Robin Hanson:

Over the next two weeks my eldest son will be rejected by some colleges, accepted by others. And then we’ll likely have to make a hard choice, between cheap state schools and expensive prestigious ones. A colleague told me the best econ paper on this found it doesn’t matter. From its 1999 abstract:
We matched students who applied to, and were accepted by, similar colleges to try to eliminate this bias. Using the … High School Class of 1972, we find that students who attended more selective colleges earned about the same [20 years later] as students of seemingly comparable ability who attended less selective schools. Children from low-income families, however, earned more if they attended selective colleges.
A 2006 NYT article confirms this:
Higher education experts have this message … Pay less attention to prestige and more to “fit” — the marriage of interests and comfort level with factors like campus size, access to professors, instruction philosophy. … A 1999 study by Alan B. Krueger … and Stacy Dale … found that students who were admitted to both selective and moderately selective colleges earned the same no matter which they attended.