The central bank is charged with a dual mandate of keeping unemployment low and prices stable. With the unemployment rate at or under 5 percent last year, the Fed resumed a campaign of hiking interest rates in December, hoping to avoid an outcome in which the economy overheats and prices spike. This week, the Fed meets again, and though it's not expected to raise rates, the market expects additional hikes in June and December.

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If Trump gooses economic growth with spending and tax cuts — or if there are signs of substantially higher inflation — the Fed might be forced to move even faster.

“Every time a Fed begins tightening monetary policy, in the effort to make sure inflation doesn’t get out of control, it does so at the risk of economic activity,” said Scott Clemons, chief investment strategist at Brown Brothers Harriman, a private bank. “Any Republican or Democrat would wish that interest rates could stay lower longer. This White House, though, could take to Twitter at 3 o’clock in the morning and say something about it.”

Josh Bivens, research and policy director at the Economic Policy Institute, agreed. “Even in more conventional administrations in the past, there has been a tension between the Fed and the president,” he said. “This is a much less conventional administration, so I think they will be pretty free to express their displeasure.”

The Federal Reserve is already beginning to lift interest rates more frequently, as the economy heats up after a long period of sluggish growth. More Americans who want jobs are now able to find them, and that is forcing companies to increase wages to attract qualified workers. Companies in turn are passing those higher wage costs on to consumers in the form of higher prices.

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While inflationary pressures remain subdued, there are signs price increases could be just around the corner. In December, average hourly earnings rose 2.9 percent from the prior year, the strongest rise in more than seven years.

The kind of tax cuts and increases in spending that Trump has proposed often boost economic growth. But they can also lead to even more money swirling around in the economy, adding to inflationary pressures. To keep prices stable for consumers, the Fed might raise interest rates further, which would encourage people to save more and spend less. That restrains inflation, but it can also slow the economy.

In 2015, the Fed judged the economy strong enough to raise rates for the first time in nearly a decade.

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How the Fed proceeds this year will be complicated by uncertainties in Trump’s policies and events abroad. In Europe, Britain is working toward withdrawing from the European Union. Trump has also pledged to launch tough trade measures on China and Mexico that could spark a trade war.

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For much of the last eight years, the Fed has largely carried the burden of stimulating the U.S. economy. The central bank kept interest rates near zero and embarked on an unprecedented bond-buying campaign. That kept the economy growing at a slow but steady pace, reduced unemployment and helped the stock market boom.

This dynamic is now changing, said Beata Caranci, chief economist at TD Bank Group. A Republican-controlled White House and Congress are ready to act together to slash taxes and boost spending. The Fed, meanwhile, has embarked on a path of tightening monetary policy by raising rates.

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The Fed is “now more worried about an overheating labor market,” said Kathy Bostjancic, the director of U.S. macro investor services at Oxford Economics. “Then you lay on top of that the potential for pretty extensive fiscal stimulus. … [T]he worry is that really could push the economy and the labor market into an overheated condition.”

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Others argue the new array of policies will be beneficial for the economy without causing higher inflation.

“I don’t think that any administration should be worried about the Fed choking off economic growth. If they implement policies that lead to higher productivity and higher economic growth, there’s no problem,” said Norbert Michel, a research fellow at the Heritage Foundation. “There should be no conflict. That doesn’t mean there won’t be.”

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Trump has expressed a range of views on interest rates. He has said that, as a property developer with outstanding debt, he “always loved” low rates. But during the campaign, he criticized the Fed for keeping rates low and feeding a speculative stock market bubble.

Congressional Republicans have also targeted the Fed, introducing legislation that would constrain its actions by subjecting interest rate decisions to a mathematical formula. They also proposed creating an external review of the Fed’s decisions — an idea Trump has seconded. The Fed and its supporters argue such a move could allow politicians to pressure the Fed to serve their short-term interests, rather than long-term economic stability.

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Trump will have significant opportunity to shape the Fed's leadership. He inherits two open positions on the board of governors, which helps set interest rates. In addition, Yellen’s term will expire on Feb. 3, 2018, while vice chairman Stanley Fischer’s will end in June of that year.

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Trump could decide to reappoint Yellen — past presidents have often sought continuity by keeping the Fed chairs of their predecessors. But analysts say he likely won’t. The Trump administration did not respond to requests for comment.

“Presumably, there will be a lot of pressure from Republicans to replace her,” said Sarah Binder, a professor of political science at George Washington University. “I wouldn’t be surprised if he tries to break the mold of recent Fed chairs, who have been pretty stellar academic economists.”

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When the Federal Reserve decided to raise interest rates at its December meeting, Trump refrained from comment. But earlier in the presidential campaign, Trump told CNBC that Yellen should be “ashamed” of herself for keeping rates low. In November, the Trump campaign featured Yellen in an ad that criticized “those who control the levers of power in Washington.”

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“The Fed has become very political,” Trump said. “Beyond anything I would have ever thought possible.”

Yellen denied the accusations. “We do not discuss politics at our meetings, and we do not take politics into account in our decisions,” she said.

Note: A previous version of this post erroneously said Yellen's term ends Feb. 1, 2018. It ends on February 3.