How much power does monetary policy have to create jobs?

That question is at the heart of the debate over the Federal Reserve’s recent policy decisions. A majority on the Fed's policy committee has explicitly endorsed keeping low interest rate policies in place until the unemployment rate falls to 6.5 percent (or inflation becomes a problem). But on Wednesday morning, St. Louis Fed President James Bullard warned that focusing on unemployment could put the central bank’s decades of work stabilizing inflation at risk.

The title of his speech at the Levy Economics Institute of Bard College's annual Minsky Conference said it all: “Unpleasant implications for unemployment targeters.” He cited work by  economists Federico Ravenna and Carl Walsh that suggests that keeping prices contained is the best way the central bank can help the economy, even when the labor market is in turmoil.

“The idea that the Fed should put more weight on unemployment does not fare very well in this analysis,” Bullard said. “In fact, such an approach might be counterproductive.”

The problem, Bullard said, is that the Fed really only has one antidote for an ailing economy -- adjusting the price of money -- and that tool's impact on unemployment is indirect.

“The monetary guys can really do one thing,” he said. “ It’s not that you don’t want to address unemployment. It’s that it’s not a good way to address unemployment efficiency.”

But while Bullard sees pursuing easy money policies to try get boost hiring as problematic, he is more open to such easing when the inflation rate is falling below the Fed's 2 percent target. Indeed, Bullard said he is becoming “concerned” that inflation is too low, and that if prices fell further, he would be ready to ratchet up the Fed’s $85-billion-a-month bond-buying program.

Bullard was one of the first Fed officials to push for changing the pace of the central bank's asset purchases to match economic conditions. He has said he would consider reducing purchases by small amounts, perhaps even at each of the Fed's policymaking meetings, as the economy improves. But Wednesday was the first time he has broached the policy of increasing bond purchases to reach the inflation goal.

“We should defend our inflation target from the low side,” Bullard said. “If we say 2 percent, we should get 2 percent.”