By David Harrison 

The House Financial Services Committee approved a Federal Reserve overhaul bill Wednesday that would change the way the central bank does business.

The bill would require the Fed to adopt a mathematical rule to determine where to set interest rates. It would require the Fed to disclose more details about bank stress tests. And it would allow members of Congress to ask the Government Accountability Office to review the central bank's monetary policy decisions.

The Republican-supported bill, which passed on a party-line vote, is one of several Fed-related bills that have been introduced in this Congress by both Democrats and Republicans. In May, the Senate Banking Committee approved financial regulation legislation that included several provisions that would affect the Fed.

The House bill, sponsored by Rep. Bill Huizenga (R., Mich.) would also require the Fed chair to testify in both chambers on a quarterly basis, rather than twice a year. It would raise the threshold under which the central bank could invoke its "lender of last resort" powers and would limit the number of firms eligible to receive the Fed's emergency loans to those that are solvent.

Under the legislation, the central bank would have to conduct a cost-benefit analysis before promulgating new rules. The Fed's vice chairman for supervision would also have to provide the House Financial Services Committee and the Senate Banking Committee with a report on proposed and anticipated rules.

The Fed didn't have a comment on the bill. But Fed Chairwoman Janet Yellen has rejected tying monetary policymaking to an explicit rule. She has also said she opposes GAO audits of Fed monetary policy. Fed officials are concerned that GAO audits could make the central bank vulnerable to political pressure and jeopardize its independence.

Last year, the House passed legislation mandating GAO audits of the Fed but the bill died in the Senate, which was then under Democratic control. It is unclear how such legislation would fare today, now that Republicans control both chambers of Congress.

Write to David Harrison at david.harrison@wsj.com