(Reuters) -Financial markets may be looking at another bout of volatility over the next six months, economists cautioned, as U.S. President Donald Trump clashes with the Federal Reserve to exert influence on monetary policy.

Trump's persistent criticism of the Fed board and Chair Jerome Powell for not lowering interest rates, his attempt to fire Governor Lisa Cook, and the nomination of White House economic adviser Stephen Miran as a Fed governor are chipping away at investor confidence in the institution's authority.

"The market has been very calm for now (but) the narrative could turn ugly in the coming months," Sree Kochugovindan, senior research economist at abrdn, told the Reuters Global Markets Forum.

"The longer-term significance of the changing Fed composition next February becomes more important," she said, especially if Federal Open Market Committee (FOMC) members start deviating significantly away from the 'Taylor rule.'

Named after its creator, American economist John Taylor in 1993, the 'Taylor rule' is a well-known formula for setting short-term interest rates based on the values of inflation and the economy's growth potential that is among metrics utilized by policymakers.

U.S. Treasury Secretary Scott Bessent said the Fed's structure prevents a president from "stacking the board", but reports suggest that Trump may seek influence by reshaping how the 12 regional bank presidents are chosen and reappointed.

The risk of a Trump-majority Fed board preventing the reappointment of some regional presidents next February is "probably underpriced", said Michael Brown, senior research strategist at Pepperstone. Though seen as a rubber-stamping exercise, "it could prove more politically influenced this time out," he added.

Steven Blitz, chief U.S. economist at TS Lombard, said the Trump administration's push represents a "potential dismantling of the Fed", even beyond the issue of central bank independence.

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