Betsey Stevenson and Justin Wolfers note that if the Federal Reserve didn't care about unemployment at all and merely tried to hit a 2 percent inflation target, that would imply that we need monetary easing. So why doesn't the Fed ease? They say that failing to hit either inflation or job-creation targets undermines credibility:
There are real costs to the Fed’s failures. Millions remain unemployed in the service of keeping inflation below its target level. We risk the possibility they may not work again as their skills atrophy and they lose hope. The Fed’s confused communications have undermined its own effectiveness and harmed its institutional prestige.
In the long run, a Fed whose word we don’t believe, and whose principles it views as optional, is a Fed that will be less able to influence the expectations of consumers and investors, rendering it less effective at pulling us out of the next economic decline.
The costs to workers and to the real economy are a quite serious matter. But as for the Fed's reputation, I'm much less sure. It seems sort of odd to think that the Fed is persistently missing its inflation target on the downside while also leaving millions to languish unemployed. The parsimonious explanation is that regardless of stated objectives, the Fed is in fact trying to target something like the current inflation trajectory. You could characterize it as a policy of "inflation that's as low as possible without pushing the economy into a new recession."
The technical term is "opportunistic disinflation." When recession hits, you try to bring back growth. But you also seize advantage of the slack in the economy to push the trend level of inflation down, rather than seeking a rapid return to full employment conditions. It's morally wrong but very consistent with the value system of modern central bankers. Recall that Jean-Claude Trichet proclaimed his disastrous turn helming the European Central Bank to be a smashing success because inflation was lower than it had ever been under the Bundesbank. By the same token, Ben Bernanke has brought us the lowest inflation of any Fed chairman of the postwar period. You may call it prolonged mass unemployment, but he may see it as a huge success.