The average cost of attending an in-state public college or university increased by more than 40 percent over the past decade, after adjusting for inflation. Public institutions have spent heavily to attract students — and to keep pace with private competitors — even as many state legislatures have cut funding.

Colleges also have shifted their pricing models, charging higher list prices but offering more aid, so that lower-income students may actually pay less.

The idea that the federal government is contributing to the problem first gained widespread attention in 1987 when William Bennett, the secretary of education at the time, wrote in an opinion piece in The New York Times that colleges were raising prices in part because they were confident the federal government would provide more aid. The idea still is often described as the “Bennett hypothesis.”

The logic is straightforward. Imagine if the government started handing out gift cards that could only be used to buy Broadway theater tickets. As there are only so many seats available, the price of tickets would probably begin to climb.

But efforts to measure the effect on tuition costs have ranged widely. Some studies have found little evidence of a significant impact. The New York Fed study, however, looked at three different increases in federal subsidies in recent years and found that each had produced a significant increase in college tuition.

Another piece of evidence: The government limits the total amount undergraduates can borrow, but for the last decade it has allowed graduate students to borrow unlimited sums. Before the change, undergraduate tuition was rising more quickly than graduate school tuition. Since the change, the pattern has reversed, according to Andrew Gillen, an independent education analyst based in Washington.

“Schools are under tremendous competitive pressure to raise as much revenue as possible from every possible source,” Mr. Gillen said.