In 1987, when he was Ronald Reagan’s education secretary, the conservative culture warrior William J. Bennett wrote a famous essay denouncing federal aid for higher education because it allowed colleges “blithely to raise their tuitions,” at little benefit to students.

Nearly two decades later, it seems, he was broadly right. Indeed, he didn’t know the half of it.

It’s not just that many colleges and universities are bleeding taxpayers. The government’s overall strategy to subsidize higher education is failing at its core task: providing less privileged Americans with a real shot at a college degree. Alarmingly, it is burdening low-income students with risks they cannot bear and steering them into low-quality educations.

“Institutions of higher education in the United States extract a lot of money without delivering value but the government has no way of influencing that,” said Andreas Schleicher, the top education expert at the Organization for Economic Cooperation and Development, the research organization for the world’s major industrial powers. “It has very few levers of control over equity-related issues.”

Take the “Bennett hypothesis.” There are many studies suggesting that a lot of colleges pocket part of the aid via higher tuition. Among the most recent studies, Lesley J. Turner of the University of Maryland finds that every additional dollar of Pell Grant money — the main federal aid program — leads to a 17-cent cut in institutional aid, on average.