The Federal Reserve’s battle against inflation reached a milestone last week, with a report showing that consumer prices rose 3% annually in June, down from a four-decade high of 9.1% a year earlier.

Perhaps more critically, a core inflation measure that excludes volatile food and energy items and is more closely watched by the Fed finally eased significantly to 4.8%, according to the Labor Department’s consumer price index.

Although that’s still higher than the central bank’s 2% target, the news raises a pointed question: How much credit does the Fed deserve for lowering inflation so far?

Some economists ascribe little or none of the progress on inflation to historic Fed interest rate increases. But the hikes get blamed for doing some damage: propelling mortgage rates higher; pushing up rates for car loans, credit card spending and other consumer purchases; tossing cold water on a high-flying stock market; and threatening to tip the economy into recession.

“I don’t think there’s been that much effect (on inflation) yet,” says Joseph LaVorgna, chief U.S. economist of SMBC Group and a former top economic adviser in the Trump administration. “Most of what has happened has not been Fed related.”

Instead, LaVorgna, along with other economists, point to the unwinding of pandemic-related supply chain bottlenecks, a sharp drop in commodity prices and a pullback in COVID-19-related consumer spending binges.

LaVorgna cites what he says are two key pieces of evidence. Core inflation began easing in October, several months after the Fed started hiking in March. Economists have said rate increases work with a “long and variable lag,” which Fed governor Christopher Waller recently put at nine to 12 months.

Also, the economy is still solid, growing at a 2% annual rate in the first quarter and an average of 2.6% since mid-2022. Typically, the Fed slows inflation by weakening the economy but that largely hasn’t happened yet, LaVorgna says.

Jonathan Millar, a former Fed economist and now senior U.S. economist at Barclays, gives the Fed more props than LaVorgna. He says the central bank has played a “supportive” role by affecting consumer inflation expectations and modestly dampening a hot job market. But he too traces most of the gains to the other factors.

“It’s very subtle … the way the Fed affects things,” Millar says. “It’s very hard to disentangle."

"The Fed's rate hikes do deserve honorable mention," says Mark Zandi, chief economist of Moody's Analytics

The debate isn’t merely theoretical. If the Fed’s 5 percentage points in rate increases since March 2022 – the most since the early 1980s – haven’t had much effect on inflation so far, perhaps officials shouldn’t be tentatively planning to raise a key rate twice more this year after pausing in June, LaVorgna argues.

“Why not wait” and see if inflation continues to drift down, he asks, rather than further boosting the risk of a recession that many economists deem likely by next year?

Others say that while Fed’s rate hikes have yet to bear much fruit, they will as the fight to lower inflation becomes more challenging. The central bank is widely expected to hike rates again on July 26.

Here's a look at what’s bringing down inflation and the part played by Fed rate hikes:

Supply chain snarls are easing

Economists generally agree the main reason inflation has slowed is that supply chain snags have improved.

In the early days of the pandemic, Americans stuck at home ordered lots of TVs, computers, furniture and other goods. Meanwhile, many truck drivers, along with port and warehouse workers, left the workforce for COVID-19-related reasons. That led to severe product shortages and price spikes as shipping containers stacked up at West Coast ports.

Now, Oxford Economics’ supply chain stress index has fallen to about half its peak early last year, though it’s still above normal.

Most shipping workers are back on the job. And consumers, no longer confined to their homes, have exhausted much of their surplus demand for new cars, couches and other toys.

Still, perhaps Fed rate hikes have helped soften consumer demand by making auto loans and credit card purchases more expensive.

LaVorgna isn’t buying it. Although consumer goods purchases have flattened after peaking in late 2020, they’re still about 7% above where they would be if the health crisis hadn’t happened, he says, citing government figures.

Yet prices for furniture and appliances were down about 1.5% annually in June after notching double-digit increases last year.

“That’s mostly not the Fed’s doing,” Millar says.

Commodity prices have come down

Prices of commodities such as oil, wheat and corn soared last year as Russia’s war on Ukraine disrupted supply networks.

Now, however, those prices have declined significantly because of weaker demand in Europe and China amid worldwide recession fears. Also, shippers have found ways to bypass the war-torn region. That has lowered gasoline prices that topped out at $5 a gallon last year and stabilized grocery bills that were skyrocketing, Zandi says.

Rent increases are slowing

Rent, the biggest inflation driver, is still rising sharply but gradually coming off its peak. Average rent increased a brisk 8.3% annually in June, down from 8.8% in April.

Rent began surging in 2021 as the pandemic led many people to move into their own apartments. The easing health crisis then triggered a widespread return of young adults to large cities.

But those trends largely have played out, Millar says.

A large supply of new apartment buildings is also moderating rent increases, says Jay Parsons, chief economist of RealPage, a real estate research and property management software company.

Rent for new leases fell for several months and Parsons expects that to more significantly affect existing leases this year.

'Supercore inflation' is easing

Fed Chair Jerome Powell has said Fed rate hikes can have their biggest impact on inflation in services excluding housing, which are mostly driven by labor costs. By making it more expensive for employers to hire and tamping down economic growth broadly, the Fed theoretically can slow job growth, thus reducing pay increases that may get passed to consumers through higher prices.

That inflation measure has softened, falling to 3.8% in June from a high of 6.6% last September, says Moody’s economist Bernard Yaros.

But LaVorgna says it’s not because rate hikes have curtailed job and wage growth.

Payroll gains slowed recently but remain sturdy and unemployment was at 3.6% last month, just above a 50-year low, LaVorgna notes Average wages were up 5.6%, below last summer’s 6.7% peak but well above the pre-COVID-19 trend of about 3.5%, according to the Federal Reserve Bank of Atlanta.

Rather, prices for services such as hotel stays and air travel have stabilized as Americans’ pent-up demand for travel and other activities is finally waning, Millar says. Jet fuel costs also have fallen along with oil prices.

The Fed gets some due, Millar and Zandi say, because job and wage growth have eased modestly, helping reduce services prices.

LaVorgna, though, attributes slightly smaller pay increases to the return of many workers to the labor force after pandemic-related absences.

Inflation expectations are stable

Millar says the Fed has a "supportive" role in bringing down inflation by hammering the message that it’s on the case and won’t let price increases get out of hand, keeping the public’s inflation expectations stable.

That’s important, he says, because it means some workers may not ask for a bigger raise and landlords may not raise rent as much because they know they won’t have to pay significantly higher costs themselves.

Absent the Fed hikes, “Maybe we would have spiraling inflation,” he says, though there’s no way to tell.

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Fed rate hikes may have bigger impact in months ahead

Although inflation has eased significantly, lowering it the rest of the way to the Fed’s 2% goal is expected to be a tougher slog, Millar says. It will likely mean slowing price gains for services like haircuts and car repairs, he says, and higher interest rates will likely play a bigger part by dampening job and wage growth more emphatically.

And as Americans' pandemic-related cash reserves run dry, higher borrowing costs will have a larger impact on spending.

“The jury is still out on how much the Fed” has contributed to the fight against inflation, he says.

This article originally appeared on USA TODAY: Inflation is down. The Fed's rate hikes may not be responsible though