Ronald G. Ehrenberg has a post at VoxEU entitled The Gender of American Academic Leaders Matters:
We find that institutions with female presidents and female provosts, and those with a greater share of female trustees did increase their share of female faculty at more rapid rates. Moreover, the magnitudes of the effects of these leaders appeared to be largest at the smaller undergraduate institutions, where central administrators may play a greater direct role in hiring decisions than they do at the larger research universities.
The prior research on corporate boards of directors suggests there is a critical mass of female directors on the board which is necessary before fundamental changes occur in board operations. Similarly, we test whether this was true in academia and find that a critical share of the board of trustees of an academic institution of 25% must be reached before the gender composition of the board influences the speed with which an institution diversifies its faculty across gender lines.