Mr. Taylor also favors restraints on other aspects of the Fed’s post-crisis response, including the bond-buying campaign it undertook known as quantitative easing.

Mr. Taylor warned repeatedly at the time that the purchases would result in inflation. “We’ve got a high inflation down the road for sure,” he said in June 2010. “When it will come, I can’t predict. But unless there’s a change in policy we’re going to have inflation like back in the 1970s, or even more.”

Instead, inflation has been persistently sluggish.

Mr. Taylor has since argued the purchases did no good and that the Fed should be restricted from buying mortgage bonds, because that provides support for a particular kind of borrowing — a decision that belongs to fiscal policymakers.

He also wants to reverse a recent change in the mechanics of monetary policy. The Fed bought bonds from banks by increasing the reserves those banks hold at the Fed. That surge in reserve balances made it impossible to raise rates by limiting the availability of reserves, the traditional method, so instead the Fed paid banks not to use the reserves.

Mr. Taylor wants the Fed to revert to the minimalist mechanics.

Mr. Powell, by contrast, has defended the utility of the bond-buying campaign and argued that the new mechanics allow the Fed to control interest rates more effectively.

Theorizing about changing monetary policy is far easier than acting on it and academics who become policymakers often adopt a more pragmatic approach. Ben S. Bernanke, the former Fed chairman, argued in the early 2000s that Japan should consider drastic actions to revive inflation. When he confronted weak inflation as Fed chairman, he did not attempt to pursue those policies.

Mr. Taylor, speaking earlier this month at the Federal Reserve Bank of Boston, suggested he might embrace that tradition. “I don’t think of policy rules as tying central bankers’ hands,” he said. “I’ve never thought of rules as tying central bankers’ hands. To me, they are ways of making monetary policy better.”