This paper provides new evidence supporting that gender differences in post-graduate educational choices contribute to the glass ceiling in the labor market. We study the decision to pursue an advanced degree form an internationally renowned institution, which greatly facilitates access to top jobs. Relying on a unique dataset on applications to a highly selective program that provides merit-based graduate fellowships to Spanish students, we show that women apply for the fellowships at lower rates than observationally equivalent male graduates. We also implemented a large-scale survey on current college students and show that female college graduates have stronger family ties than males, which restricts their geographical mobility and has a negative effect on their educational aspirations. Importantly, the previous pattern is reversed in STEM fields: female graduates in STEM participate in the fellowship program at equal or higher rates than comparable males. In fact, we show that female STEM students originate from more educated families, have higher academic ability, and higher educational and earnings aspirations than women in other fields.