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.
That is Ronald Ehrenberg in VoxEU. Also,
…the gender of the chair of faculty search committees, in the science and engineering fields at major research universities in the US, influences the likelihood that female PhDs will apply for positions at these universities.
Apparently knowledge of the gender of the chair of the search committee signals something to potential female applicants about the seriousness of the department in wanting to expand female faculty employment and in providing leadership opportunities for female faculty.