​How many college grads are actually baristas?

It seems like everyone has heard about college grads who are stuck serving up lattes at Starbucks (SBUX), earning barely more per hour than the price of a venti caramel Frappuccino.

But is that really happening to America's newest college grads? In what may cause a huge sigh of relief to parents and students everywhere, not so much, according to new research from the Federal Reserve Bank of New York.

The recession and recovery years have been tough for the millennial generation, which graduated into a weak labor market while owing an average of $30,000 in student debt. Anecdotes are common about recent grads failing to find work in their areas of study and turning to low-paying service jobs such as baristas and waiters.

But those anecdotes aren't supported by economic data, according to the N.Y. Fed researchers who found only a small percentage of grads worked in low-pay service jobs in the four years following the recession.

"People love to use the image of a college-educated barista," said Richard Dietz, assistant vice president at the N.Y. Fed. "We realized it was a lot less pervasive than you might be led to believe."

Only about 9 percent of all recent college graduates worked in a low-skill service job from 2009 through 2013, the four years following the recession.

And for 20-somethings who are worried about getting stuck in those jobs forever, the researchers had some additional good news: The percentage who are employed in service jobs drops by half by the time they reach their mid-20s, which suggests that they're transitioning to jobs better tailored to their skills.

Still, that's doesn't mean everything's peachy keen for recent grads. Many are struggling to get into what Dietz and research officer Jaison Abel describe as "college jobs," or professions where at least 50 percent of the workers indicated that they needed at least a bachelor's degree. They found about 45 percent of grads worked in noncollege jobs in the years following the recession, meaning they're underemployed or working in jobs that don't match their skills.

How does that stack up with past generations? Clearly worse, Abel said.

"When you extend that analysis out to all college grads, it's roughly about one-third," Abel said.

One recent exception was in the early 1990s, when the recession in that period left about 48 percent of recent college grads underemployed. That was the era when Gen X came of age, as celebrated by movies such as "Reality Bites," when 20-somethings struggled to get an economic foothold. But that passed quickly, and the boom that followed allowed many to find better jobs and prospects.

Millennials are also shifting into better jobs. About 59 percent work in college jobs by the time they reach 26 or 27, compared with 48.4 percent of college-educated 22- and 23-year olds.

And underemployment doesn't necessarily mean minimum-wage work. About half of underemployed millennials hold relatively high-paying jobs, such as in information processing and business support, where the average wage is slightly more than $59,000, the researchers found. The largest share, about one-quarter, are in office and administrative support roles, where the average annual pay is $37,207 -- far more than a barista would take home.

And even if college grads are temporarily stuck in noncollege jobs, the researchers found evidence showing they're more likely to be working in higher-paying jobs than their counterparts without college educations.

"For most people, a degree does tend to pay off if you look at the financial costs versus benefits," said Dietz. "When you see the figures of underemployment, it could make you believe they are almost worse off as if they didn't go to college. But what we're saying is this is temporary. And secondly, even among those who are underemployed, there's evidence that they tend to get better jobs and get paid more."