Manufacturers posted 379,000 job openings in July, the Bureau of Labor Statistics reported Wednesday. That’s up more than 280 percent — close to quadruple — since the recession ended more than seven years ago.

When it comes to actually filling those jobs, though, the rebound has been far more gradual. Hiring is up just 36 percent since the end of the recession and has been pretty much flat over the past year. Tens of thousands of manufacturing jobs are going unfilled.

However, according to a new paper by economists Andrew Weaver and Paul Osterman, three-quarters of manufacturers that Weaver and Osterman studied weren’t having trouble finding workers at all. One possibility is that what companies mean by an “opening” has changed — that in an age of online job listings, automated résumé screenings and increasing temporary and contract work, companies are posting more jobs than they ever expect to fill.

Weaver and Osterman offer a more industry-specific explanation: The manufacturing industry has become so specialized that companies are looking for hyperspecific skills that few outside workers could be expected to have. But companies have also become less likely to offer training for new hires.

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