Mr. Kocherlakota now says that his views had already had begun to change. He had given a speech on Michigan’s Upper Peninsula in the summer of 2010 asserting that the Fed largely lacked the power to reduce unemployment because the problem was not a lack of job openings, but a lack of workers qualified to fill those openings.

“Monetary stimulus has provided conditions so that manufacturing plants want to hire new workers,” Mr. Kocherlakota said back then. “But the Fed does not have a means to transform construction workers into manufacturing workers.”

Over the next two years, Mr. Kocherlakota said that a wave of research gradually convinced him that he was wrong. Mr. Kocherlakota had speculated, for example, that some workers might be unable to take jobs in other cities because their mortgage debts exceeded the value of their homes. Research by his own staff, however, found little evidence of this “house lock” phenomenon.

“It’s a little embarrassing to say this, but you make a speech in August of 2010 and it inspires a whole quantity of work where people say, ‘This is what Kocherlakota says and we will now show in this paper that Kocherlakota was wrong,’ ” he said. “There’s a number of ways that people can react to that, and I reacted in the only way that a sensible person can, which is to update.”

In September 2012, shortly after the Fed announced a fresh expansion of its stimulus campaign, Mr. Kocherlakota returned to Michigan’s Upper Peninsula to announce that he had changed his mind. Contrary to his prediction, inflation was slowing. That meant the Fed had the opportunity and responsibility to do more.

The speech surprised people on both sides of the debate about Fed policy. Proponents of stimulus hailed Mr. Kocherlakota for what they described as intellectual honesty. Some of his former allies saw evidence that he had never shared their understanding of the way the economy works.

“Suffice to say that I am very surprised by his current policy views and how he articulates them,” Stephen Williamson, a professor of economics at Washington University in Saint Louis, said in an email. “I don’t think his views have changed. I think this is just a side of Narayana we didn’t know was there.”