PALO ALTO, Calif. (Reuters) - Unemployment is at a decade low, the American economy is growing, and inflation is nowhere in sight, yet for two leading candidates to head the Federal Reserve, the central bank needs shaking up.

FILE PHOTO - Kevin Warsh, addresses the Shadow Open Market Committee during a symposium in New York March 26, 2010. REUTERS/Lucas Jackson

The Fed is credited by most economists for its rapid response to the 2008 financial crisis. Under Chair Janet Yellen whose term expires next year, it has been able to shift into post-crisis mode, ceasing to add to its balance sheet and embarking on a series of rate hikes that will take interest rates back to “normal”.

For former Wall Street banker Kevin Warsh, who served as a Fed governor at the time of the financial crisis, the economic recovery is characterized by bloated central bank balance sheets, financial risks, and a hidebound institution that needs new approaches.

“We should not allow a failure of imagination, a failure of courage,” to impede changes to how the Fed is run, Warsh said in remarks at the Hoover Institution, an intellectual home of conservative economics where he is a visiting fellow.

While he did not refer to a potential candidacy for the Fed Chair job, Warsh’s speech struck some in the audience as an audition. Warsh and Stanford University economics professor John Taylor have emerged as potential frontrunners to succeed Yellen whose term ends in February 2018.

Warsh, a Wall Street lawyer by training rather than one of the Phd economists who have come to dominate monetary policy in recent years, called for “fresh air from the real side of the economy, fresh air from the markets,” in revamping the Fed.

He says the central bank has left the public confused, lacks a long-term strategy, and is too beholden to short-term stock market and other events.

Warsh, who was consulted frequently by former chair Ben Bernanke when at the Fed, was speaking at the Hoover Institution, a center of conservative thinking on monetary policy that has in recent years tried to amp up its profile in the Washington policy debate.

Along with being close to Bernanke, Warsh has family connections to President Donald Trump, and is on one of the president’s White House advisory panels - advantages some feel put him on any short list for consideration.

IF TRUMP WANTS RULES, THERE IS TAYLOR

Hoover is also Taylor’s intellectual base.

Taylor is a favorite among Republicans who feel the Fed should be held closely to a formula, a “Taylor rule”, for setting interest rates and give up some of the discretion policymakers currently enjoy.

The list of possible chairs is a long one for a president who has surrounded himself with a not always coherent set of economic advisers -- from trade skeptics and gold standard advocates to Wall Street insiders.

At this point Trump has not indicated whether he thinks the Fed needs fundamental reform. He has not taken much interest in the nuances of monetary policy and has three open vacancies on the Fed’s seven-member board of governors.

Trump, who is skeptical of the statistics that are the current Fed’s stock-in-trade, also has not indicated whether he is inclined to stick with an economist like Taylor to run the central bank or will turn to a Wall Street figure like Warsh, as he has done for other top economic appointments

While attending a two-day conference, neither Warsh nor Taylor referred publicly to whether they want to be Fed chair. But neither were shy in saying they think the Fed and monetary policy needs to change.

In a speech on Thursday night, Taylor compared current times to the situation Paul Volcker faced in the 1970s when he wrangled a sometimes resistant Fed board to battle inflation with aggressive interest rate increases.

The implication: that it would be possible to steer a reluctant central bank towards the sort of regime he and some members of Congress feels it needs, where rules are agreed for setting interest rates and followed as closely as possible.

Commercial banks would also be freed from regulation if they agree to set aside more capital, and the U.S. would make the case internationally for a more rules-based central bank system.

“The idea is a package” of changes that the central bank could adopt to overcome what he feels are potentially “destructive” divisions over policy, Taylor said.

But some policymakers listening to both Warsh and Taylor wondered whether Trump would actually want the kind of radical change outlined at Hoover.

St. Louis Fed president James Bullard told Reuters that with the Fed hitting its targets, Trump might not want to pick “somebody that’s going to deviate substantially from the Bernanke-Yellen policy.”