WASHINGTON — Federal Reserve Board Gov. Daniel Tarullo is not backing a "too big to fail" bill introduced by Sens. Sherrod Brown and David Vitter this week and doesn't plan to, either.

Sens. Sherrod Brown, D-Ohio and David Vitter, R-La. released Wednesday their highly anticipated bill to tackle "too big to fail," which included higher capital standards for the largest institutions and regulatory relief for smaller banks.

In advance of the bill's unveiling both senators published an an op-ed in the New York Times that suggested there was a "real and growing bipartisan consensus" on their approach, including from key regulators like Tarullo who they termed "a progressive," and Thomas Hoenig, vice chairman of the Federal Deposit Insurance Corp., who was described as "a conservative."

But Tarullo, at least, does not appear to support the bill. (A spokeswoman for Hoenig said he was traveling and could not be reached for comment.)

The Fed governor has repeatedly said that wholesale funding, which is susceptible to debilitating runs, remains a significant problem that still needs to be tackled in the efforts to address "too big to fail." Tarullo has not expressed support for the Brown-Vitter bill, which did not address the wholesale funding issue, according to a source familiar with Tarullo's thinking.

(Tarullo was not available for comment.)

The governor, who is responsible for bank and regulatory supervision at the U.S. central bank, had previously endorsed legislation by the senators that would limit the non-deposit liabilities of any single institution relative to U.S. gross domestic product. It's possible the senators misconstrued his endorsement for a previous bill for their latest "too big to fail" bill.

Spokespersons for Brown and Vitter did not immediately comment.

Tarullo has also been outspoken in calling for higher capital requirements for the largest banks. Speaking in 2011, he suggested the largest banks could face capital requirements that range between 8.5% and 14%. Ultimately, however, regulators agreed to a smaller capital surcharge for large banks, which said the largest institutions would face a 9.5% capital requirement.

The senators' latest bill would set a 15% capital requirement for institutions with more than $500 billion of assets and an 8% requirement for regional banks between $50 billion and $500 billion of assets. It would also impose a number of additional changes, such as scrapping proposed Basel III requirements, requiring bank subsidiaries to capitalize separately and restricting the ability of bank holding companies to move assets or liabilities across banking and non-banking affiliates.

Tarullo has previously raised his concern that "large amounts of short-term, non-deposit, runnable funding" had gone unaddressed directly with Brown during a Senate Banking Committee hearing in February.

"My view is that's the problem we need to address," said Tarullo, during a round of questioning with Brown about his previous bill. "I think your legislation takes one approach to addressing it, which is to try to cap the amount that any individual firm can have, and thereby try to contain the risk of the amplification of a run."

Tarullo suggested at the time there could be other ideas like placing limits on different kinds of duration risk, imposing higher requirements if you have more than a certain amount, or even placing uniform margins on any securities lending.

"I think from my point of view that the importance of what you have done is to draw attention to the issue of short term, non-deposit, runnable funding," said Tarullo. "And that's the one I think we should be debating in the context of 'too big to fail,' and in the context of our financial system more generally."

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