How much do politics mean to the Federal Reserve? In this, the most politically divisive year in memory, it’s a legitimate question.

Given the potential drag from the uncertainty resulting from the election campaign, politics may mean a lot. More so than usual this year, in fact.

Indeed, one big bank thinks the election could determine the outlook for interest rates, with victory by one leading to increases, the other to cuts.

The U.S. central bank officially has been independent of the executive branch since the 1930s but rarely has been exempt from the influence of politics. According to some accounts, Lyndon Johnson physically intimidated William McChesney Martin, the Fed chairman at the time, because an interest rate increase then ran contrary to LBJ’s guns-and-butter policies.

Richard Nixon installed Arthur Burns at the Fed, who ran an expansionary policy ahead of the 1972 election while talking tough about inflation. Jimmy Carter then named the hapless G. William Miller, who once was outvoted by his own Fed on a rate hike and oversaw stagflation.

Such fecklessness led to Carter’s subsequent appointment of Paul Volcker, who became the St. George who slew the dragon of inflation at the risk of opposition from all sides, as he pushed interest rates to unheard-of levels as high as 20%. Ronald Reagan reappointed him for a second term, not without hesitation because of his fierce independence, but because not to have done so would have upset the financial markets.

Then came Alan Greenspan, who served under four presidents. After being named by Reagan, he was reappointed by George H.W. Bush, who would later bitterly complain that tight Fed policies cost him re-election in 1992. When Bill Clinton delivered his first address to Congress, Greenspan was seen seated prominently next to Hillary. Greenspan convinced Clinton that tighter fiscal policy would pave the way to lower interest rates, and in turn economic growth.

Whether that explains the prosperity of the 1990s — or the technology boom and the delayed effects of the Reagan tax cuts of the previous decade — will be left to economic historians to explain. In any case, the Clinton economic team assiduously avoided criticizing Fed policy. And under Treasury Secretary Robert Rubin, it asserted a strong dollar was in the interest of the U.S., which further restrained inflation and attracted international capital to fuel that decade’s boom.

Ben Bernanke got the nod to succeed Greenspan from George W. Bush, and was reappointed by Barack Obama after the financial crisis. But once the economy was on the mend, Obama selected Janet Yellen, who was originally named to the Fed Board of Governors by Bill Clinton and went on to be president of the San Francisco Fed.

Now the Yellen Fed is in the midst of a contentious campaign. Which, in theory, should make no difference whatsoever for monetary policy.

Minutes of last month’s Federal Open Market Committee indicated a split between those who expressed caution about the sturdiness to take another rate hike and those who thought it overdue. Still, the minutes were a bit out of date as they reflected the panel’s deliberations back on July 26-27. Since then, there have been strong reports on employment, retail sales, housing and industrial production for July. Financial conditions also have been more salubrious, notably with the stock market averages reaching records while credit spreads have narrowed in the corporate bond market.

Given all that, New York Fed President William Dudley suggested in a Fox Business News interview earlier this week that the markets were underestimating the odds of a Fed hike. The federal funds futures market isn’t putting more than a 50% probability on a rate increase until next year.

Market participants should take Dudley’s observations seriously, and not just because as New York Fed president he is the vice chair of the FOMC. (That’s different from the Board of Governors, whose vice chair is Stanley Fischer.) The New York Fed head has that status because of the city’s status as the nation’s financial capital.

Beyond that, Dudley’s former gig was chief U.S. economist at Goldman Sachs, so he has better knowledge of the markets’ interaction than perhaps anybody at the central bank. You learn a lot being around trading desks and meeting a bank’s clients that you don’t get out in academia.

In that vein, the observations of William Lee, Citigroup head of North America economics, also are most enlightening. His Fed call is contingent on the outcome of the presidential election.

If Clinton wins, he looks for a quarter-point increase in the fed funds target, from 0.25-0.50% currently, at the Dec. 13-14 FOMC meeting. Polls show she’s ahead and this is the consensus Fed call.

But uncertainty about the presidential race may be restraining U.S. economic growth by as much as 1.25 percentage points on an annual basis, in gross domestic product, Citi estimates. That will contribute to delaying a hike until after the election to December, which isn’t surprising given the excuses from Yellen & Co. previously for not raising rates. There was the Chinese devaluation last August, which didn’t matter in December, then there was the market turmoil, weak global growth and then Brexit.

If Trump wins, however, Citi’s conjecture is “a trade contraction would induce a recession sooner rather than later.” In that event, it implies “we have seen the cyclical high points for U.S. rates.”

In other words, Trump would make rate cuts for Americans again. A Clinton win would keep the U.S. on track for normalizing rates.

Ignore politics at your peril.