It’s no longer just prices. Now wages, too, are flashing inflation signals.

Wages in the third quarter were up 4.2% from a year earlier, the fastest increase since 1990 as labor shortages in a widening range of industries prompted employers to raise pay. Meanwhile, inflation has topped 5% for the past four months, the hottest in decades.

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It’s no longer just prices. Now wages, too, are flashing inflation signals.

Wages in the third quarter were up 4.2% from a year earlier, the fastest increase since 1990 as labor shortages in a widening range of industries prompted employers to raise pay. Meanwhile, inflation has topped 5% for the past four months, the hottest in decades.

At first blush, this looks like the start of a process where wages push up prices, which then prompt employees to ask for, and receive, higher wages. That sort of wage-price spiral has historically been a key ingredient in persistently high inflation.

But economists aren’t predicting that yet. They note in only a few industries so far do higher prices seem directly due to higher wages.

Wages and prices are often thought to have “an iron lockstep relationship and that’s just not the case here,” said Peter Matthews, economics professor at Middlebury College. While firms will attempt to pass on higher labor costs to customers, differences in how various sectors tend to respond will determine the impact on inflation, he said.

Last quarter, wages in leisure and hospitality rose 7.6% from a year ago—much higher than the 4.2% overall pace, according to the Labor Department’s employment cost index, released Friday.

In that sector, though, labor makes up a relatively large share of overall costs, and it is one of the few in which higher wages seem to be driving prices. Restaurant prices have climbed at a 6.8% annual rate in the past six months, the fastest pace since 1981, according to Labor Department data. Wages are up an average of 15% this year at company-owned McDonald’s Corp. restaurants in the U.S., the company said. The Chicago-based burger chain is still struggling to hire the workers needed to keep stores open at full hours, executives said.

“Wage increases were initially concentrated among lowest-wage restaurant workers,” said Veronica Clark, a Citi economist. The pass-through to prices seems to be showing up in several other low-wage sectors, she said. Domestic services climbed an annualized 6.9% since March, without seasonal adjustment, while recreation service prices jumped 5.2%, near the highest since records began in 2010.

Prices have surged even more for factory goods, but those increases seem linked to key materials, energy and shipping rather than wages. Factory pay growth accelerated to 3.7% in the last quarter, the fastest increase since 2001, but still within historical norms.

Decades ago widespread unionization and cost-of-living adjustments meant wages responded relatively quickly to higher inflation. Since then declining unionization, slower-to-adjust minimum wages and lower productivity growth have restrained wage growth except when unemployment is low. Even in the third quarter wage growth lagged behind inflation.

Lawrence Katz, a labor economist at Harvard University, sees the current dynamic as more of a one-off adjustment as low-wage workers exploit their strongest bargaining power in decades.

“The relative price of fast food and deliveries may go up because of a tight labor market, but I don’t see that as a persistent wage-price spiral,” he said. “It’s like when you raise the minimum wage substantially you will jack up the prices of fast food this year, but not for 10 straight years.”

Whether wages keep accelerating depends largely on how long labor shortages last. Sarah House, senior economist at Wells Fargo, expects workforce participation to rebound next spring, as health concerns and child care conflicts recede and savings are exhausted. “That could take the edge off some of the wage pressures.”

But the longer the pandemic goes on, the bigger the risk that workforce exits will be permanent, said

Paul Ashworth, chief North America economist at Capital Economics. He notes that shortages aren’t limited to low-wage industries, with the job-opening rate in most industries up 50% from pre-pandemic levels.

Even in the most labor-intensive industries, businesses often face a delicate balance between passing on wage costs and preserving market share. Andreea Pfeifer, owner of girlFriday, a high-end cleaning service in Chicago, started raising wages in May to retain and recruit employees as demand boomed. Squeezed margins prompted her to increase her prices in June and July.

“I have never gone back to any [long-term] client and changed their pricing. But I had to do it this year,” said Ms. Pfeifer. The overall price increase of 7% to 10% was the highest possible without sacrificing customers, she said, though not enough to offset the rise in labor costs. And despite offering wages of over $20 an hour and a $500 signing bonus, “it’s been crickets,” said Ms. Pfeifer.

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Higher wages in low-wage sectors have already had a sizable impact on inflation.

Goldman Sachs economists estimate that wages for low-paid workers rose 6% in the third quarter, a three-decade high, which they said added 0.15 percentage points to inflation, as measured by the price index of personal consumption excluding its volatile food and energy components. If that wage pressure stays elevated, it could contribute up to 0.5 percentage points to annual inflation in 2022, Goldman said.

However, neither wage nor price data currently signals a spread beyond low-wage services that might threaten the Fed’s 2% inflation target, said David Mericle, Goldman’s chief U.S. economist. “If overall wage growth is running not at 4% but at 6% or something like that, then I think it’s harder to reconcile that with actually achieving the Fed’s inflation target,” he said.

“The key question is really what will happen with wage growth now that the enhanced unemployment benefits have expired, and [the third-quarter] numbers are too dated to tell us the answer,” Mr. Mericle added.

Write to Gwynn Guilford at gwynn.guilford@wsj.com