Inflation in the United States accelerated in September, with the cost of housing and other necessities intensifying pressure on households, wiping out pay gains and ensuring that the Federal Reserve will keep raising interest rates aggressively.

Consumer prices, excluding volatile food and energy costs, jumped 6.6% in September from a year ago — the fastest such pace in four decades. And on a month-to-month basis, such “core” prices soared 0.6% for a second straight time, defying expectations for a slowdown and signaling that the Fed’s multiple rate hikes have yet to ease inflation pressures. Core prices typically provide a clearer picture of underlying price trends.

Overall prices rose 8.2% in September compared with a year earlier, down slightly from August, the government said Thursday in its monthly inflation report. But from August to September, prices increased 0.4%, faster than the July-to-August increase. Though cheaper gas helped slow the broadest measure of inflation, costlier food, medical care, and housing pointed to the breadth of price pressures across the economy.

“We still have no evidence that inflation is decelerating,” said Matthew Luzzetti, an economist at Deutsche Bank. “Let alone the clear and convincing evidence that the Fed is looking for.”

Stock markets fell sharply in early trading, but then rebounded and moved higher. The Dow Jones was up 560 points, or 1.9%, in mid-day trading.

Thursday’s report represents the final U.S. inflation figures before the Nov. 8 midterm elections after a campaign season in which spiking prices have fueled public anxiety, with many Republicans casting blame on President Joe Biden and congressional Democrats.

Speaking Thursday in Los Angeles, Biden acknowledged the pain that inflation is causing many people, while suggesting that the latest figures showed “some progress.”

“Americans are squeezed by the cost of living,” the president said. “It’s been true for years, and folks don’t need to read a report to tell them they’re being squeezed. Fighting this battle every day is a key reason why I ran for president.”

Even with widespread price spikes, the September data showed that the prices for many physical goods, including clothing, used cars, furniture, and appliances, dropped last month. A key factor is that supply chain snarls have eased, and many large retailers such as Walmart and Target have discounted some items to clear excess stockpiles.

Yet the price drops were not as steep as many economists expected, and they were more than offset by sharp increases in service prices, including health care, auto repair, and housing.

A measure of housing costs jumped 0.8% in September, the largest such increase in 32 years. The Fed’s rate hikes have led to much higher mortgage rates — the average on a 30-year fixed home loan is nearly 7% — and caused home sales to tumble and prices to falter. But declining house prices will take time to feed through into the government’s measure.

The cost of health insurance jumped 2.1% from August to September and more than 28% over the past 12 months — a record one-year increase. The cost of auto repairs surged 15% in September from a year earlier, also a record high. The supply chains of many car parts are still disrupted.

“The primary driver of inflation has rotated away from goods prices and to services,” said Eric Winograd, U.S. economist at AB. “Services inflation is heavily influenced by wages, and so it is going to take a meaningful weakening of the labor market to bring inflation to heel.”

Inflation in services is also being fueled by steady consumer demand. Though there are signs that lower-income Americans are cutting back, higher-income households still appear willing to spend on travel, restaurant meals, and services like veterinary care.

Both Delta and American Airlines, for example, reported strong revenue growth this week, driven by increased demand from travelers. Airfares rose a brisk 0.8% from August to September.

Service businesses are having to rapidly raise wages to attract the workers they need. Those higher labor costs, in turn, are often passed on to consumers in the form of higher prices.

Inflation has swollen families’ grocery bills, rents, and utility costs, among other expenses, causing hardships for many and deepening pessimism about the economy despite strong job growth and historically low unemployment.

Kasondra Mathews is among those feeling the squeeze. Mathews, 50, who lives near Denver, has been working overtime as a nurse’s assistant to keep up with her rent and grocery bills. Her rent has increased roughly 5% a year for the past several years, shrinking her budget for other items.

With her daughter a senior in high school and headed soon to college, Mathews has found ways for her to apply to her preferred schools for free. She’s also forgoing any visits to a college to avoid travel expenses.

“We didn’t get to do college tours, because we can’t afford it,” she said. “I couldn’t do the things you might want to do for your senior.”

As the elections near, Americans are increasingly taking a dim view of their finances, according to a new poll by The Associated Press-NORC Center for Public Affairs Research. Roughly 46% of people now describe their personal financial situation as poor, up from 37% in March. That sizable drop contrasts with the most steady readings that had lasted through the pandemic.

The September inflation numbers essentially guarantee that the Fed will raise its key short-term rate by three-quarters of a point for a fourth straight time when it next meets in early November. The Fed has already raised its key short-term rate by 3 percentage points since March, the fastest pace of hikes since the early 1980s. Those increases are intended to raise borrowing costs for mortgages, auto loans, and business loans and cool inflation by slowing the economy.

At their last meeting in late September, Fed officials had projected that by early next year, they would raise their key rate to roughly 4.5%, which would be the highest level in 14 years. Some economists now predict that the Fed will have to boost rates even higher to defeat what appears to be an entrenched bout of inflation. The risk is that such higher borrowing costs would push the economy into recession.

Fed policymakers said at the September meeting that inflation was “showing little sign so far of abating,” according to minutes from the Fed’s most recent meeting.

Used car prices dropped 1.1% from August to September, the third straight decline. Wholesale used car prices have fallen much faster, yet dealers have resisted passing on those declines to consumers, resulting in much bigger profits.

Lael Brainard, vice chair of the Federal Reserve, noted this week that retailers have also reported healthy profit margins, having raised prices more than they have increased wages.

“The return of retail (profit) margins to more normal levels could meaningfully help reduce inflationary pressures in some consumer goods,” Brainard said.

Some large chains have started to cut prices. But it’s not clear how much effect on inflation that will have in the coming months. Walmart has said it will offer steep discounts on such items as toys, home goods, electronics, and beauty. Target began offering holiday deals earlier this month.

But after jacking up prices for the past 18 months, companies are reluctant to reverse course. Until consumer demand slows further, forcing more companies to compete on price, costs for many goods will likely stay high, economists say.

“There’s a saying in economics that prices go up like rockets and down like feathers,” said Eric Swanson, a former Fed economist who is now a professor at the University of California, Irvine. “You’re kind of seeing that a little bit.”