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When federal aid increases, the goal, of course, is to help students afford their tuition.

But in reality, is that actually how the situation plays out? It’s a question that’s been part of the federal aid debate for decades, and it’s at the heart of a new paper by David Feldman and Richard Archibald, both professors at the College of William and Mary.

They start with an idea called the Bennett Hypothesis: the argument is that increased federal aid leads to higher tuition, because colleges know that their students will get help from the government.

It is true that colleges can “tax” federal aid, the researchers write. That is, they can give out less of their own aid than they would have otherwise, confident that federal subsidies will make up the difference. Over all, this happens rarely -- and almost never at public institutions.

The researchers also found little evidence that federal aid increases drive up list prices, which are often determined by what upper-income families -- who may be unaffected by financial aid -- are willing to pay.

“If the social goal of federal financial aid policy is to make higher education more affordable to many low-income families, there is ample evidence that it does so,” they write, “despite the fact that some of this aid displaces grant aid the institutions might otherwise have given.”