[fastaguy88]

While it is true that departments often fund their graduate students for the first year (or possibly 2) out of their own budgets, their budgets are largely determined by the generosity of their Deans (who got the money from indirect costs from grants) or their own indirect costs. And they will not be admitting students if they do not see a clear path for them to be externally funded after their first year or two.

[BeetleB]

Oh yes. As I said, the math department guaranteed 6 years. If they can't guarantee it, they won't admit the student.

The engineering departments, however, admitted students regardless of funding as long as they met the bar. On the application they'd ask the candidate if they wanted the admission to be contingent on funding.

Universities like MIT that admit only if they have funding for engineering are the outliers. Usually they're private universities.