This is why graduation rates are so tricky: The colleges that have the lowest rates are the very same ones that are taking the biggest chances on students. Is it worth it to admit the students on the margins of educational success when you know half of them will drop out? Especially when the costs of dropping out are so high? How low can a graduation rate get before it does more harm than good?

“There is a legitimate policy conversation about where you draw that line,” said Lanae Erickson Hatalsky, an author of the Third Way paper, “but no one is even having that conversation right now.”

Getting first-generation college students to succeed presents challenges that more elite colleges often don’t face.

The University of La Verne is a commuter college 30 miles east of Los Angeles and, according to Third Way, has a six-year graduation rate of 59 percent. Its student body is 44 percent Hispanic, and 46 percent of all students are Pell grant recipients.

For these students, money is a huge roadblock to graduation.

“That is the No. 1 reason our students give when they drop out,” said Beatriz Gonzalez, vice provost for the University of La Verne.

Many of her students also work to support themselves or their families, she noted, so they tend to spend much less time on campus and therefore feel less attached to the university.

Another reason students drop out, Ms. Gonzalez said, is that they don’t feel sure they belong. For them, any setback or poor grade can make them question whether they should be in college in the first place.