Vassar has taken steps to hold down spending on faculty and staff. Amherst and the University of Florida have raised new money specifically to spend on financial aid for low-income students. American University reallocated scholarships from well-off students to needy ones. Grinnell set a floor on the share of every freshman class – 15 percent – whose parents didn’t go to college.

Over the last decade, dozens of colleges have proclaimed that recruiting a more economically diverse student body was a top priority. Many of those colleges have not matched their words with actions. But some have.

These colleges have changed policies and made compromises elsewhere to recruit the kind of talented poor students who have traditionally excelled in high school but not gone to top colleges. A surprising number of such students never graduate from any college.

This education gap is a problem not only for the teenagers on the wrong end of it. It’s a problem for the American economy. The economic differences between college graduates and everyone else have reached record levels. Yet for many low-income children – even many who get A’s in high school and do well on the SAT – college remains out of reach. No wonder that upward mobility is less common in the United States than in many other rich countries.