We study how the promotion of a female professor affects future hiring decisions and PhD students in the department. We exploit a large-scale natural experiment which generates exogenous variation across Spanish university departments in promotions to Associate and Full Professor positions. Between 2003 to 2007, the composition of committees in national qualification exams was randomized and applicants were significantly more likely to be promoted if, by luck of the draw, they were assessed by a committee including a strong connection such as a colleague, a co-author or a former advisor. Using information from 3,700 departments in all academic disciplines and around 3,000 promotions, we find that the (exogenous) promotion of women to Associate or Full Professor does not lead to an increase in the number of women hired or promoted in the department within the following ten years or to an increase in the share of female PhD students. However, a larger presence of female faculty is likely to affect enrolled students, as PhD students exhibit a preference for same-sex advisors.