilarities among firm boards, i.e., board structure) has no effect on CSD. The results contribute by showing that a single theoretical approach can provide an adequate explanation for board diversity. The study contributes methodologically by demonstrating the design and measurement of board diversity indices, and a three-dimensional stakeholder-relevant CSD index. The findings benefit regulators and corporate executives in better understanding firms’ CSD practices and stakeholders’ expectations.

Appendix

Method of Measuring Unweighted Diversity-of-Boards Index (UW_DoB)

First, the dissimilarity between a given firm and another firm is measured using a mathematical distance function defined by Han et al. (2006) as follows:

$$d(i,j) = \frac{{\sum\nolimits_{f = 1}^{p} {\delta_{ij}^{(f)} d_{ij}^{(f)} } }}{{\sum\nolimits_{f = 1}^{p} {\delta_{ij}^{(f)} } }},$$

(6)

where d(i, j) is the dissimilarity between objects i and j (i.e., firm i and firm j); p is represented as the number of structural attributes of the firm board examined in this study. These two data points are represented as (x _i1, x _i2, …, x _ip ) and (x _j1, x _j2, …, x _jp ), respectively. The indicator $\delta_{ij}^{(f)} = \, 1$ with the assumption that attributes f is equal weighted relative to the contribution.

Then, the contribution made by an attribute f to the dissimilar function between firm i and firm j (i.e., d ^{( f)} _ij ) is calculated. However, that computation is unique to each data type. As attributes are measured using different data types, d ^{( f)} _ij is calculated using different formulas based on the data type of the attribute. The structural attributes of boards in this paper contain binary and ratio scale data types, so the following formulas focus on these two data types:

If attribute f is binary: d ^{( f)} _ij  = 0 if x _if  = x _jf , or otherwise d ^{( f)} _ij  = 1;

(a)If attribute f is ratio scale, it is treated like an interval scale attribute with the following formula: $d_{ij}^{\left( f \right)} = \frac{{\left| {x_{if} - x_{jf} } \right|}}{{\max_{h} x_{hf} - \min_{h} x_{hf} }},$ where h runs over all nonmissing objects for attribute f.

The contribution of dissimilarity for all the different attributes (i.e., d ^{( f)} _ij ) is normalized by these formulates, and hence expresses on a common scale from 0 to 1. The average distance (dissimilarity) to all the other boards is taken as follows (note that 1 is subtracted from the number of firms in the sample in the denominator of the formula because this study compares a firm with other firms without the firm being compared with itself, because such a comparison is meaningless):

$$D(i) = \frac{{\sum\nolimits_{j = 1}^{k} {d(i,j)} }}{k - 1},$$

(7)

where k is the number of firm boards; D(i) is the average dissimilarity of firm board i to all other boards in the sample, namely UW_DoB of each firm board. See Table 10.

Table 10 An example of an unweighted diversity-of-boards index’s calculation with four firms’ data

The dissimilarity function between firm i and firm j (i.e., d ^{( f)} _ij ) for each attribute f is computed in the dissimilarity matrix as follows:

$$\left[ {\begin{array}{*{20}c} 0 & {} & {} & {} \\ {d_{1,2}^{(f)} } & 0 & {} & {} \\ {d_{1,3}^{(f)} } & {d_{2,3}^{(f)} } & 0 & {} \\ {d_{1,4}^{(f)} } & {d_{2,4}^{(f)} } & {d_{3,4}^{(f)} } & 0 \\ \end{array} } \right].$$

Binary Scale Data Types (Attribute 1 and Attribute 4)

Because attributes 1 and 4 are binary, d ^{( f)} _ij becomes 0 if the attributes of firm board i and firm board j match, and 1 if the attributes differ. This study gained d ^{( f)} _ij for attribute 1 (i.e., d ⁽¹⁾ _{i, j} ) in the dissimilarity matrix as follows:

$$\left[ {\begin{array}{*{20}c} 0 & {} & {} & {} \\ 1 & 0 & {} & {} \\ 0 & 1 & 0 & {} \\ 0 & 1 & 0 & 0 \\ \end{array} } \right].$$

This study gained d ^{( f)} _ij for attribute 4 (i.e., d ⁽⁴⁾ _{i, j} ) in the dissimilarity matrix as follows:

$$\left[ {\begin{array}{*{20}c} 0 & {} & {} & {} \\ 0 & 0 & {} & {} \\ 0 & 0 & 0 & {} \\ 1 & 1 & 1 & 0 \\ \end{array} } \right].$$

