When the development offices of massive, astoundingly wealthy universities such as Harvard, Yale, Stanford, and Columbia make their pitches to prospective donors, the No. 1 message is always the same: financial aid.

The idea, bolstered by profile after profile of talented students from humble backgrounds accepted into these elite schools, is that giving to Harvard (endowment: $35.7 billion) and Yale ($25.4 billion) helps low-income students from poor towns and neighborhoods afford tuition. The institutions aren’t just leading producers of cutting-edge research; they’re actually engines of upward social mobility. So while it may seem like these schools are obscenely large hedge funds attached to finishing schools for children of privilege, they’re actually key guarantors of the American dream.

But the latest research by the Equality of Opportunity project — helmed by Stanford’s Raj Chetty, Brown’s John Friedman, and Harvard's Nathaniel Hendren — suggests that this is a myth. Chetty and Friedman, along with co-authors Emmanuel Saez, Danny Yagan (both at UC Berkeley), and Nicholas Turner at the US Treasury, used a massive data set covering 10.8 million people born between 1980 and 1982 to estimate individual colleges’ effect on students’ odds of moving into a higher rung of the income distribution.

They were able to match individual college attendance records from the Department of Education to both those students’ future incomes — up to age 34 for the oldest 1980 students — and their parents’ incomes, as indicated in their tax returns. That, in turn, let them see how many kids born into the bottom 20 percent of the income distribution (household income of $25,000 or below for the 1980 cohort) were able to escape and make it to the top 20 percent, or even the top 1 percent. What’s more, because the sample size is so massive, they can break that down by individual schools.

The good news is that elite schools are pretty good at getting the poor kids they teach into the top 20 percent, and astoundingly good at getting them into the top 1 percent. At Harvard, more than half of students born into families in the bottom fifth of the income scale reached the top 20 percent of earnings ($58,000 a year for adults their age), and about one in eight got into the top 1 percent ($197,000 a year) by age 32 to 34. Stanford did even better: 18.5 percent of bottom-quintile attendees were in the top 1 percent.

But there’s a problem: These schools teach barely any poor kids. For the 1980-’82 cohort, only 3 percent of Harvard students came from the bottom fifth of the income distribution. For Stanford, the share was only 3.6 percent. These students are underrepresented at elite schools, relative to their share of the overall population, by a factor of five. As a handy interactive the New York Times created using this data shows, the schools have gotten modestly better in years since.

As of the class of 2013, 4.5 percent of Harvard students and 4 percent of Stanford students came from the bottom fifth. By contrast, 15 percent of Harvard students and 17 percent of Stanford students came from the top 1 percent, families making $630,000 or more a year. The schools were three to four times more likely to enroll scions of the ultra rich as they were to enroll low-income kids.

Instead, the true heroes that come out of the research are not Ivies, but less selective schools that accept a large number of students from low-income backgrounds and help them climb the income scale. They include schools like the City College of New York, or Cal State Los Angeles, or University of Texas Pan American (which has since become UT Rio Grande Valley). All three of those schools took more than a fifth of their students from the bottom fifth of the income scale, and all three are in the top 10 schools ranked by the share of students who move up two or more income quintiles.

There are two big lessons to be learned here. One is that schools like Harvard and Stanford should probably be recruiting and enrolling vastly more low-income students, because when they do, the results are truly incredible; they just haven’t shown much of an ability to enroll a student body that reflects the economic makeup of the country. And the problem isn’t one of financial aid (which is already very generous at these schools) but of outreach; these schools just aren’t getting through to thousands of high-achieving poor kids.

The second lesson is that policymakers ought to be paying way more attention to the CUNYs and UT Rio Grande Valleys of the world. There’s a big category of unsung heroes, colleges that are successfully catering to and lifting up students with low incomes, and we don’t fully know yet what they’re doing right or how to copy it.

