What are friends for? Climbing the income ladder, for one.

People with higher incomes have a lot of higher-income friends, while those with lower incomes mostly socialize with each other. And that effect seems to be particularly strong at the top.

If you are in the top 10 percent by socioeconomic status (which social scientists abbreviate as “SES”), then on average a third of your Facebook friends will also be in the top 10 percent. Meanwhile, the bottom half of the distribution will provide maybe 1 in 6 of your friends.

Some of this is obviously an artifact of our educational sorting system: If you went to Harvard Law School, you probably know a lot of rich lawyers. But that’s clearly not all that is going on here. Chetty, et al., looked at neighborhoods as well as individuals and found that growing up in an area with a high degree of “economic connectedness” has a significant impact on adult outcomes.

“Children who grow up in counties where low-SES individuals have more high-SES friends tend to have much higher rates of upward mobility,” the authors write. In fact, these effects are so strong that it predicts mobility better than almost anything else about a neighborhood: better than race or residential segregation, much better than mean household income or income inequality. Those other variables seem to lose much of their predictive power once economic connectedness is taken into account.

Now, of course, we should note that low-income folks living in neighborhoods with a high connectedness quotient aren’t necessarily the same as those living in less connected neighborhoods. A sociologist of my acquaintance likes to point out that he spent years living in a subsidized housing project populated entirely by people living below the poverty line — only it was Princeton’s graduate student housing. It’s telling that on the project’s associated website, the top two Zip codes for economic connectedness seem to be Stanford, Calif. (home to the eponymous university), and Cambridge, Mass., where Harvard is located.

But the places at the top aren’t all college towns, and the effect this research has demonstrated is so strong that it’s hard to believe it hasn’t identified something real. And also something troubling, because knowing what’s hampering social mobility doesn’t necessarily get you much further toward fixing it.

When we talk about social mobility as a problem that we need to “fix,” we are implicitly assuming a policy solution, such as legislation or institutional affirmative action. But usually we’re not talking about a problem as private and personal as whom we choose for our friends.

Chetty’s team suggests there are two key forces driving differences in economic connectedness between low-SES and high-SES people: exposure and “friending bias.” Disadvantaged people don’t frequent the same places as the privileged — on average, they go to different schools and colleges (if they go to college at all), attend different churches, join different sporting leagues. But even if you could somehow equalize those things, the researchers suggest that would close only about half the gap, because of friending bias — the propensity of people to mostly befriend others like them.

One can imagine policies that could tackle both of these factors, but they are impracticably draconian, such as forcing every young person to do national service in socioeconomically diverse groups that are too small to allow for much sorting by background. (And come to think of it, that sounds a lot like the World War II draft — which might help explain why mid-century America was so relentlessly middle-class.)

Short of that, one can sketch out institutional policies that would help on the margins, such as eliminating tracking in schools or reorganizing colleges into small cohorts deliberately designed for socioeconomic diversity.

But it’s harder to see how change happens in the real world, where millions of families make billions of private decisions about what’s right for them.

It is not, after all, an accident that so many high-SES young people grow up mostly around other high-SES young people. It’s a choice by parents who already know what this research is telling us: Peer effects matter.

They can be all in favor of diversity, but in practice, that diversity will often be highly managed — affirmative action for affluent children of color, or curated programs to bring a controlled number of carefully selected poorer kids into affluent schools. And if they conclude those controls have failed in some way, many of them will move their children before they will allow them to end up with a critical mass of friends from markedly lower socioeconomic strata.

Which is why as we search for fixes, we’ll probably keep opting for less-than-half-measures such as those above, even though they don’t seem to be fixing the problem — or rather, because they aren’t fixing the problem.