A major reason the Federal Reserve insists Americans shouldn’t fret about the risk of runaway inflation boils down to a letter Alexia Figueroa received from the hotel she worked at for 15 years.

Figueroa was furloughed from her job as a restaurant hostess and server at the Kimpton Nine Zero Hotel in Boston last March, and she’s waited for the call to come back ever since. The job helped her family buy a house and provided health insurance for her two children.

Then last week, Figueroa learned that she and dozens of others had been fired.

“The recovery looks like it is coming soon, but when they sent me the letter saying I don’t have the job, it’s like they are keeping me away from the recovery,” said Figueroa, 39. “To find another hospitality job is hard for me in this moment.”

By many accounts, the economy is projected to grow at its fastest pace in four decades this year, bolstered by President Joe Biden’s $1.9 trillion stimulus package and more widespread vaccinations. The rosier picture has economists debating whether such a forceful turnaround will overheat the economy and trigger cycles of inflation unseen for decades.

The Fed isn’t worried. Its explanation typically includes academic debates about what constitutes inflation or what the mathematical link is between unemployment and prices.

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But the answer this time is also much simpler: Despite the headline numbers, the economy is still in bad shape for millions of Americans. And for many workers like Figueroa, jobs may not come back even if the economy booms again.

The bleak reality is coming into sharper focus as the Biden administration rolls out its infrastructure and jobs package, one that’s designed to confront global climate change and rebuild America’s roads, bridges and other infrastructure. The package could provide additional support to the economy in the years to come, but there are more imminent challenges, especially as coronavirus cases rise again across the United States.

All the while, the scars of pandemic are far from healed.

The leisure and hospitality sector — which largely employs people of color and women — is down almost 3.5 million jobs, or about 20% of its pre-pandemic level. Workers who had been in the bottom 25% of earners faced an unemployment rate of around 22% in February, compared with the overall rate of 6.2%, according to a recent speech by Federal Reserve Governor Lael Brainard.

Economists say many of the 9.5 million jobs still missing from the labor market will gradually return. But it’s unclear how long it will take, and which jobs will vanish forever in the meantime. Businesses are increasingly looking to technology and automation to cut the cost of labor, compounding the risks of long-term unemployment for some of the country’s most vulnerable workers.

The bleak picture shows the darker side of the Fed’s plan to keep interest rates near zero for quite awhile. Historically, the Fed raised rates and slowed the economy to keep inflation from creeping too high, even at the cost of higher unemployment.

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Now the Fed goes by a new playbook, one that tolerates higher inflation if that means more people can get a job.

But if all of that growth leaves behind people like Figueroa, the Fed’s path to getting as many people back to work as possible will be even harder to forge.

“Although the outlook has brightened considerably, the fog of uncertainty associated with the virus has yet to lift completely, and current employment and inflation outcomes remain far from our goals,” Brainard said.

Federal Reserve Chair Jerome Powell has long said that getting the pandemic under control is the best way to heal the economy. Vaccinations help people return to jobs that depend on person-to-person contact, Powell says. As people spend money on long-awaited vacations and entertainment, hotels and concert venues will be able to bring workers back on the payroll, for example.

But some jobs may never return. In her speech, Brainard cited a December survey that found roughly half of chief financial officers from large firms and about one-third of those from small firms, said they were “using, or planning to use, automation or technology to reduce reliance on labor.”

Many companies already had plans to automate jobs before the pandemic. But Robert Kaplan, president of the Federal Reserve Bank of Dallas, told The Washington Post that the pandemic accelerated that shift. Kaplan said it’s hard to think of a business in his district — which spans Texas and parts of Louisiana and New Mexico — that doesn’t mention automation and ways to trim costs in their conversations.

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Restaurants are using technology for online preorders and pickups, Kaplan said. Package delivery and logistics centers are on a similar path. Call centers that were already exploring ways to automate will likely ramp up those efforts, Kaplan said.

In other cases, businesses say they can’t predict how quickly customer demand will rebound as the pandemic winds down, making them hesitant to rehire.

