The answer to this question depends on whether this issue is institutional grant aid or federal and state financial aid.
Institutional grant aid reduces the tuition prices facing students. It allows institutions to charge different prices to different students—frequently based on their financial circumstances but sometimes based on their high school grades, test scores, athletic ability.
When colleges raise their tuition, they frequently increase their aid budgets to help students pay the higher prices. But giving these discounts means the college gets less revenue relative to the published price. So, there is a close relationship between sticker prices and institutional grant aid.
Federal and state financial aid is different. Some people argue that the simple forces of supply and demand mean that when the government gives students more money, colleges will raise their prices. This idea is sometimes called the “Bennett Hypothesis” (after former U.S. Secretary of Education William Bennett, who popularized the idea in 1987).
The empirical evidence about this impact is weak—outside of the for-profit sector. But even if this aid does put upward pressure on sticker prices, it’s a small price to pay. The point of the federal student loan and grant programs is to increase demand for college. Without federal student aid, lots of low- and moderate- income students would not go to college—they simply would not be able to pay. So, if we can make higher education possible for more people, it’s a fair trade-off that there might be some upward pressure on sticker prices.