American workers have much to celebrate this Labor Day — booming economic growth, tax cuts, and historically low unemployment rates overall and for blacks, Hispanics and women.

Amid the boom, however, there has been a vexing exception — wages.

Worker pay has begun to increase after years of stagnation, but wages continue to lag. With the economy at what economists traditionally call full employment and job openings exceeding job seekers, the wage lag has stumped experts.

“That’s a bit of a puzzle,” said Peter Morici, an economist at the University of Maryland. “We haven’t seen a lot of wage growth.”

Preliminary figures from the Bureau of Labor Statistics (BLS) indicate that the average hourly wage of all private workers in July was $27.05, a slight increase over the previous month. Average pay is up 4.1 percent since President Donald Trump took office.

After controlling for inflation, though, workers are barely treading water. Inflation-adjusted wages are up just 1 percent since Trump took office and actually declined from July 2017 to July of this year.

Alan Tonelson, an economic policy analyst who founded the RealityChek blog, said companies can keep wages down through offshoring and mass immigration.

“These are really two sides of the same coin, and that coin is employers still have great access to employees offshore,” he said.

Some sectors have performed particularly poorly. Trade, transportation and utilities workers had exactly the same hourly pay in July as they did in January 2017, after adjusting for inflation. Inflation-adjusted manufacturing wages actually have declined by 0.3 percent.

Automotive and parts workers have seen an average hourly pay increase of just 41 cents since January 2017; after factoring in inflation, that represents a decline of 1.3 percent.

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“Automotive wages have sunk like a stone,” Tonelson said.

Workers in other sectors have done better. Wages among construction workers are up 1.7 percent since January of last year in real terms. Leisure and hospitality workers have gotten an average raise of almost 1.9 percent.

Morici said rising pay for unskilled workers is a sign that businesses are running out of options when it comes to filling vacancies because of the dwindling pool of available workers for the service sector.

“We’ve seen a lot of wage growth simply because you can’t import a McDonald’s hamburger,” he said.

Morici added that managers also have seen better play because American companies have gotten leaner and shed middle management. The managers who remain have higher skills, bear greater responsibilities, and — as a result — can command higher salaries.

Overall, the workers at the bottom and top of the pay scale have enjoyed the biggest gains since 2007, according to an analysis by the liberal-leaning Economic Policy Institute (EPI). The workers in the middle have seen the slowest pay growth.

Some experts question whether businesses actually are as desperate for workers as they claim. Steven Camarota, a researcher who has studied the link between immigration and wages, pointed out that the labor force participation rate remains near an all-time low.

After hitting bottom at 62.3 percent in September 2015, the share of people 16 and older who are employed or actively looking for jobs rebounded somewhat, according to BLS data. But the rate in July, 62.9 percent, was exactly the same as in January 2017 when Trump took office.

That represents millions of people who are neither employed nor actively looking for work. They do not count in the official unemployment statistics but potentially could be lured into the workforce.

“There’s still too many people sitting on the sidelines,” said Camarota, director of research at the Center for Immigration Studies (CIS). “It never got back to the 2000 level. It never got back to the ’89 level in 2000.”

Morici agreed: “A lot of people who are employed are underemployed. That [unemployment] number doesn’t mean the same thing it used to.”

“Workers got so hammered down … they tended to cling to jobs like children do to a parent in a crowd. They’re reluctant to move.”

Another factor that could be impacting wages, Morici said, is declining mobility of workers. He pointed to studies showing that compensation rises faster for workers who jump to other companies. But workers are changing jobs less often than they did before the Great Recession, he said.

“Workers got so hammered down … they tended to cling to jobs like children do to a parent in a crowd,” he said. “They’re reluctant to move.”

Morici pointed to another factor — a productivity slump that has taken hold of the economy since the recession. That put a drag on wages, he said.

“You can’t pay workers more if they don’t produce more,” he said.

Morici said productivity has been particularly bad in the low-wage service sector. He attributed that, in part, to badly run businesses that do not make good use of technology even when they invest in it.

Tonelson said a seemingly endless supply of cheap labor “knee-capped productivity” at businesses that rely on low-skilled workers.

“It’s absolutely destroyed any incentive that business owners may have had to automate,” he said. “They’ve been addicted to very cheap, illegal immigrant labor.”

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Morici said there are signs that productivity is pulling out of the doldrums. That should pay dividends to workers, he said.

“I would suspect now we’re going to have to have more wage growth,” he said.

But Tonelson expressed concern that productivity and wages are not as closely linked as they used to be.

“That relationship, basically, has fallen apart in recent decades,” he said.