Plenty. A study of 4 million U.S. workers’ career paths, by job market analytics firm Burning Glass Technologies and the nonprofit Strada Institute for the Future of Work, says that underemployment — defined as working at a job that doesn’t require your degree — is tough to climb out of. About four in 10 new college grads (43%) are underemployed, the report says, and of those, two-thirds will still be working at low-skilled jobs five years later. A decade after graduation, three out of four college graduates in that group will be overqualified for the job they’re doing. In all, people who are initially underemployed are five times more likely to remain so in the long run than new grads whose first jobs after college required a degree.

The problem of underemployment is especially acute for women. Not only do more women (47%) than men (37%) start out underemployed after college, but women are more likely than men to stay that way. “This gender gap persists over time and holds true across every [college] major except engineering,” notes the report.

For both sexes, underemployment is expensive. Recent college grads ages 22 to 27 doing non-bachelor’s-level work earn, on average, $10,000 less per year than their peers whose entry-level jobs called for a sheepskin. Now that the average student leaves college with $39,000 in debt (up from $30,000 just five years ago), that stings.

The prevalence of underemployment, usually rampant during recessions, in the current robust economy is “surprising, and scandalous,” notes Matt Sigelman, CEO of Burning Glass. Part of the reason is that “there’s been a big shift among students in recent years away from the humanities into majors that sound more practical, but really aren’t.” Majoring in business, for example, “sounds career-minded, but where exactly does it lead?”

Good question, absent specific skills that companies want. Most employers hiring entry-level finance grads, for example, prefer they have some knowledge of enterprise software like SAP — yet college finance departments rarely teach it. “The idea that ‘you’ll figure it out later’ is a myth that schools perpetuate,” he says. “So most students don’t start to focus on what employers want until they’re well into their senior year, which is way too late.”

As for why women — even in STEM fields like mathematics and computer science — are more likely to start out (and stay) underemployed than their male counterparts, the research is inconclusive, but Sigelman sees two possible reasons. First, he says, “avoiding underemployment after college takes a conscious strategy” for finding that all-important first job, “and mentors can really help. Men may have stronger professional networks right out of school than women do.”

A second possibility, Sigelman adds, is that men are more inclined to go after openings where the job description includes skills they haven’t got yet. “A man who has a few of the requirements, but not all, is likely to apply anyway, with the idea that he can learn on the job,” he says. Women, by contrast, “more often think they’re underqualified if they don’t meet all the criteria. So they don’t apply.”

Anne Fisher is a career expert and advice columnist who writes “Work It Out,” Fortune’s guide to working and living in the 21st century. Each week, she’ll answer your most challenging career questions. Have one? Ask her.