“What I’m hearing from small businesses, medium-sized businesses and large business is that wherever possible right now, they’re looking for ways to use technology more than in the past to run leaner, and to be more efficient,” Kaplan said.

Such permanent shifts in the labor market could pose a crucial test for the Fed. The central bank is supposed to guard against inflation — the annual change in the price of goods and services — and get the economy to full employment. Its main policy lever rests in interest rates, which the Fed can raise or lower depending on what’s happening in the economy.

Inflation has tracked well below the Fed’s 2% target for years, even as unemployment fell in the years after the Great Recession. That dynamic challenged the long-held view that as the labor market tightened and employers raised wages to compete for scarce workers, prices would rise as businesses passed high labor costs onto consumers.

Inflation is expected to pick up quickly this year, but Powell says any price increases will be temporary and won’t pulse through the entire economy. Still, economists and Wall Street investors are trying to pin down how much inflation the Fed will tolerate before it raises rates.

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Just as important will be how the Fed judges progress in the labor market, particularly for low-wage workers and people of color who didn’t benefit until the tail end of the expansion that followed the Great Recession.

Raphael Bostic, president of the Federal Reserve Bank of Atlanta, described the uneven recovery as “the signature characteristic” of the pandemic’s economic fallout. In a speech last week, Bostic highlighted disparities across wage levels, gender, race and industry and said eliminating persistent gaps “is essential if we are to generate stronger economic growth.”

When it comes to monetary policy, Bostic said looking to the overall unemployment rate won’t be enough.

“I’m going to be committed to pushing back against the notion that we’re all fine if the aggregate number is at a certain point, but some of these targeted populations are still in significant distress, or in a more of a crisis type of period,” Bostic told reporters.

Many economists say the official unemployment rate leaves out millions of workers. They say a more precise gauge is the employment-to-population ratio, which measures the number of people employed against the total working-age population.

The ratio for Black prime-age workers is 7.2 percentage points lower than for White workers, which is 77.8%. The ratio is 6.2 percentage points lower for Hispanic workers than for White workers — an increase in each gap of about three percentage points from pre-pandemic lows in October 2019, according to Brainard’s speech.

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Measuring how many people are out of work is one challenge. Making sense of this unusual and complex crisis is yet another.

Abigail Wozniak, a labor economist at the Federal Reserve Bank of Minneapolis, says there are still “a lot of asterisks” when assessing the health of the U.S. economy. Three rounds of stimulus checks, enhanced unemployment benefits and a host of other relief measures have all helped families stay afloat over the past year.

The unprecedented levels of fiscal support make it hard to draw clear-cut conclusions about the labor market, for example. At the same time, Wozniak notes that not all Americans have been able to access aid, blurring the picture even more.

“The unemployment rate is dramatically worse than we’ve seen in the past, but the level of support is dramatically better,” Wozniak said. “And so when we try to create this picture of overall well-being, we’re just in a very new territory.”

Eventually, the flood of support from Congress will wear off. Businesses that experiment with leaner staffs or automation may decide to stick with it.

And economists fear that the longer people are out of the workforce, the harder it is to get back in.

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“While there’s some exuberance, rightfully so, that the economy is going to rebound and rebound fast, and we’re going to see a lot of growth, the way that will be experienced by workers is going to be just as uneven and unequal as the recession was,” said Molly Kinder, who focuses on low-wage workers and women at the Brookings Institution.

That is Figueroa’s worry too.

Figueroa, who is from El Salvador, said she’s depended on stimulus payments and extended unemployment benefits to help support her family. Her husband also works in hospitality as a server, but he is employed only two days per week.

She fears what losing her job means for her family’s financial stability and worries about paying her mortgage. The Unite Here Local 26 Union, which represents much of Kimpton Nine Zero’s staff, said the company violated its contract and did not have grounds to fire its employees. In a statement, the hotel said its actions “comply with the union contract that has been in place for years.”

Other Boston hotels have committed to recalling their own workers if business returns, making it more difficult for her to find a position. Figueroa says she has the training, but she needs the job.

“We are here, ready to work,” Figueroa said. “We already know our job, so we don’t have to train as much. We know what we do, and we love what we do.”