As you have probably heard by now, the president is trying to fire Federal Reserve Governor Lisa Cook, over unproven allegations of mortgage fraud. The context here is, of course, that the president has been trying to influence the makeup of the Federal Reserve for months, and pushing the central bank to lower interest rates. But if he is successful in making the Fed less independent, it might actually achieve the opposite of what he wants.

If —and it’s a big if — the president’s attempted firing goes through, it could open the door to more presidential influence at the Fed.

“In the longer term, the issue is whether the Fed is able to act independent of executive influence,” said Matthew Paniati, a senior analyst at Capital Advisors Group.

“Because if they can’t, that has very significant macroeconomic implications in my view,” said Paniati.

If people believe the Fed is influenced by a president more than by inflation data, the less faith they have that inflation will be managed well.

“That sends a signal to the bond market that there’s more risk of inflation going forward,” said Kathy Jones with the Charles Schwab Center for Financial Research.

And inflation is an investment killer.

“Investors want to be compensated for tying up their money for longer periods of time, because there’s always some risk that inflation will erode those returns,” said Jones.

So when investors are more worried about inflation, they charge more. They charge higher interest rates in the bond market, which the Fed does not control — it only controls short-term interest rates. The market controls long-term rates, that affect everything from car loans to mortgages to government debt.

“That’s the irony of this whole battle, I think, is that the more the president pushes on the Fed to cut interest rates, the more risk is that long-term rates go up,” said Jones.

It is also possible that concerns over inflation and Fed independence are just peanuts, that this whole brouhaha is ignoring an even bigger risk to long term interest rates.

“The main issue is just the budget deficit,” said Gershon Distenfeld, director of income strategies at Alliance Bernstein. 

He said the government is getting in over its head when it comes to debt, and because of that, investors will charge higher long-term rates. Either way, markets have not panicked just yet. 

“And I think it’s because you’ve had decades of Fed credibility that have kept the market believing that Fed independence is still there,” said Marvin Loh with State Street Markets.

Investors are waiting, like everyone else, to see how this all plays out.