U.S. factories are hiring again. Or they’re trying to, anyway. 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.

What’s behind that gap? The Wall Street Journal last week offered a simple explanation: Companies can’t find enough skilled workers. Manufacturing jobs have become more technical, but workers haven’t kept up. That’s left companies with a glut of low-skilled workers and a shortage of applicants who can really do the job.

This “skills mismatch” theory is a favorite of corporate executives and the think tanks they fund. But it is based on scant evidence. Individual companies may be struggling to fill specific jobs, but the data shows little sign of an industrywide shortage of skilled workers. In fact, it’s not clear that companies are really trying hard to fill many of these jobs at all.

For starters, it’s worth defining what “skilled” means in this context. Even today, manufacturing jobs rarely require a college degree. Some 62 percent of manufacturing production workers have no education past high school, and 80 percent have neither an associate nor a bachelor’s degree. Those numbers are pretty much the same for younger workers, suggesting manufacturers aren’t replacing less-educated older workers with more-educated young ones. Manufacturing jobs don’t generally require formal certifications, either. Just 11.5 percent of manufacturing workers have either licenses (issued by the government) or certificates (issued by a private group), one of the lowest certification rates of any industry.

Rather than degrees or licenses, what employers say they are struggling to find are workers with industry-specific skills, such as how to program the machines that do much of the physical work in modern factories. But according to a new paper by economists Andrew Weaver and Paul Osterman, companies looking for workers with specialized computing skills don’t have any more trouble filling their vacancies than anyone else. (Advanced math was more of a stumbling block.) And three-quarters of manufacturers that Weaver and Osterman studied weren’t having trouble finding workers at all. Other researchers have similarly found little evidence for a serious skills gap, either in manufacturing or in other sectors.

The latest economic data doesn’t show much sign of a skills mismatch, either. If finding qualified workers is so hard, for example, then companies should be offering higher pay to attract and retain precious workers. That isn’t happening. Average hourly earnings for manufacturing workers were up 2.5 percent in August from a year earlier, before adjusting for inflation; that’s the same rate of growth as for workers in the rest of the private sector. Nor are companies pushing their existing employees to work overtime; weekly overtime has trended down since the start of the year.

Similarly, if qualified workers are such hot commodities, we would expect to see companies poaching them from each other. But the number of factory workers voluntarily quitting their jobs (whether to take new ones or for some other reason) has risen only slowly in the recovery and remains well below its prerecession level.

So if there is no shortage of workers, why are so many jobs going unfilled? One possibility is that companies got spoiled during the recession, when they could pick and choose between an almost unlimited number of available workers. Another 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. There’s some evidence for this: Recruiting intensity — a measure of how hard companies are trying to fill open positions — remains below prerecession levels in both the manufacturing sector and the economy overall.

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. Companies, the authors write, “are unwilling or unable to solve their skill challenges through internal training, even for skills that are highly specific to a particular plant.”

Even if companies invested in more training, though, it’s unlikely they would go on a hiring spree. Ultimately, the slow pace of job growth in manufacturing isn’t companies’ fault any more than it is workers’. The cause is more fundamental than that: Due mostly to automation, U.S. factories now produce more than ever with fewer workers. That’s a trend no job-training program will reverse.