In a new NBER paper, "Accounting for the Rise in College Tuition," Grey Gordon and Aaron Hedlund create a sophisticated model of the college market and find that a large fraction of the increase in tuition can be explained by increases in subsidies.
With all factors present, net tuition increases from $6,100 to $12,559. As column 4 demonstrates, the demand shocks — which consist mostly of changes in financial aid — account for the lion’s share of the higher tuition.
Specifically, with demand shocks alone, equilibrium tuition rises by 102%, almost fully matching the 106% from the benchmark. By contrast, with all factors present except the demand shocks (column 7), net tuition only rises by 16%.
These results accord strongly with the Bennett hypothesis, which asserts that colleges respond to expansions of financial aid by increasing tuition.
So to boil this down to the bone. Universities know that you'll pay "x" for tuition. If the government gives you $1000, magically your tuition increase to x + $1000.
These guys didn't need a study, they just needed to read my blog.