Companies with higher CEO pay compensate their boards more generously.

"In fact, there is strong evidence that companies with higher CEO pay compensate their board members more generously, a clear indication that board members are engaged in a corporate liaison with CEOs rather than serving as independent parties that can assess the appropriate award for a CEO’s performance. As Schwartz (2017) argues, because they are less invested as stakeholders, board members are less generous with their time than they are with doling out money to executives."

empirical