Update |Professor Andrew Sum, the original source for Romney’s claim, says the candidate and the news media have “misrepresented” his findings, and that fact-check site Politifact has “ignored” his corrections to their misleading report. Details here.

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In last night’s presidential debate, Mitt Romney made a claim that was specific, shocking, and false. “Fifty percent of college graduates this year,” he said, “can’t find work.”

There are a few ways of interpreting this statement, but none of them add up.

A study published this summer found that for college graduates under the age of 24, the unemployment rate for the twelve months ending in March of this year was 9.4%. More recent data for college grads aged 21-25 put the number at 6.8%.

So where did Romney’s 50% figure come from? An Associated Press article about a study of “underemployment” among college grads. This is going to take a little unpacking, so bear with me.

For the purposes of this AP story, a person was defined as “underemployed” if they were working in a job that required less education or fewer skills than they possess, were working part-time other than by choice, were working outside their field of expertise, or were working for less money than their similarly situated peers.

Even in good times, underemployment is common, and it’s particularly common among young college graduates — a job that doesn’t require a college degree may be a stepping-stone to one in the same field that does, for instance, or an internship or a part-time gig may get your foot in the door.

Among all employed young college graduates in 2007, before the current recession began, more than a third — 34.7% — were considered underemployed. In fact 26.8% of all working college grads, regardless of age, were underemployed that year, up from 25.2% in 2000. Underemployment is hardly ideal, in other words, but it’s not an acute crisis, it’s a long-term reality of our economy.

So what happened to underemployment rates in the current recession?

They went up, as you’d expect. In 2010, the most recent year for which data have been published, the underemployment rate for employed college grads under 25 was 39.1%. Unemployment for the same cohort stood at about 10%, which means the total for unemployment and underemployment combined was about 45%. According to the AP, that figure has risen to a bit over 53% in the last two years.

But there’s something very strange about the AP’s numbers. Take a look at this, from the AP story:

“About 1.5 million, or 53.6 percent, of bachelor’s degree-holders under the age of 25 last year were jobless or underemployed. … Out of the 1.5 million who languished in the job market, about half were underemployed, an increase from the previous year.”

According to that passage, which has been repeated in a Politifact article on the Romney claim, underemployment among recent college grads stands at about 25% of the total group, as does unemployment. And from what I can see that doesn’t fit with the published data at all.

According to official government statistics, the unemployment rate for all Americans aged 20-24 currently stands at 13.9%, and hasn’t crossed the 15% threshold at any time in the last year. Unemployment among Americans aged 16-24 who have college degrees is, as you’d expect, considerably lower.

Unless I’m missing something huge, then, the government’s figures don’t back up the AP’s claim of 25% unemployment among recent college grads. Not even close.

So what’s the reality? As far as I can make out, among recent college graduates something like seven to ten percent — not fifty percent — “can’t find work.” A little less than half of the rest are “underemployed,” which means they’re doing jobs which aren’t a particularly good fit for their preferences and their degree. Most of those would be in a similar predicament if the economy was booming, but a significant minority, maybe ten or twenty percent of the total, have been dumped in that category by the downturn.

So there you go.