Now, like most successful falsehoods, this one seemed to have at least some basis in reality. It is true, after all, that American students have not done that well on international tests compared to kids in other rich countries. And it is also true that American companies have said that they can’t find enough qualified workers for all the positions they have. Couldn’t these two things be related? And, more to the point, explain why unemployment stayed so high for so long? Well, it certainly seemed that way to, among many others, the U.S. Chamber of Commerce, JP Morgan CEO Jamie Dimon and economist Tyler Cowen, who, back in 2011, had speculated that unemployment might stay around 10 percent forever because the people who had lost their jobs during the crash allegedly lacked the skills to add any value in the marketplace.

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What made this story so seductive to Washington was that it depoliticized the economy. It said that unemployment was high not because we did not have enough stimulus — which, of course, really was the case — but rather because workers did not have enough education. It was something that, whether or not you fully agreed with it, gave Democrats like President Barack Obama and Republicans like Sen. Marco Rubio (R-Fla.) a chance to come together over the most uncontroversial of issues.

There was only one problem. This was — or at least should have been — obviously wrong. Now, that’s not to say that trying to help workers keep up with the demands of an ever-changing economy is not a good idea. It is. But rather that acting like our failure to do so was a big part of the reason millions of people could not find work was as bad as ideas get. For one thing, it did not explain why people who were skilled enough to have a job in 2007 supposedly were not in 2008. And for another, it did not show up in any of the data, either. Indeed, if certain types of workers were in short supply, then the ones that existed should have seen their employment, hours, and wages all go up even in the face of the slow recovery. In other words, businesses should have been in a bidding war over them, and only them. But, as the liberal Economic Policy Institute has taken pains to point out, nothing of the sort was going on. What was happening instead was that all of these labor market indicators were falling for every profession, no matter how skilled they were. Which — surprise, surprise — is exactly what you would expect if our problem was one of inadequate demand rather than inadequate training.

None of this is hindsight bias. All of it was clear enough as it was going on. But in case it wasn’t, the fact that unemployment has now fallen to 3.9 percent is a pretty good sign that workers had enough skills all along. Unless, that is, you think it’s more likely that they mysteriously gained and lost them as economic growth went up and down.

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But what about all those companies that were saying they had a shortage of qualified applicants? Was that just a self-serving illusion? Well, according to recent research from economists Alicia Sasser Modestino, Daniel Shoag and Joshua Ballance, the answer is actually yes, much more than you might think. They found that, in the years after the crash, the more people who were unemployed, the more conditions companies put on their job openings. Now, it’s worth pointing out that this wasn’t the full story — some jobs really did require more skills (or at least credentials) than they did in the past — but it was a big part of it. In particular, the researchers estimate that increased unemployment explained about 18 to 25 percent of the increase in job requirements during this time. Although, to be fair, that might not be as cynical as it sounds. It might have just been the most rational way to sift through a stack of résumés back when there were six unemployed people for every job opening, as opposed to the fewer than one that there is today.

Not that it really matters. Whether or not business leaders were deliberately overstating the existence of the “skills gap,” they were in fact overstating it, not only saying that jobs required more skills the higher unemployment was, but also, the researchers found, that they took fewer the lower it was. So it was always a mirage. Just a convenient one.