There is another side to it that, unfortunately, I was unaware of until my son told me when he began working at Yale. The key is being accepted.
While undegraduate are expected to pull the load, with the endowment and research grants at Yale, Harvard and Ivey league, Masters/PhD is virtually 100% paid for in each of the Colleges, irrespective if it is a PhD in English or nuclear physics. In retrospect, with my daughter while the Lottery Scholarship paid for most of undergraduate, the research grant funded her TA position during her PhD at SUNY Stoneybrook. I would throw her a few hundred as needed, but both son and daughter completed degrees with no debt. My son did create some debt with his MBA. Yale has a continuing education employee benefit to study anywhere BUT Yale. He got his MBA at the local Albertus Magnus (private Catholic University) but the stipend wasn't enough to cover 100%.
My brother, who is a professor at an Osteopathic Medical School, primarily teaching organic chemistry and associate dean for admissions, relayed an interesting dialog. Potential students typically have two or three acceptance letters deciding between. Invariably, during the admissions interview the applicant will ask the question "How much are you going to pay me to attend?" As I look back it was similar with my daughter. She was accepted at University of Calif Davis, but with the tight State budget they didn't have the funds to offer her. Univ of South Florida sent her a rejection letter so she accepted at Stoneybrook. A couple days later, the professor at So Florida called, looking forward to working with her, blah, blah, blah. Apparently the Admissions office sent the letter out in error, but since she already accepted at Stoneybrook, didn't back out.