For months, the Fed has been warily watching the U.S. economy’s robust job gains out of concern that employers, desperate to hire, would keep boosting pay and, in turn, keep inflation high. But January’s blowout job growth coincided with an actual slowdown in wage growth. And it followed an easing of numerous inflation measures in recent months.

The past year’s consistently robust hiring gains have defied the fastest increase in the Fed’s benchmark interest rate in four decades — an aggressive effort by the central bank to cool hiring, economic growth and the spiking prices that have bedeviled American households for nearly two years.

Yet economists were astonished when the government reported Friday that employers added an explosive 517,000 jobs last month and that the unemployment rate sank to a new 53-year low of 3.4%.

“Today’s jobs report is almost too good to be true,” said Julia Pollak, chief economist at ZipRecruiter. “Like $20 bills on the sidewalk and free lunches, falling inflation paired with falling unemployment is the stuff of economics fiction.”

In economic models used by the Fed and most mainstream economists, a job market with strong hiring and a low unemployment rate typically fuels higher inflation. Under this scenario, companies feel compelled to keep boosting wages to attract and keep workers. They often then pass those higher labor costs on to their customers by raising prices. Their higher-paid workers also have more money to spend. Both trends can feed inflation pressures.

Yet even as hiring has been solid in the past six months, year-over-year inflation has slowed from a peak of 9.1% in June to 6.5% in December. Much of that decline reflects cheaper gas. But even excluding volatile food and energy costs, the Fed’s preferred inflation gauge has risen at about a 3% annual rate over the past three months — not so far above its 2% target.

Those trends have raised questions about a core aspect of the Fed’s higher rate policy. Chair Jerome Powell has said that conquering inflation would require “some pain.” And the Fed’s policymakers have forecast that the unemployment rate would rise to 4.6% by the end of this year. In the past, an increase that large in the jobless rate has occurred only during recessions.

Yet Friday’s report suggests the possibility that the long-standing connection between a vigorous job market and high inflation has broken down. And that breakdown holds out a tantalizing possibility: That inflation could continue to decline even while employers keep adding jobs.

“Their model is that this inflation is driven specifically by wage inflation,” said Preston Mui, senior economist at Employ America, an advocacy group. “In order to get that down, they think we have to bring some pain in the labor market in terms of higher unemployment. And what the past three months have shown us is that that model is just wrong.”

That said, it’s possible that Friday’s report could still nudge the Fed in the opposite direction: The consistently strong job growth might convince Powell and other officials that, despite signs that wage growth is slowing, a powerful job market will inevitably reignite inflation. If so, their benchmark rate would have to stay high to cool the pace of hiring.

With that outlook in mind, Wall Street traders are now pricing in an additional Fed rate hike this year: Investors foresee a 52% likelihood that the Fed will raise its benchmark rate by a quarter-point in both March and May, to a range of 5% to 5.25%. That’s the same level that Fed officials themselves had predicted in December.

Many economists say the pandemic so disrupted the job market that it is acting differently than it has in the past.

“There are a lot of norms …. that aren’t normal anymore,” Labor Secretary Marty Walsh said Friday. “We’re seeing a lot of companies maybe not doing layoffs in January that they normally would have because they went through a pandemic where they lost people and they didn’t come back.’’

At a news conference this week, Powell argued that much of the easing in inflation since fall has reflected falling prices for goods — items like used cars, furniture and shoes — as well as sharply lower gas prices. Those price declines reflect a clearing of formerly clogged supply chains, he suggested, and will likely prove temporary.

And Powell reiterated one of his central concerns: That inflation in the labor-intensive services sector is still rising at a steady 4% pace and shows no sign of slowing. Much of that increase is a consequence of strong wage growth at restaurants, hotels and transportation and warehousing companies, with fewer workers available to take such jobs.

“My own view,” the Fed chair said, “would be that you’re not going to have a sustainable return to 2% inflation in that sector without a better balance in the labor market.”

Yet even with the vigorous job gains, several measures of wage growth show a steady easing: Average hourly pay grew 4.4% in January from a year earlier, down from a peak of 5.6% in March.

“More focus should be placed on the earnings data,” said Rob Clarry, investment strategist at Evelyn Partners, in a research note. “The high headline (job) reading does not appear to be translating into further inflationary pressure — an important finding for the Fed.”