For decades, policymakers, researchers and journalists have relied on a single metric to judge whether colleges are committed to serving low-income students: the percentage of their students who receive Pell Grants. But while such data are useful in comparing colleges based on their records of enrolling low-income students, they don’t reveal anything about the schools’ commitments to making college affordable for these individuals.

In 2008, Congress recognized the need for better information about how much money low-income students are really paying at different colleges. As part of legislation to reauthorize the Higher Education Act, the law governing federal student-aid programs, lawmakers required colleges to report their average “net price”—the average amount of money that students and their families must pay after all grant and scholarship aid is deducted from the “list price.”

Congress specified that colleges should report the net price broken down by income, but only for first-time, full-time students who receive federal financial aid. These data provide a reasonably clear picture of the financial hurdles that low-income students face at individual campuses, and they open a window onto how colleges are spending their institutional aid dollars.

Related: A fight in Maryland to stop colleges from stripping low-income students of institutional aid

Despite the availability and value of net price data, however, some higher-education experts continue to judge colleges based solely on how many Pell Grant recipients they enroll. For example, in 2014, the Education Trust released a paper entitled Tough Love that called on policymakers to penalize colleges at which fewer than 17 percent of freshmen receive Pell Grants.

Under the proposal, colleges that fail to meet the 17 percent Pell threshold within three years of the enactment of such a policy would lose access to institution-based federal aid. “If there is to be a shared responsibility for college access and success, then at some point the federal government should no longer permit low-access institutions of higher education—or their affiliated foundations—to take advantage of the tax code to receive tax-deductible charitable donations or institutional campus-based aid,” the authors wrote.

Related: Why UW-Madison’s plan to become bigger “merit aid” player is bad for U.S. public higher education

In a new report that New America is releasing today, entitled “Undermining Pell III: The News Keeps Getting Worse for Low-Income Students,” I argue that while such an approach is well-intentioned in its efforts to push colleges that have been “engines of inequality” to become more socioeconomically diverse, it doesn’t go far enough. (The report was funded by Lumina Foundation, which is also among the various funders of The Hechinger Report.)

That’s because it would hold harmless wealthy colleges that enroll a large share of low-income students but that charge them almost as much as their families earn in a year. Institutions like Baylor, Southern Methodist and the University of Miami—all of which provide merit aid to more than one-third of their non-needy freshmen, while charging their lowest-income freshmen an average net price of more than $20,000 a year—would escape scot-free.

I agree with Ed Trust that a federal solution is needed to push colleges to become more socioeconomically diverse. But any such plan must also hold all institutions accountable for making college affordable for low-income students. Because if a college enrolls a large number of Pell Grant recipients but doesn’t come close to meeting their remaining financial need, it may well be setting these students up for failure.

Related: College, federal financial aid increasingly benefits the rich

In the first two editions of Undermining Pell, published in 2013 and 2014, I proposed that the federal government take a carrot-and-stick approach to address these issues.

The carrot is to help schools that simply don’t have the resources to keep down net prices for the low-income students they serve. The plan would offer Pell “bonuses” to financially strapped four-year colleges that serve a substantial share of Pell Grant recipients (more than 25 percent of the student body) and graduate at least half of their students schoolwide—with the aim of having these schools use the money to boost their institutional aid budgets and therefore reduce net prices for the most financially needy students.

The stick is for wealthier colleges that divert aid in hopes of “buying” more affluent students to rise in the U.S. News rankings and increase their net revenues. These schools—which tend to enroll a relatively small share of low-income students but charge them high net prices—would be required to match at least a share of the federal Pell dollars they receive.

Related: How public colleges use merit aid to compete in the out-of-state student arms race

That’s one possible approach to combating these problems.

More recently, my colleagues and I at New America offered another approach that is far more ambitious in its scope. Our plan would create a new federal-state partnership in which states would receive formula funds from the federal government that they would have to match and send to colleges that enroll (and serve well) a substantial share of low-income students.

To be eligible for such funds, states would be required to maintain—and encouraged to increase—their investment in higher education. Colleges would be required to enroll low-income students, charge only what students could afford, and show evidence of positive outcomes. We would give colleges five years to increase their socioeconomic diversity. Ultimately, low-income students would have to make up at least 25 percent of the student body at participating colleges.

Our proposal would eliminate unmet need for all students, limiting the price they pay for college to their Expected Family Contribution (EFC), the amount the federal government determines a family can afford to contribute toward their children’s education. Federal, state and institutional funds would make up the difference between students’ EFC and the net price at the participating institution.

Related: Financial aid not always going to neediest college students

Both the carrot-and-stick proposal and the federal-state partnership plan are aimed at ending the merit-aid arms race and ensuring that colleges function as engines of opportunity rather than perpetuators of inequality.

[Cross-posted at Hechinger Report]

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Stephen Burd is a senior policy analyst in the Education Policy Program at the New America Foundation.