The end of distressingly high inflation is coming into view. Consumer prices gained 6.5% in December, down from June's 9.1% annual rate, the highest since 1981. There is good reason to think inflation will keep falling, Federal Reserve Chairman Jerome Powell said earlier this month.

"The process of getting inflation down has begun," Mr. Powell said at the Economic Club of Washington, D.C.

Even so, inflation is far above the Fed's 2% target. Even excluding the volatile food and energy categories, core inflation was 5.7% in December. So how does it fall all the way back to 2%?

Markets seem optimistic it will do so of its own accord, and are betting the Fed will therefore cut rates this year. Mr. Powell disagrees.

Who is right depends on three sectors: goods, shelter, and other services, excluding food and energy. They face different forces reflecting the mechanics of how inflation is measured, and the macroeconomic backdrop. A recession would tamp down price gains, while accelerating growth would keep them high.

Goods Deflation

Surging prices for manufactured goods such as autos and furniture drove much of the initial inflation burst in 2021 as consumer spending, fueled by low interest rates, government stimulus and pandemic habit shifts, collided with blocked-up supply chains. Prices for core goods rose 12.3% from a year earlier in February 2022, and rose just 2.1% from a year earlier in December 2022. These goods represent about 22% of the CPI and 23% of the price index of personal-consumption expenditures, which the Fed prefers.

That surge is over. Supply chains have mostly healed. Consumer demand has shifted back toward services from goods. Core goods prices were up just 2.1% in the year through December, contributing 0.5 percentage points to the CPI's 6.5% increase -- down from February 2022, when they drove 2.5 percentage points of that month's 7.9% increase. For the three months ended December, core goods prices actually fell at an annualized 4.8% rate.

Lower spending on goods, ongoing improvement in supply chains and falling shipping costs should continue to ease price pressures in coming months, said Blerina Uruci, chief U.S. economist at T. Rowe Price.

Alan Detmeister, economist at UBS, estimates core goods deflation will shave 0.4 percentage points off overall inflation by December.

But the deflationary drag from goods prices could peter out, as inventory returns to normal and global growth revives. Veronica Clark, economist at Citi, sees goods prices rising 1.6% in the 12 months ended this coming December.

Rent Deflation: Wait For It

Soaring demand for houses and apartments from low interest rates and remote working caused shelter to contribute more than half of December's 5.7% core CPI inflation. But as Mr. Powell put it, disinflation in housing "is in the pipeline."

Economists agree: they expect this category to continue rising through the spring, but then to decelerate. Jake Oubina, senior economist at Piper Sandler, forecasts shelter inflation will fall from 8.1% in March to 5.3% by December.

That reversal comes down to how pandemic-driven shifts interact with inflation methodology. To measure what tenants and homeowners pay for housing, the CPI includes new and existing leases, and thus reflects changes in new leases with a lag. Those new leases are now slowing sharply; Zillow's index of new leases declined at a three-month annualized rate of 3% in December. This portends a steep deceleration in the CPI's housing measure, which grew 7.5% in December, said Mr. Oubina.

He expects housing will continue to boost inflation but that its contribution to the 12-month increase in CPI will peak in June and shrink by 0.7 of a percentage point by December, relative to a year earlier. That is for the CPI, of which shelter makes up nearly one-third. Housing is just 15% of the PCE index and thus has less influence there.

Core Services

Once food, energy, goods and shelter are excluded, what remains are core service prices excluding shelter -- what some economists call "supercore" inflation.

It is still running at around 4%, Mr. Powell said. Until it drops, "we see ourselves as having a lot of work left to do."

Mr. Powell and other officials have recently emphasized that wages constitute a large share of the costs that go into theseservices. The shortage of workers worries economists and policy makers, who see that as a conduit for inflation.

Hourly pay for private-sector workers rose at an annualized rate of 4.6% in the three months through January, compared with an average rate of 3.3% in 2018 and 2019.

While wage growth has shown signs of decelerating recently, it remains at levels that make it hard for the Fed to reach its inflation target, said Ms. Clark, of Citi.

"It is easier for inflation to go from 7% or 8% to 4% or 5% than it is to go from there to 2% to 3%. That is much harder given what's happening in the labor market," she said.

A more optimistic take comes from a wage series constructed by economists from the White House Council of Economic Advisers. It shows that pay for nonmanagement workers in services that go into "supercore" prices grew just 4% in January, down from 9.7% in October, 2021.

Recession, Or Not

Economists who expect inflation to fall back to the Fed's target by year-end generally expect the process to be assisted by a recession as higher interest rates stifle spending, and declining profits drive firms to shed workers, pushing unemployment up from January's 53-year low of 3.4%.

Monetary policy affects the economy with a delay, so little of the decline in inflation so far is because of the Fed's rate increases in the past year, said Mr. Detmeister. "The biggest impact shouldn't be until probably late this year at the earliest," he said.

By the middle of this year, "we expect to see the economy going into a recession and the unemployment rate increasing up to 4.5% by the end of this year, and to 5.5% by the end of next year," said Mr. Detmeister. He sees core inflation falling to 2.3% by year-end.

But there is as yet no sign of such a recession in consumer spending, which drives around 70% of U.S. output. Incomes, excluding transfer payments, are now rising faster than inflation, which will buoy spending and keep a downturn at bay, said Neil Dutta, head of economics at Renaissance Macro Research.