* Fed's Stein: decision not to taper in Sept was "close call"
* Hawk Lacker warns Fed could lose face if it acts in October
* Kocherlakota - Fed has only itself to blame for volatility
FRANKFURT/STOCKHOLM/HOUGHTON, Mich., Sept 26 (Reuters) - The Federal Reserve confused financial markets over scaling back its bond buying, three top officials said on Thursday, with one arguing the central bank should link tapering to drops in the jobless rate and another calling for a broad remake of strategy.
Fed Board Governor Jeremy Stein said he would have been comfortable with acting at the Sept. 17-18 meeting, and the decision to keep buying bonds at an $85 billion monthly pace had been, for him, a "close call".
"But whether we start in September or a bit later is not in itself the key issue - the difference in the overall amount of securities we buy will be modest," he told a monetary policy conference in Frankfurt.
"What is much more important is doing everything we can to ensure that this difficult transition is implemented in as transparent and predictable a manner as possible. On this front, I think it is safe to say that there may be room for improvement," he said in prepared remarks.
The Fed's decision to stand pat on bond buying stunned financial markets, which had anticipated it would begin to slowly reduce the program, signaling the beginning of the end to an unprecedented five years of ultra-easy monetary policy.
Federal Reserve Chairman Ben Bernanke explained the decision last week by pointing to the disappointing performance of the U.S. economy in the second half of 2013. It also noted headwinds from tighter U.S. fiscal policy, which could worsen as leaders in Washington fight over a deal to keep the government funded and lift the U.S. debt limit.
Investors are now focused on Fed meetings in October and December, although some economists say the central bank could hold fire until 2014 to make sure the U.S. economy has decisively regained cruising speed.
But Richmond Federal Reserve President Jeffrey Lacker, one of the Fed's most hawkish officials who has been urging for months that it taper bond buying, said that the central bank had boxed itself in by failing to move last week.
"It could be hard to do it (tapering) in October without losing face, but I don't see why we couldn't do it," he told a banking conference in Stockholm. "It's going to be harder for us to communicate credibly in the future," he told reporters. Lacker is not a voting member of the policy committee this year.
A third official, Minneapolis Fed chief Narayana Kocherlakota, said the Fed had only itself to blame if markets swing wildly in "misguided" reaction to its meeting-by-meeting decisions on bond buying.
"It is a problem of the (Fed's) own making, because we have not been sufficiently clear about what we are going to do down the road," he said.
He called for a renewed focus by Fed policymakers on bringing down unemployment, like former Fed Chairman Paul Volcker's single-minded focus on bringing down inflation in 1979.
The central bank, he said, should do whatever it takes to drive U.S. unemployment lower, although not necessarily by buying even more bonds. For instance, it could lower the interest rate it charges banks to keep their excess reserves at the Fed, he said.
What matters is not the specific "tactic," he said, but the overall strategy.
"What the committee chose to do in September was fully consistent with everything that had been communicated," Kocherlakota told reporters after his talk. But what has been communicated, he said, is insufficient, as is the level of stimulus the Fed is providing the economy.
"I think we've set ourselves up in a very awkward position where every action, no matter how minute the economic consequences of that action, and every communication about that action, no matter how minute that communication might be, is having very undue consequences on people's beliefs about the course of future policy," he said. "We should be communicating more effectively that we are about having the economy recover as fast as possible, as long as inflation stays close to, possibly temporarily above, but close to 2 percent."
Kocherlakota is one of the Fed's most dovish members, and on Thursday reiterated the Fed should keep interest rates near zero until unemployment reaches 5.5 percent, though he cast doubt on whether the rate truly captures the state of the labor market.
The nation's jobless rate fell to 7.3 percent in August, but remains well above historically normal levels. The decline was also subject to caution because it reflected the departure of workers from the labor force, rather than being entirely due to stronger new job creation.
There are millions of Americans who have either given up looking for work or are getting fewer hours of employment than they would like, due to the still-tepid state of the labor market following the nation's severe 2007-2009 recession.
Stein, who has talked about the risk of Fed bond buying leading to asset bubbles, said that one way to reduce uncertainty and accompanying market volatility would be to link cuts in bond buying directly to economic data.
"My personal preference would be to make future step-downs a completely deterministic function of a labor market indicator, such as the unemployment rate or cumulative payroll growth over some period," Stein said. "For example, one could cut monthly purchases by a set amount for each further 10 basis point decline in the unemployment rate."
This echoed a suggestion made earlier in the year by St. Louis Fed chief James Bullard, perhaps signaling growing support on the Fed's policy-setting committee to adopt such an approach.