How to measure how much schools are helping the poorest students

The study’s authors track the schools they examined using a variety of metrics, but three stand out as most important:

Access rates , or the share of a school’s student body coming from the bottom 20 percent of the income distribution

, or the share of a school’s student body coming from the bottom 20 percent of the income distribution Success rates , or the share of those poor students who wind up in the top 20 percent (or top 1 percent) as adults

, or the share of those poor students who wind up in the top 20 percent (or top 1 percent) as adults Mobility rates, or the share of a school’s student body that comes from the bottom 20 percent and winds up in the top 20 percent or top 1 percent; you can derive mobility rates by multiplying access rates by success rates

If you sort schools by access rates, you get a dramatically different picture than if you sort by success rates. The top schools by top 20 percent success rate tend to be specialized around a high-skill, high-earning profession like health or engineering. The top three are all pharmacy schools, with the California Maritime Academy, Rose-Hulman Institute of Technology, Harvey Mudd College, and the Advanced Institute of Hair Design not far behind.

But these schools don’t tend to enroll a whole lot of poor kids. For instance, 1.7 percent of Rose-Hulman students come from the bottom 20 percent, according to the most recent data. The best-performing of the high-success rate schools on access, MCPHS University (formerly Massachusetts College of Pharmacy and Health Sciences), enrolls 8.9 percent of its students from the bottom 20 percent — better than most Ivies, but still not ideal.

These schools are very good at getting the low-income students they do have into the top fifth of the income distribution. But their overall impact is limited, since they don’t enroll very many of those students to start with.

This is even more true when you look at upper-tail success rates: the share of poor kids who end up not just in the top 20 percent but the top 1 percent. The best schools by that metric tend to be highly selective universities and liberal arts colleges. Claremont McKenna tops the list, followed by Rhodes College, Stanford, Harvey Mudd, Caltech, Columbia, Johns Hopkins, and Penn. (St. Louis College of Pharmacy sneaks in right before Princeton, Harvard, and MIT.)

If you're a poor kid who gets into one of these schools, you have a shockingly good chance of winding up as one of the very richest people in America. Nearly a third of Claremont McKenna's students from the bottom 20 percent wind up in the top 1 percent; at Caltech and Columbia, they have a 15 percent chance of ending up at the top of the ladder. Given that the typical poor kid has way less than a 1 percent chance of ending up in the top 1 percent, that's pretty damn good.

But most of these schools don’t enroll many poor people either. Only 4.8 percent of Claremont McKenna students come from the bottom fifth of the income scale; at Princeton, only 2.2 percent do. While that handful of students gets a great deal, these schools are enrolling so few of them that their overall effect on social mobility is minimal.

On the other end of the spectrum, sorting schools by access reveals a great number of schools that enroll lots of poor kids but don’t offer much in the way of mobility. The top school by access isn’t very representative (the United Talmudical Seminary, a Satmar yeshiva in Brooklyn), but Moultrie Technical College, a public technical college near the Florida border in Georgia, provides a good case study. Nearly half of students come from the bottom fifth of the income scale — very good numbers if a school is really trying to help with social mobility. But a mere 2.9 percent of those low-income students make it to the top fifth of the income scale.

Moultrie’s overall mobility rate — access divided by success — is 1.3 percent. Barely more than one in 100 students are poor kids who make it to the top after attending the school. That’s the exact same share as Princeton, though the two schools come to their dismal rankings through very different means.

Those, in sum, are the two types of problem schools. There are the highly effective schools that barely enroll any poor kids but do tons for the few they do have, and the highly ineffective schools that enroll a lot of poor kids but offer them little.

Which schools do best?

If you sort schools by their overall mobility rate — the access they provide to poor students, multiplied by their success in economically advancing those students — the top 10 looks unlike any US News ranking you’ve ever seen:

None of these are uber-selective Ivies or Ivy-adjacents like Stanford or MIT. Pace and Stony Brook are probably the most selective of the bunch, and they’re substantially less selective than US News’s top schools. Instead you get a list of what the New York Times’s David Leonhardt dubs “America’s great working-class colleges.”

Some, like Pace and Stony Brook (and Cal State Poly Pomona) enroll a decent but not extraordinary share of low-income students, and then rocket a huge share of them to the top of the income scale. Others, like Cal State LA or UT Pan American, have more modest success rates but also enroll more low-income students. But all of them, through whichever means, wind up devoting a significant share of their resources to elevating low-income students to the top of the income distribution.

