(Adds statements from hearing, details of new bill, Taylor rule)
By Michael Flaherty and Alistair Bell
WASHINGTON, July 10 (Reuters) - A surge of Republican pressure is bringing the Federal Reserve's long-held independence into question again, as conservative lawmakers seek to place the U.S. central bank under tougher scrutiny.
"We continue to respect the Fed's independence in monetary policy," Congressman Jed Hensarling said at a hearing on Thursday. But he added that the independence must come with "appropriate transparency and accountability."
The Fed has faced political pressure at various points in its 100-year history, starting with its inaction during the Great Depression, and over its high-inflation policies of the 1970s. The Fed's involvement with bank bailouts and the economic stimulus after 2008 has also brought the ire of politicians.
With Democrats controlling the Senate since the 2008 financial crisis, the central bank and its supporters have had the luxury of shrugging off Fed-related laws from the Republican-controlled House of Representatives.
But a Republican takeover of the Senate in November's midterm elections would increase the chances of some of those measures hitting the Senate floor, adding more momentum to Republican efforts to change the way the Fed functions.
President Barack Obama is likely to veto any controversial legislation aimed at the Fed. While very rare, presidential vetoes can be over-ridden by a two-thirds vote in each chamber.
"I think there's a chance of legislation that affects us," Richmond Fed President Jeffrey Lacker told reporters in Lynchburg, Va., last month. "I think it's something that people within the system are aware of. I just hope it's legislation that's constructive and useful."
At least two of the Senate seats up for grabs feature candidates who strongly support auditing the Fed, including Rep. Cory Gardner of Colorado and Rep. Steve Daines of Montana. Polls show Daines well ahead in his race while Gardner is neck and neck with his Democratic opponent.
Republican Thom Tillis, running in the North Carolina Senate race, also seeks to rein in the Fed, his spokesman said.
"The Federal Reserve must be more transparent, particularly related to monetary policy, which means increased accountability to Congress," Tillis spokesman Daniel Keylin said.
Bills under proposal include measures to restrict the power of the Fed chair and to strip the Fed of its low-unemployment mandate.
H.R. 5018, introduced on Monday, would require the Fed to conduct more cost-benefit analyses, provide transparency for Fed stress tests on banks and on international regulations, and take a more rules-based approach to monetary policy.
Testifying on Thursday was former Treasury official and Stanford economist John Taylor, creator of the Taylor Rule, a monetary policy parameter stipulating how much nominal interest rates can be changed relative to inflation or output.
"When policy has been rules based, the economy has performed well," Taylor said on Thursday.
Simon Johnson, a former chief economist at the International Monetary Fund, expressed concern at any legislation that restricts the Fed's flexibility in conducting policy.
"The experts need to have the ability to make those decisions," Johnson said. "I don't think micro-management of the Federal Reserve is a good idea." (Editing by James Dalgleish)