A top Federal Reserve official on Friday offered an equation-studded defense against critics who say the U.S. central bank is not doing enough to combat high unemployment, saying that too little is known about the Fed's current tools to use them with abandon.

With unconventional tools like bond-buying, a properly cautious Fed should aim to bring unemployment and inflation back to normal "much more gradually than what would appear to be optimal," the president of the San Francisco Fed, John Williams, told the Society for Computational Economics in Vancouver, Canada, on Friday.

Williams, who has supported the Fed's current bond-buying program, said that though his models call for "attenuating" the use of the Fed's unconventional tools compared with other more traditional tools, the current situation still calls for a "strong" response.

That is because the Fed is not as sure about the effects of bond buying as it is about its traditional policy lever of a short-term interest rate target, he said. The greater the uncertainty, the larger the chance that overly aggressive policy could overheat the economy.

The San Francisco Fed released the text of Williams' working paper on Tuesday.

On Friday, Williams provided a few new nuggets on his thinking, saying that using unconventional policy with moderation is like taking out an insurance policy.

With "a policy designed for uncertainty about parameters, you pay a small price if actual uncertainty is low, but you are actually guarded against bad outcomes," he said.

The Fed is buying $85 billion in Treasurys and housing-backed securities each month to push down long-term borrowing costs in a bid to fuel economic growth and hiring.

The bond-buying, known as quantitative easing, is meant to add to monetary stimulus by pushing down long-term borrowing costs when short-term rates cannot be pushed any lower. The Fed has kept short-term borrowing costs near zero since December 2008.