My heretical take is explained here.
Bernanke’s discussion of the issue is a bit evasive — not to mention a couple weeks old. But he recommends that the Fed be patient in tightening after zero-lower-bound episodes and explicitly relates this to the idea of price-level targeting.
It does not take a wild imagination to conclude this means he supports allowing inflation to overshoot the 2% long-term target in the late cycle to compensate for prospective (or even past, if you want to be more radical) periods of inflation undershoot.
Of course, Bernanke is not now in charge of policy, so how is this relevant? I would note that he is now more free to express his view on than he was when he was Fed chair. And I would infer from that that the idea is probably less radical than it sounds and may have support within the current FOMC.
If the Fed wants to hit 2% on average over time, it would seem as though it would have to. And actual Fed speech has been not-inconsistent with this take, although also not dispositive.
If my now-fairly-old take is right, then the Fed now finds itself in an awkward sitch. The Fed does not want the unemployment rate radically to undershoot the natural rate, whatever it might be. And yet, inflation remains stuck below 2% at a time when the Fed would probably prefer it be slightly above 2%.
Life would be easier for the Fed if inflation were to start to rise again. It would eliminate the need for Sophie’s Choice. But if I am right that the Fed would all-else-equal prefer to see inflation above 2% in the late cycle, then that is a dovish influence and it does reduce the risk of recession in the next year or so.