The Class of 2013 will face an "extremely difficult" job market when college students graduate in the months ahead, according to a new research report.

Unemployment remains high for young college grads. For those who will find jobs, many will probably have to settle for low-level positions, the Economic Policy Institute said Wednesday.

The unemployment rate for recent college grads between the ages of 21 to 24 has averaged 8.8% over the last year, according to Labor Department data.

Once you also include young grads who are working part-time for economic reasons, and those who have stopped looking for a job in the last year, the so-called "underemployment rate" is a whopping 18.3%.

Sure, the job market has improved during the past few years. But both these rates remain higher than pre-recession levels.

Meanwhile, graduating in the wrong place at the wrong time is likely to affect the earnings potential of these students over their entire careers.

"On average, they are not going to do well," said Heidi Shierholz, an EPI economist and co-author of the report. "They will face lower earnings, than they otherwise would have, for maybe the next couple of decades."

Young college grads who work full-time are now making about $3,200 less each year than they were in 2000, after adjusting for inflation. The average hourly wage for these workers was $16.60 last year, down from $18.14 in 2000.

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And young graduates with jobs may be questioning whether college was worth it.

As of 2012, about 52% of employed college grads under age 25 were not working in jobs that require a college degree, said Andrew Sum, an economist at Northeastern University. That's up from 47% in 2007 and 40% in 2000.

But EPI said the job problem for recent college grads stems more from weak demand for goods and services, rather than a lack of the right education or skills.