[Question] How valuable is it to attend a top global university?

Hi, I currently face the option to invest a huge amount of time into researching and applying to US universities and scholarships, with a small chance of payoff (plus there is the cost of tuition). I am struggling to tell whether it is worth the investment.

I plan to study maths and economics and do some kind of longtermist career, most options are still on the table: technical AI safety, governance, etc.

Oxbridge don’t offer the subjects I want to study so if I don’t go to America I will go to a good, but not globally famous, university.

For the type of degree/​career I’m looking at, how valuable is it to go to a globally recognised university rather than just a good one?

Thanks for your help!