Ratio Scale Data Types (Attribute 2 and Attribute 3)

This illustration computes d ^{( f)} _ij for attributes 2 and 3 (which are ratio scales). In this scenario, the data of each attribute are treated like an interval scale (see b) for the formula). To compute d ^{( f)} _ij for attribute 2 (i.e., d ⁽²⁾ _{i, j} ), this study let max_h x _h = 0.5726 and min_h x _h = 0. The following dissimilarity matrix is then obtained for attribute 2 (i.e., d ⁽²⁾ _{i, j} ):

$$\left[ {\begin{array}{*{20}c} 0 & {} & {} & {} \\ 1 & 0 & {} & {} \\ 0 & 1 & 0 & {} \\ {0.21} & {0.79} & {0.21} & 0 \\ \end{array} } \right].$$

The figures shown in column 1 of the matrix for attribute 2 above (that is 0, 1, 0, 0.21) are calculated as follows.

The dissimilarity score for attribute 2 for firm 1 compared with firm 1:

d ⁽²⁾_1,1  = 0 (because there is no dissimilarity between firm 1 and itself).

The dissimilarity score for attribute 2 for firm 1 compared with firm 2:

$$d_{1,2}^{(2)} = \frac{{\left| {0 - 0.5726} \right|}}{0.5726 - 0} = 1.$$

The dissimilarity score for attribute 2 for firm 1 compared with firm 3:

$$d_{1,3}^{(2)} = \frac{{\left| {0 - 0} \right|}}{0.5726 - 0} = 0.$$

The dissimilarity score for attribute 2 for firm 1 compared with firm 4:

$$d_{1,4}^{(2)} = \frac{{\left| {0 - 0.1217} \right|}}{0.5726 - 0} = 0.21.$$

Attribute 3 is also a ratio scale. As with calculating attribute 2, the d ^{( f)} _ij for attribute 3 (i.e., d ⁽³⁾ _{i, j} ) in the dissimilarity matrix is as follows (details of calculating individual figures are not shown here):

$$\left[ {\begin{array}{*{20}c} 0 & {} & {} & {} \\ 1 & 0 & {} & {} \\ {0.42} & {0.58} & 0 & {} \\ {0.67} & {0.33} & {0.25} & 0 \\ \end{array} } \right].$$

The dissimilarity matrices for the four attributes are computed using formula (1). For example, the dissimilarity between firm 1 and firm 4 (d(1,4)), for the combined four attributes, is obtained as follows (all four attributes are assumed to have equal weights, hence the indicator δ ^{( f)} _ij is 1):

$$d(1,4) = \frac{{1*d_{1,4}^{(1)} + 1*d_{1,4}^{(2)} + 1*d_{1,4}^{(3)} + 1*d_{1,4}^{(4)} }}{4} = \frac{1*0 + 1*0.21 + 1*0.67 + 1*1}{4} = 0.47.$$

Similarly, the resulting dissimilarity matrix obtained for the data described by the four attributes of mixed types is

$$\left[ {\begin{array}{*{20}c} 0 & {} & {} & {} \\ {d(1,2)} & 0 & {} & {} \\ {d(1,3)} & {d(2,3)} & 0 & {} \\ {d(1,4)} & {d(2,4)} & {d(3,4)} & 0 \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} 0 & {} & {} & {} \\ {0.75} & 0 & {} & {} \\ {0.10} & {0.65} & 0 & {} \\ {0.47} & {0.78} & {0.37} & 0 \\ \end{array} } \right].$$

Finally, the diversity-of-boards index of each firm board is calculated based on formula (2), which is the average difference of a given firm with all other firms when the dissimilarity distance is measured.

For example, the UW_DoB of firm board 1 is

$$D({\text{firm}}1) = \frac{d(1,1) + d(1,2) + d(1,3) + d(1,4)}{4 - 1} = \frac{0 + 0.75 + 0.1 + 0.47}{4 - 1} = 0.44.$$

Similarly, by using the above computations, the UW_DoB of firm board two, three, and four are 0.73, 0.37, and 0.54, respectively. These results indicate that firm board 2 is the most diverse (dissimilarity), while firm board 3 is the least diverse (dissimilarity).