# Disentangling Director Attributes: Human Capital versus Social Capital of Directors
## 5 Multivariate Analysis
### Robustness Tests
#### 5.2.2 Logit Regression  
We next test the robustness of our main results by estimating logit regressions to test whether greater levels of human capital increase the likelihood of a director being highly connected. Specifically, we investigate whether the likelihood of being in the 75 th quantile of \(AGG\) is influenced by human capital. The following logit regression equation is estimated:  
\[\ln\left(\frac{P\left(AGG_{it}^{Q75}=1\right)}{1-P\left(AGG_{it}^{Q75}=1\right) }\right)=\alpha+\beta_{1}HCl_{it}+\beta_{2}FEM_{it}+\beta_{3}NZ_{it}+\beta_{4}DIR +\sum_{y=1}^{Y}\theta_{y}Year_{yt}+\varepsilon_{it} \tag{9}\]  
where \(P\) is the probability of director \(i\) in year \(t\) being in the 75 th quantile. The dependent variable is coded as one if director \(i\) in year \(t\) is in the top 25 th percentile of \(AGG\) and 0 otherwise; \(HCl_{it}\) represents the human capital index for director \(i\) in year \(t\) and all other variables are consistent with Equation (1). Robust standard errors \(\varepsilon_{it}\) are clustered at the director level ([PERSON], 2009).  
Table 7 reports the results of the logit model regressions. As logit regression coefficients are typically reported in log-odds units, which are hard to interpret, we report odds ratios which represent the change in the odds of being highly connected arising from a one-unit change in \(HCl\), with 1 representing no change. The overall evidence in Table 7 supports our previous findings that there is a strong causal relationship between human and social capital. In both specifications we observe an odds ratio significantly higher than 1, ranging between 1.317 and 1.155. These findings indicate that a director with an \(HCl\) score of 1 point higher, has between a 15% and 32% chance of being a high-connected director. Of the control variables, female directors are between 37% and 52% more likely to be highly connected; unsurprisingly, directors with more directorships are extremely more likely to be better connected. Overall, the findings support the main analysis, predicting a positive relationship between human capital and social capital.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **1** & **2** \\ \hline  & **AGG\({}^{Q75}\)** & **AGG\({}^{Q75}\)** \\ \hline  & **LOGIT** & **LOGIT** \\ \hline Constant & 0.022 *** & 0.003 *** \\  & (\(-\)18.25) & (\(-\)21.12) \\ HCI & 1.317 *** & 1.155 *** \\  & (14.08) & (6.89) \\ FEM & 1.520 *** & 1.369 * \\  & (2.81) & (1.86) \\ NZ & 1.505 *** & 0.745 ** \\  & (4.17) & (\(-\)2.53) \\ DIR & & 13.945 *** \\  & & (14.58) \\ \hline Observations & 12,211 & 12,211 \\ Pseudo R2 & 0.104 & 0.286 \\ Log & \(-\)6155 & \(-\)4903 \\ Wald Chi2 & 397.7 & 457.9 \\ p(F) & 0.000 & 0.000 \\ Year fixed effects & Y & Y \\ \hline \hline \end{tabular} This table presents results for logit regressions where each observation represents a director for a given year between 2000 and 2015. The dependent variable equals one if a director is in the top 25% quantile of \(AGC\) at time \(t\), and zero otherwise. Odds ratios are reported representing the likelihood of a change in the dependent variable arising from a one-unit change in the independent variable. \(AGG\), is the PCA connectivity factor. \(HCl\) is the human capital index score of the director, \(FEM\) is a dummy variable that equals 1 if the director is a woman. \(NZ\) is a dummy if the director was domoiled in New Zealand, \(DIR\) is the number of directorships of the director Z-statistics, displayed in parenthesis below each odds ratio estimate, are based upon robust standard errors clustered at the director level. Year dummies are included but not shown. * \(p<0.10\), ** \(p<0.05\), *** \(p<0.01\).  
\end{table}
Table 7: Logit regressions for the relationship between human capital and social capital—top 25%.