The most prominent piece of legislation, sponsored by Representatives Bill Huizenga of Michigan and Scott Garrett of New Jersey, is a result of a yearlong series of hearings orchestrated by Mr. Hensarling’s committee to review the Fed’s performance on the occasion of its 100th anniversary.

It would require the Fed to set interest rates based on a published rule like the Taylor Rule, a formula written by the Stanford University economist John B. Taylor that specifies the appropriate level of interest rates based on the pace of inflation and the gap between actual and potential economic output. The Fed would be required to explain deviations from its rule, although it could change the rule. It would also be subject to audits by the Government Accountability Office.

The Fed has moved in the direction favored by Republicans in recent years, most notably by adopting an explicit inflation target in 2012. But the Fed’s chairwoman, Janet L. Yellen, and other officials have emphasized the need for flexibility. Professor Taylor, for example, argues that under his formula the Fed should already have raised short-term interest rates above 1 percent, while the Fed has indicated it plans to keep rates near zero into next year to encourage job growth.

Professor Taylor said at Thursday’s hearing that the legislation left the Fed “enough flexibility” to deviate from the rule in a crisis. “It seems to me to be the essence of transparency and accountability,” he said. “How could someone object to that?”

Simon H. Johnson, an economics professor at the Massachusetts Institute of Technology, responded that the legislation would not succeed in making monetary policy more predictable, but instead inject politics into the process.