The higher pay is a sign that businesses are having to compete hard for workers. Many business leaders have complained they cannot find the workers they need, especially for skilled jobs like welders or computers coders.

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Economists had expected that companies would start to raise wages significantly to attract -- and keep -- the talent they want. But pay had been creeping up slowly for much of the recovery. That appears to be changing now that there are more job openings than unemployed Americans.

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"Wage growth is definitively accelerating. Employers are now struggling to fill open positions and have no choice but to raise wages quickly," said Mark Zandi, chief economist at Moody's Analytics. "Everything points to strong wage growth going forward."

Some economists warned that faster wage growth could be a sign the economy may be starting to overheat.

"This report suggests that wages are moving higher and inflation is moving higher. The Federal Reserve is likely to keep raising interest rates," said Sam Bullard, senior economist at Wells Fargo.

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The last time unemployment was this low, during the dot-com boom, wage growth was significantly faster -- well above 3.5 percent. It's unclear how much higher it will go in this business cycle, but several metrics, including the Employment Cost Index and Atlanta Fed's Wage Growth Tracker, are showing upward momentum.

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Workers still might not feel better off, however, because inflation has also risen 2.9 percent in the past year, meaning much of the pay increase is getting wiped out by more expensive gas and rent.

People who change jobs are seeing the biggest pay gains, Zandi said. He is especially encouraged by the double-digit pay hikes for Millennials who switch jobs, an indication that the economy is starting to lift the fortunes of more workers.

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After years when most of the wage gains were going to the top earners, middle-class families are finally seeing some significant gains, said Martha Gimbel, research director for the Hiring Lab at Indeed.com.

"Wage gains are largely hitting workers in low-wage and middle-class industries, which is incredibly exciting," said Gimbel. "Industries we typically associate with middle-class workers like real estate, residential building management and food manufacturing are seeing gains."

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This year is on track to be the best for job gains since 2015. The U.S. economy averaged 207,000 jobs a month so far this year, a healthy pace that indicates companies continue to grow and don't anticipate a downturn anytime soon.

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Manufacturing employment was the one weak spot in August, shedding 3,000 workers. Economists say this could be an early sign that President Trump's tariffs are starting to hit the industry, but they aren't ready to sound alarm bells yet since U.S. manufacturers added more than 250,000 jobs in the past year. August could just be a one-month blip.

Hiring has been strong in nearly every industry this year from manufacturing to health care. Even retail, which many predicted would decline as stores like Toys R Us shuttered for good, has added 62,000 jobs in the past year.

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Job gains in August suggest that Trump's trade war has yet to have a widespread hit to workers, although a handful of companies have announced layoffs already and more have threatened to ax jobs if Trump moves forward with additional tariffs, especially on China.

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Trump has been touting the low unemployment rate and strong job gains since he took office as proof he is delivering results and his critics are wrong about him.

Trump's top economist, Kevin Hassett, put out a report this week arguing that wages are growing faster than the Labor Department statistics indicate because the 2.9 percent figure does not include health care and other benefits, nor does it include bonus payments or tax cuts.

"We find that wage gains are 10 to over 20 times more than the headline measures," Hassett said. By his calculations, wage growth adjusted for inflation is 1.4 percent, significantly higher than the 0.1 percent reported by the Labor Department last month.

Have you received a pay raise or not in the past year? The Washington Post would like to hear your story. Email: heather.long@washpost.com