# Disentangling Director Attributes: Human Capital versus Social Capital of Directors
## 5 Multivariate Analysis  
### Main Regression Analysis  
We observe thus far, a significantly positive relationship between human capital and social capital. To further test this relationship, we estimate the following ordinary least square (OLS) model:  
\[AGG_{it}=\alpha+\beta_{1}HCI_{it}+\beta_{2}FEM_{it}+\beta_{3}NZ_{it}+\beta_{4 }DIR_{it}+\sum_{y=1}^{Y}\theta_{y}Year_{yt}+\varepsilon_{it} \tag{7}\] \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline Variable & \multicolumn{3}{c}{Quartiles} & \multicolumn{3}{c}{Mean Difference (High–Low)} \\ \hline  & Low & 2 & 3 & High & 2—Low (T Stat) & 3—2 (T Stat) & High—3 (T Stat) & (High–Low) (T Stat) \\ \hline Observations & 3054 & 3052 & 3053 & 3052 & & & \\ \hline HCI & 5.03 & 5.84 & 6.23 & 7.22 & 0.81 *** & 0.40 *** & 0.99 *** & 2.19 *** \\  & & & & (13.25) & (6.12) & (14.30) & (33.46) \\ DIR & 1.02 & 1.05 & 1.05 & 1.72 & 0.03 *** & 0.00 & 0.67 ** & 0.70 *** \\  & & & & (5.30) & (0.10) & (1.72) & (41.74) \\ \hline \multicolumn{10}{l}{_Panel B: Univariate Tests of Human Capital (HCI) Differences between Directors Grouped by Characteristics_} \\ \hline  & Obs & 0 & Obs & 1 & Mean Difference & & T Stat \\ \hline NZ & 3617 & 6.73 & 8594 & 5.81 & \(-\)0.93 & *** & (\(-\)18.17) \\ FEM & 11,142 & 6.08 & 1069 & 6.05 & \(-\)0.04 & & (0.43) \\ New & 10,710 & 6.38 & 1501 & 3.92 & \(-\)2.46 & *** & (\(-\)41.68) \\ \hline  & & & & & & & \\ \end{tabular} This table presents a univariate analysis of director attributes for the relationship between human capital and connectivity. Each year, directors are sorted into four quantiles based on their measure of _AGG_. The high group includes directors who are in the top 25 th percentile of _AGG_, while the low group includes directors who are in the bottom 25 th percentile of _AGG_. _AGG_ is the PCA connectivity factor. _HCI_ is the human capital index score of directors, _DIR_ is the number of directorships a director holds. Female is a dummy variable that equals 1 if a director is a woman. New Zealand is a dummy if the director was domictaled in New Zealand, New Director is a dummy variable if this is the first year that a director has held a public company directorship. The difference in the average _HCI_ measures between quartile groups are tested for significance using the two-tailed two-sample _t_-test with unequal variances. **_p_ < 0.05, ***_p_ < 0.01.  
\end{table} 
Table 4: Univariate analysis. where \(AGG_{ii}\) is our measure of connectivity, \(HCI_{it}\) represents the index for director \(i\) in year \(t\)'s human capital, \(FEM_{it}\) is a dummy variable that equals one if the director is a female, in year \(t\), and zero if a male, \(NZ_{it}\) is a dummy variable that equals one if the director resides in New Zealand, in year \(t\), and zero otherwise, \(DIR_{it}\) represents the number of directorships held by director \(i\) in year \(t\), and \(Year_{yt}\) is a set of year dummies to control for time-series trends. Robust standard errors \(\varepsilon_{it}\) are clustered at the director level ([PERSON], 2009) assumed to be I.I.D. over directors and time. We estimate the regressions with \(DIR\) in some specifications to test the robustness of the relationship. The correlation coefficients in Table 4 indicate that \(DIR\) has a positive relationship with \(HCl\) and \(AGG\), thus we expect that including \(DIR\) will significantly reduce the explanatory power of \(HCl\) in regressions. We only include director age (AGE) in some specifications as reliable information on director age is missing for approximately 39% of the sample, consistent with previous studies ([PERSON] et al., 2012). We present the OLS results in Table 5. Overall, the directions of the relationships broadly agree with the correlations in Table 2. Column 1 of Table 6 includes \(HCl\), \(FEM\), and \(NZ\) as explanatory variables. We observe that the coefficient on \(HCl\) is positive and significant at the 1% level.