# Disentangling Director Attributes: Human Capital versus Social Capital of Directors
## 5 Multivariate Analysis
### Robustness Tests
#### 5.2.1 First Differences Regression  
To address endogeneity, we begin by rerunning our regressions using first differences. To do so, we examine whether changes in human capital affect contemporaneous and future changes in connectivity or changes in connectivity affect future changes in human capital, or both happen.  
We begin by taking observations for every third year to allow for enough variation in the human capital and connectivity measures which change slowly over time (see [PERSON] et al. (2012) for a discussion on time-invariant variables). Specifically, we calculate the change in \(AGG\) and the independent variables between 2000 and 2003, 2003 and 2006, 2006 and 2009, 2009 and 2012, and 2012 and 2015. The reduced sample includes 4500 director-year observations and 2229 changes. The average change in \(AGG\) is \(-0.13\) with a median of \(-0.05\) and standard deviation of 1.36. This suggests that changes in connectivity, on average, have been negative. This result is consistent with boards increasing the number of independent board members over time, resulting in fewer directors sitting on multiple boards. The average change in \(HCI\) is 0.77 with a median of 1 and a standard deviation of 1.04, suggesting that changes in human capital have on average been positive and more consistent than connectivity. We estimate the following model:  
\[\Delta AGG_{it-(t-3)}=\beta_{1}\Delta HCI_{it-(t-3)}+\beta_{2}\Delta NZ\ _{it-(t-3)}+\ \beta_{3}\Delta DIR\ _{it-(t-3)}+\sum_{y=1}^{V}\theta_{y} Year_{yt}+u_{it} \tag{8}\]  
where \(\Delta AGG_{t-(t-3)}\) is the change in connectivity, \(\Delta HCI_{it-(t-3)}\) is the change in human capital, and \(\Delta NZ_{it-(t-3)}\) is the change in the director's place of residence, which can be one of three values, \(-1\), \(0\), or \(1\). \(\Delta DIR\ _{it-(t-3)}\) is the change in the number of directorships held by a director. Finally, we include year dummies \(Year_{yt}\) to control for the time fixed effects on changes in connectivity. We exclude \(FEM\) from the regression as it does not change over the sample period.  
Table 6 presents the OLS estimates for Equation (2), where column 1 presents contemporaneous changes of \(AGG\) on \(HCI\). The coefficients on \(HCI\) are positive and significant after controlling for \(DIR\). These results suggest that current changes in human capital are positively related to current changes in director connectivity. Specifically, the results in column 1 indicate that increasing human capital by one point over a three-year period also increases their level of connectivity by 0.062. Column 2 provides the results for the impact of a current change in \(HCI\) on future changes in \(AGG\) which again shows a positive and significant coefficient. The results in column 2 indicate that when directors increase their human capital by one point over a three-year period, they achieve an increase in \(AGG\) of 0.101 in the next period. The coefficient on \(HCI\) is also larger compared to that in column 1. Overall, the evidence supports a causal relationship where an increase in human capital leads to an increase in connectivity. Column 3 investigates the relationship between changes in connectivity on future changes in human capital. The results are insignificant, suggesting that increases in connectivity have limited effects on human capital. This result also suggests that we do not have a simultaneity issue but also reinforces the need to control for human capital when examining the impact of social capital.