Here's some interesting new data from Jaison Abel and Richard Dietz of the Federal Reserve Bank of New York. The vast majority of U.S. college grads, they find, work in jobs that aren't strictly related to their degrees:

There are two different things going on in this chart. First, a significant number of college grads appear to be underemployed: In 2010, only 62 percent of U.S. college graduates had a job that required a college degree.

Second, the authors estimated that just 27 percent of college grads had a job that was closely related to their major. It's not clear that this is a big labor-market problem, though — it could just mean that many jobs don't really require a specific field of study. (You can find Abel and Dietz's longer paper here, and note that they are excluding people with graduate degrees in this second chart — so no doctors, lawyers, college professors, etc.)

There's an important twist here, too. The chances of finding a job related to your degree or major go up a few points if you move to a big city:

The authors' argument is that "big cities have more job openings and offer a wider variety of job opportunities that can potentially fit the skills of different workers." The odds of finding a match between college degree and job are about 6 percentage points higher in a place like New York City than in, say, Syracuse.

Of course, a key caveat here is that landing a job unrelated to your major isn't necessarily the end of the world. Indeed, it's the most common outcome by far. (My specific math degree doesn't really come in handy for journalism all that often, but college itself was still useful.)

The research does, however, hint at one possible advantage of large cities — and might help explain why workers in denser cities tend to be more productive. If there's a policy upshot here, it's that the broader economy could stand to benefit if large cities loosened up some of their restrictions on housing and made it easier for more people to live there — a point that writers like Matt Yglesias and Edward Glaeser have made over and over again.

Related: Maybe college isn't for everyone. But it's probably for you.