NEW YORK — A dozen college presidents, most representing non-flagship public schools, gathered here recently for an annual media dinner. Many spoke persuasively about the need for greater public investment in higher education.

They spoke of stressed budgets. Bigger class sizes. Efforts to serve more demographically diverse and sometimes underprepared students. Greater demand from undergrads for wraparound services such as psychological counseling, tutoring and internship placement.

Toward the end, the presidents were asked whether they thought it was likely the country would someday adopt “free college,” as many Democrats are proposing.

Not a single hand went up.

Then they were asked whether they thought free college was a good policy, as opposed to a probable one. Surprisingly, given the stories we’d heard, not a single hand rose then, either.

Which suggests the institutions that theoretically stand to benefit most from free college live in an entirely different political reality than the 2020 Democratic candidates pushing for it.

To be sure, both groups are deeply concerned about public disinvestment in higher education. State postsecondary funding was cut in the most recent recession (as in earlier downturns), and it never fully recovered. In fact, in inflation-adjusted terms, state funding per full-time-equivalent student today is about where it was in the 1980s, according to the State Higher Education Executive Officers Association.

That’s despite the fact that workers today are more frequently expected to have postsecondary education and that an educated workforce has become more critical to local economic growth. These and other factors argue for allocating more, not less, public money to higher ed.

Instead, state policymakers have been shunting more of the costs of higher education onto students themselves. Back in 1980, tuition covered about a fifth of the cost of a student’s education, with the rest paid for by state and local appropriations. Today, tuition instead funds nearly half. In some states, the student’s share is even higher. In Vermont, for instance, 87 percent of educational revenues come from tuition.

At the dinner, presidents shared their battle scars from these funding wars. Some talked about begging for every dollar, in both good economies and bad. Some gave dire warnings about what the future holds if trends continue.

“In 15 to 20 years, half our states will be out of the public funding of higher education,” predicted F. King Alexander, president of Louisiana State University. “And we will have completely federalized our higher education system on tuition and fees on the backs of students.”

His pessimism is born of experience.

Louisiana cut his school’s appropriations 16 times over the course of nine years. Many of those cuts came in the middle of the year, thanks partly to revenue shortfalls resulting from then-Gov. Bobby Jindal’s (R) tax cuts. The school coped by raising tuition for students, though not by enough to offset the funding cuts. It also reduced class availability (which meant students had to delay credits needed for graduation) and eliminated positions for instructors and counselors, Alexander said.

“Students are paying more and getting less,” he added.

In this context, free college can understandably sound like a pipe dream. Designing it is politically tricky, too, given the challenges of fiscal federalism, as Urban Institute scholar Matthew Chingos has pointed out.

Many of the major free-college plans propose eliminating tuition as it stands today and completely replacing it with some sort of federal-state funding match. But that could reward bad actors that have been charging high net tuition (such as Vermont). Likewise, it would punish states that had been doing right by their students and charging low tuition.

Moreover, enticing red states to direct a lot more tax revenue to higher ed may be difficult, even if the federal funding match is generous. The detailed free college plans available generally have states paying about 30 to 50 percent of the cost; recall that Obamacare’s Medicaid expansion offered a much more generous match ($9 from the feds for every $1 from the state), and many states still left the money on the table.

Any national free college plan would also likely involve more federal oversight to ensure colleges maintain quality, which could rub states’ rights-obsessed officials the wrong way.

Alexander remains hopeful that some sort of federal-state funding match — if not necessarily one that requires completely eliminating tuition — might still convince states like his to direct some additional tax dollars into higher ed. Or if not his current state, his future one: Days after that dinner, he announced plans to depart LSU for Oregon State, where he anticipates fewer legislative battles over state appropriations.

In a sense, his career transition may be telling. Even if Democrats unexpectedly succeed in passing a federal free college plan, we still might see the same kinds of sorting we saw for Obamacare: more educational investment by states that prioritize it, and not enough by those that don’t.

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