Which colleges are best at enrolling and graduating low-income students?

For years, popular rankings of universities and colleges have been blamed for pushing universities and colleges to shift financial aid away from needy students to wealthier graduates of top private and suburban high schools who can help them raise their standings.

Now the government has introduced another ranking meant to shame them into doing a better job enrolling low-income students and making sure they graduate.

The schools are being scored for the first time based on the number of recipients of Pell Grants they enroll — grants that go to children of families earning around $40,000 or less, and used as a measure of low income — and the proportion who actually get degrees.

The Obama administration hopes the public exposure will encourage colleges and universities to admit more such students, and help them finish.

It also proposes a total of $5.7 billion in financial bonuses over 10 years to be shared among the schools that do the best job of this, though that is part of the president’s 2017 budget request, and requires congressional approval.

The new list gives an early look at which schools those might be.

For example, among public universities, 58 percent of the students at California State University at Stanislaus get Pell Grants, and 53 percent graduate within six years—an even higher percentage than the overall average graduation rate for that campus. At the City University of New York’s Bernard M. Baruch College, 45 percent of the students are on Pell Grants, and 69 percent graduate.

The top performer among private, nonprofit institutions: Agnes Scott College in Georgia, 45 percent of whose students are eligible for Pell Grants. Of those, 71 percent graduate within six years.

And while the most selective campuses have much smaller percentages of Pell students, the government ranks them, too. Amherst does best, with 22 percent of its enrollment Pell-eligible, and 94 percent of them finishing within six years.

What the department did not report are the colleges and universities that do the worst. But government data provided on request show they include the University of Maine at Augusta, where 57 percent of the students get Pell Grants, but only 9 percent graduate; Franklin University in Ohio, where the comparable figures are 47 percent and 11 percent; and Bluefield State College in West Virginia, 59 percent and 12 percent.

There are complications with preparing lists like this — complications on which higher-education lobbyists have seized to block them.

The college-by-college graduation rates reported by the Department of Education for low-income students are largely wrong, for instance, according to independent reviews, including by The Hechinger Report.

That’s because, while colleges and universities themselves are required to disclose the graduation rates of their students who get Pell Grants, if asked, they don’t have to report them to the government.

The Education Department instead has calculated this statistic using an obscure database that was designed to keep track of student loans, which means the many students who get Pell Grants but don’t take out any loans to pay for college don’t show up.

The Hechinger Report found the graduation rates for Pell recipients the government reports are off by an average of 10, and as much as 59, percentage points.

So in its new list, the department took the surprising step of relying instead on graduation data collected by someone else — The Education Trust, which advocates for low-income students.

The Education Trust did not calculate the six-year Pell graduation rates of every university and college, however, so hundreds are not included in the data.

Meanwhile, the Department of Education plans eventually change the way colleges and universities report their graduation rates.

In its report, the Obama administration pushed other measures it has already proposed to improve the college-going and graduation rates of low-income students, and took credit for others already in force, including the American Opportunity Tax Credit, which goes to certain families that pay college or university tuition.

In fact, more than half of the $34 billion a year in tuition tax credits like these goes to households earning more than $100,000 a year, according to the Tax Policy Center. This despite research showing that 13 out of 14 students in those families would have gone to college even without the tax breaks.

This story was produced by The Hechinger Report, a nonprofit, independent news organization focused on inequality and innovation in education. Read more about higher education.