"Overall, the (Federal Open Market Committee's) response to tightening after the COVID pandemic was not textbook," requiring an accelerated stop to ongoing asset purchases and the fastest interest rate hikes in 30 years, Waller said in a note co-authored with Fed senior adviser Jane Ihrig.

"When looking back, there are lessons to be learned," the two wrote, chief among them that Fed statements "should be careful to use language that allows the Committee the flexibility it needs to respond to changing economic and financial conditions."

As it stood, the Fed's pledge in 2020 to maintain loose monetary policy until the job market had been largely healed from the pandemic and inflation was on track to move above the central bank's 2% target kept it sidelined as prices started to surge far more than policymakers had in mind.

The economy was in deep disarray at the time that pledge was made, and the Fed was also putting in place a new framework meant to ensure inflation did not continue to fall below its 2% target.

At it was, policy rules and even different rate-hike criteria the Fed had used in the past would have opened the door to increases in the central bank's benchmark overnight interest rate in the spring of 2021, the two wrote.

The Fed's first rate hike occurred in March of 2022.

Waller and Ihrig said their "intent is not to criticize" the Fed's decisions of the last few years but "to assess these policy strategies should central banks be confronted with a similar crisis in the future."

Indeed, many of the arguments are familiar ones laid out by Waller and others in earlier public comments.

The two also noted that the Fed's policies had "coincided with stable financial markets, a strong labor market, and inflation moving down from its peak."

But they could be relevant to an upcoming review of the Fed's operating framework, a document that tilted policy towards attention to the job market and was used to argue for a promise to lift inflation above target for a period of time in order to make up for inflation shortfalls - the criteria that acted as a constraint on central bankers as inflation rose.

(Reporting by Howard Schneider; Editing by Paul Simao)

By Howard Schneider