Janet Yellen said last month her main unfinished business as chair of the Federal Reserve was getting inflation back to the central bank’s 2 percent target. A return to her former home in the San Francisco Bay Area would solve that.

Metropolitan areas in the western U.S., those with more than 1.5 million residents, saw 3.4 percent inflation over the past year. That includes 2.9 percent in San Francisco, 3.5 percent in Seattle and 3.6 percent in Los Angeles, the government reported Jan. 12. By contrast, larger metro areas in the Northeast and Midwest registered price gains of less than 2 percent, while in the South it was 2.1 percent.

The Fed targets national inflation and puts less weight on regional disparities such as those in the West, where housing prices are surging and local job markets are booming, partly on the back of technology-industry riches. On the other hand, policy makers are counting on that relationship between unemployment and price pressures, known as the Phillips curve, to lift inflation back to their goal.

“That the strong cities are seeing an uptick in inflation suggests the direction that the national economy will be heading over time,” said Stephen Stanley, chief economist at Amherst Pierpont Securities and a former researcher at the Federal Reserve Bank of Richmond. “The cities and states that are stronger will get there sooner.”

American consumers can have vastly different experiences with inflation depending on what’s purchased and where.

“Much of the disparity in these regional CPIs can be tied to differences in rents both for renters and homeowners alike,” said Brent Meyer, policy adviser and economist at the Atlanta Fed, who put together the bank’s “mycpi” tool that allows individuals to calculate individualized measures of inflation.

Owners’ equivalent rent, or the implicit rent a homeowner would earn from leasing the property, rose 4 percent in San Francisco, 4.4 percent in Los Angeles and 6.6 percent in Seattle. While U.S. population growth has slowed in recent years, the West has been roaring. Idaho, Nevada, Utah and Washington posted the biggest percentage gains in 2017 from a year earlier, according to the latest Census Bureau data.

The West has “very strong job growth, combined with inadequate housing supply and new construction, especially in California,” said Lawrence Yun, chief economist at the National Association of Realtors in Washington. “Because of very high home prices in California, workers and companies are moving to nearby states, which is also fueling their housing market and rents.”

Greg Jones, 59, a musician and retail worker in Oakland, has been looking for an apartment and is shocked at how much rents have risen in recent years, with a small bedroom in someone else’s house going for $1,500 a month. One advertisement indicated the tenant shouldn’t use the home’s kitchen, while another studio apartment was available to “vegetarians only,” Jones said.

“This is ridiculous and out of control,” he said. “It gets worse by the month. It gets more and more expensive.”

Fed policy makers in December penciled in three rate hikes for 2018 to ensure a tight labor market doesn’t lead to price surges or financial instability, even as inflation has remained below target. Investors expect a rate increase at the March 20-21 meeting, which would be the first under a new chairman, Jerome Powell, nominated by President Donald Trump.

The Phillips curve suggests there’s a relationship between tightening labor markets and rising prices, meaning the current 4.1 percent U.S. unemployment rate should be generating higher wages and inflation. Fed leaders have been perplexed because prices, as measured by their preferred measure that’s tied to spending, have gained less than 2 percent almost every month since around mid-2012.

Looking at cities, though, there’s some evidence the link is not broken. Fed research in 2014 by economist Michael Kiley that examined 24 large metro areas since 1985 found “the Phillips curve is very strong across metropolitan areas.”

Still, the relationship isn’t perfect and there are exceptions. The St. Louis Fed has looked for “Phillips curve effects” by counties and metro areas in the bank’s district that includes Arkansas and parts of Illinois, Indiana, Kentucky, Mississippi, Missouri and Tennessee. 

“It is not as much correlation as you would think,” St. Louis Fed President James Bullard said last week. The research hasn’t been published.

Bullard has been among the Fed policy doves arguing against rate hikes until inflation starts rising closer to target. On a national level, labor market effects on wages and prices seem minimal, he said.

In the West, though, the higher inflation is coinciding with glowing labor markets. Jobs in Utah were up 2.8 percent in the year through November, while payrolls increased 2 percent or more in Nevada, Oregon, Idaho and Washington, Labor Department figures show. Employment in California rose 1.7 percent, still above the national rate.

In the South, Atlanta is among cities with the strongest job growth and faster inflation. Employment was up 2.1 percent in November from the same month a year earlier, while prices increased 3.2 percent in the 12 months through December.

“Places with tight labor markets have higher inflation,” said Jonathan Wright, an economics professor at Johns Hopkins University in Baltimore and a former Fed economist. Economists have had “perhaps more luck in finding a Phillips curve than you get with the national data.”