FILE PHOTO - San Francisco Federal Reserve President John Williams speaks to Reuters in San Francisco, California, U.S. on September 27, 2016. REUTERS/Stephen Lam/File Photo

PHOENIX (Reuters) - With falling U.S. unemployment expected to put upward pressure on inflation, the Federal Reserve should keep raising interest rates gradually, San Francisco Federal Reserve President John Williams said on Wednesday.

“As long as the data continue to show steady growth and we see the uptick in inflation that we’re expecting, my own view is that we should continue to raise interest rates slowly over the coming year,” Williams said in remarks prepared for delivery to an economics forecast luncheon.

The Fed is widely expected to raise rates when policymakers meet next month and Williams has said he supports continued, gradual rate hikes as long as the economy stays on its current path. Fed Chair Janet Yellen signaled her expectation for further rate hikes ahead in testimony earlier Wednesday.

Williams, who will have a vote on monetary policy next year when Governor Jerome Powell is expected to take over from Yellen as Fed chair, said he expects the U.S. economy to grow about 2.5 percent this year and slower after that. Unemployment, now at 4.1 percent, should continue to fall next year and bottom out at about 3.75 percent, he said.

Though inflation has remained well under the Fed’s 2-percent goal, puzzling some Fed officials including Yellen because inflation usually strengthens as the economy gains speed, Williams said the weakness is easily explained.

Slow-growing healthcare costs and falling prices in other sectors like mobile phone plan pricing that are not very sensitive to economic cycles have been offsetting price increases in other sectors, researchers at the San Francisco Fed said in a paper published this week.

To boot, Williams said Wednesday, it often takes 12 months for inflation to pick up after the economy shifts to higher gear.

“The next time you see a headline about stubbornly low inflation, you can smile to yourself, knowing that the mystery isn’t all that mysterious after all,” he said. “With the economy doing so well this year and based on the historical pattern, I expect to see a rise in inflation in 2018.”