New York (CNN Business) The Federal Reserve insists it's immune to President Donald Trump's bullying. Investors, however, think otherwise.

Trump has repeatedly attacked the Fed on Twitter, demanding lower interest rates to pump up the nation's economy.

Those presidential tweets have driven market expectations of interest rates significantly lower — and that in turn influences the Fed's own decision making, according to a working paper published on Monday by the National Bureau of Economic Research, a group that conducts influential research on economics and the workings of the markets.

To put it another way: Trump is boxing the Fed in to embrace the policies he wants.

This president wants to have a scapegoat if the economy goes badly."

"We provide evidence that market participants believe that the Fed will succumb to the political pressure from the President, which poses a significant threat to central bank independence," the researchers from Duke University and the London Business School wrote in the paper, which has not been peer-reviewed.

Congress designed the Fed to be free from short-term political interference. That independence is supposed to give it flexibility to do what's best for the economy, regardless of how that might impact the next election. History shows that central banks that buckle to political pressure fail to tame inflation before it gets out of hand.

Trump has persistently scolded Federal Reserve Chairman Jerome Powell for aggressively raising interest rates last year. The president has compared Powell to a "golfer who can't putt" and even suggested his handpicked Fed chief is a "bigger enemy" than Chinese President Xi Jinping.

"This president wants to have a scapegoat if the economy goes badly. He's preparing that case for his voters," Narayana Kocherlakota, the former president of the Minneapolis Fed, told CNN Business.

Trump tweets, markets react

By examining tick-by-tick fed funds futures data in the seconds after Trump's tweets criticizing the Fed, the researchers found "market-based evidence" that the president "influences expectations about monetary policy."

"The average effect of these tweets on the expected fed funds rate is strongly statistically significant and negative," the paper said.

The researchers found that over the past year, Trump's tweets have lowered market expectations of interest rates by a tenth of a percentage point. Although that may sound small, the academics argue this is significant given that a typical rate cut by the Fed is a quarter of a percentage point.

The Fed closely monitors market expectations of interest rate moves. The central bank never wants to completely surprise investors. Blindsiding markets can spark mayhem that spills over into the real economy.

For instance, Goldman Sachs and others argued in June that the Fed had no choice other than to lower interest rates because Wall Street widely expected it. Failure to do so would create a "hawkish shock," Goldman argued. The Fed ended up lowering rates in July for the first time since 2008 and cut borrowing costs again this month.

"Our findings suggest that market participants believe that the erosion to central bank independence is significant and persistent," the researchers in the NBER working paper wrote.

Kocherlakota, the former Fed official, said he doesn't think the research provides enough evidence to prove that Trump is threatening the central bank's independence. For instance, he noted that inflation expectations, both from the public and investors, remain tame. There is no fear of runaway inflation.

"If the president was literally threatening independence, we should see that the Fed is losing control of inflation expectations," said Kocherlakota, who is now an economics professor at the University of Rochester.

The White House and the Federal Reserve declined to comment.

Powell pledges to ignore political attacks

The Fed has fiercely defended its independence in the Trump era.

Last week, Powell declined to respond to a Trump tweet calling Fed officials "boneheads."

"I continue to believe that the independence of the Federal Reserve from direct political control has served the public well over time," Powell said during the press conference.

Powell added that the Fed "will continue to conduct monetary policy without regard to political considerations" by focusing squarely on "facts, evidence and objective analysis."

In August, the four living former Fed chiefs wrote an unprecedented op-ed warning that an erosion of the central bank's independence would undermine financial markets and damage the economy.

"We ended up with stagflation," Kocherlakota said. "Back then, the president was using covert means to influence the Fed. Here we have a president overtly complaining about his appointee."