It would be unusual for Trump to continue that line of criticism once he is in the White House, because presidential administrations usually decline to discuss monetary policy, but it seems unlikely that he would appoint Yellen to another term.
Yellen has defended herself and the Fed against the criticism. "I can say emphatically," she told a September press conference, "that partisan politics plays no role in our decisions about the appropriate stance of monetary policy."
Analysts say Trump's statements are less likely to affect her decisions than the choices he makes on policy - and how those choices might affect economic growth and inflation.
"If she thinks the economy needs more rate hikes, she'll do them," said Ryan Sweet, the director of real-time economics at Moody's Analytics. "He really doesn't change her plan. The economy will change her plan, if needed."
The plan the Fed has inched toward all year is a measured normalization of interest rates, which have now sat near zero for the longest stretch in American history.
Fed officials have already taken a first, small step to raise rates. They are expected to raise again in December. Forecasts by board members and regional bank presidents indicate that officials expect rates to rise by about a half-percentage point in 2017 and nearly a full point in 2018.
Trump's plans could accelerate those hikes - or sweep them off the table.
People are reassessing their view on what growth and inflation are going to look like in a new Trump administration. If the tea leaves are right, it looks like we're headed for a little higher growth and a little higher inflation.
The effects are particularly hard to predict because it is unclear how aggressively Trump will move on several fronts of economic policy, including taxes and trade, and what he will ultimately win congressional support for.
Trump might, for example, push Congress to approve massive tax cuts and infrastructure spending increases, which could, at a moment when unemployment is low, both accelerate economic growth and inflation. He might erect high tariffs on imports from China, Mexico and other countries, a move his team predicts would increase growth but which other economists have forecast would push America into recession.
"Trump's exact policies are unknown," researchers at the investment bank ING wrote in a report this week. "Fiscal stimulus and tax cuts could generate inflationary pressure," forcing the Fed to raise rates more quickly.
"However, a protectionist approach could damage growth and call for further easing" -- meaning, rate cuts and other monetary stimulus to prop up growth.
Financial markets are focusing on the upside so far, with US stocks rallying after Trump's win and bond yields suggesting an expectation of higher growth to come. Analysts say that appears to reflect a belief that Trump and Republican leaders are more likely to find common ground on tax cuts and deregulation - which forecasters believe would boost growth - than on potentially growth-dampening trade restrictions.
"It's fair and safe to say that the market is thinking of this in net positive terms," said Tom Porcelli, chief US economist for RBC Capital Markets.
"People are reassessing their view on what growth and inflation are going to look like in a new Trump administration. If the tea leaves are right, it looks like we're headed for a little higher growth and a little higher inflation."
Perhaps the biggest unknown, for the Fed and for markets, is what sort of Congressional moves the Trump administration might champion to increase oversight of the central bank. Republicans have floated several proposals, some of which would add only modest new accountability measures, and others that would curb the Fed's independence or change its policy mandate.
Analysts at JPMorgan Chase wrote this week that they see those more aggressive proposals as "less likely" for Trump to sign into law than less aggressive ones.
"Nonetheless," the analysts wrote, "these are risks that bear monitoring."