Part of what makes this finding so interesting is that the researchers don’t really know why these schools are doing so well. Cal State, LA, Pace, and CUNY suggest that being in a major, rich metropolis helps — but then how does one explain the presence of University of Texas Pan American, in the small city of Edinburg? Maybe it’s about what students study at these places; maybe they’re heavier on science, engineering, and math majors who go on to higher-earning careers. Except that doesn’t really seem to be the case, if you compare high-mobility schools with all schools:

“You see almost no difference in the distribution of majors,” Brown economist John Friedman, one of the paper’s authors, told me. “From a statistical perspective, the distribution across these fields has very low explanatory power.”

That’s part of what makes this research so exciting: It lets us distinguish between high-performing and low-performing schools (in a way that correlates highly with other measures of higher ed quality), but it also creates an agenda for follow-up research seeking to identify what makes, say, the Technical Career Institutes in New York so much more effective than Moultrie Technical College at making poor students substantially better off. And that research in turn can help worse-performing schools adapt best practices and starting producing more social mobility themselves.

What this research implies about hyper-selective colleges

There’s also more research to be done on what would happen if schools with high success rates but low access — schools like Claremont McKenna or the Ivy League — started letting in dramatically more poor students. Perhaps those schools are so effective at helping the poor students they do get because of networking effects (they meet rich students, who help them out) that would go away if the student body became more representative of the country.

But the preliminary data suggests that’s not true, and that these schools could enroll many more poor kids than they do with little ill effect. “At all institutions, kids from poor families and rich families have very similar outcomes,” Friedman notes. You wouldn’t expect that if poor kids are just riding on rich kids’ coattails. Also, the authors examined schools where the share of poor kids enrolled rose over time (most notably Harvard, which saw a big jump in low-income enrollment between 1998 and 2002), and checked to see if they became less successful at elevating those kids economically. The answer was … not really.

“There’s a very small negative correlation between changes in access and changes in outcomes but the magnitude is so small — it’s minus .08,” Friedman says. “So if you had a 10 percentage point increase in access, that would predict that only 0.8 percent fewer of your students would make it into the top 20 percent.” For context, a 10 percentage point increase in access would involve Princeton increasing its enrollment of low-income students sixfold — and it would barely change the school’s effectiveness at making them richer.

Friedman is sure to note that this isn't experimental data; you’d need a school to suddenly change its admissions policy to let in more low-income students, and then for another school with very similar characteristics to hold its admissions constant, and then you’d have a quasi-experimental data set that could provide more definitive answers.

But the study certainly suggests that the Harvards, Stanfords, and Princetons of the world could be doing much, much more to foster social mobility.

The complication is that it’s not like tons of poor overachieving kids are applying to these schools and getting rejected. Nor is the problem one of cost; in many cases, selective schools’ larger endowments enable them to offer enough financial aid to make attendance cheaper than going to a non-selective school.

The problem, as Stanford's Caroline Hoxby and Harvard's Christopher Avery have found, is that “the vast majority of low-income high achievers do not apply to any selective college.” Indeed, a majority don’t apply to any selective college but do apply to at least one non-selective school. That evidence suggests that elite schools need to be doing a lot more to solicit applications from low-income students, a task made more difficult by the fact that these students are too geographically dispersed for college admissions departments to do traditional recruitment through high school visits.

Luckily, Hoxby and the University of Virginia's Sarah Turner conducted a large-scale randomized study where they sent mailers to high-scoring high schoolers in poor households offering information on applying to highly selective schools, including advice on crafting an application, a waiver of application fees, and information on the net cost of attendance. They found that the intervention, which costs a mere $6 per student, made students 46 percent likelier to enroll in a selective school.

Hoxby and Turner have argued that schools should partner with the College Board or another institution to do this kind of outreach en masse, and greatly increase their share of lower-income students. That would be an excellent start, if these institutions are going to have the effect on economic mobility they like to bill themselves as having.