I think that I usually understand what Paul Krugman is saying, even when I disagree with him. However, I do not think that I understand Why Inflation Targets Need to be Higher well enough to say whether or not I agree with him.
What I think he is saying is that the Phillips Curve constrains the ability of the Fed to set a credible inflation target. So, if the Fed says, "We are going to aim for 2 percent inflation," the market is going to say, "Sorry, but that will only raise aggregate demand enough to get you to 6 percent unemployment, which won't get you to 2 percent inflation (because of the aforementioned Phillips Curve). Therefore, we don't believe you, and so we won't let inflation go up at all."
On the other hand, if the Fed says, "We are going to aim for 3 percent inflation," the market is going to say, "That works," and inflation will go up.
So you get this discontinuity. If we have 0 inflation now, the Fed can credibly commit to 3 percent inflation, but not to 2 percent inflation. Anywhere between 0 inflation and 3 percent inflation is "no man's land" in this model.
I may be misinterpreting this. But if I am not misinterpreting it, I think that "no man's land" is too strange to be true. I don't buy these sort of discontinuities. If Krugman wants to say that the Fed cannot credibly commit to raise inflation at all, he can try telling that story (really pushing the Phillips Curve and a liquidity trap, I suppose). But, generally speaking, economic models with discontinuities of this sort are artifacts of strange assumptions, not reasonable descriptions of the real world.
I am willing to believe that the world is nonlinear. I can see where it would be hard to keep inflation steady at 5 to 10 percent, because I think that money demand becomes more unstable at that point, with the incentives kicking in for financial innovation to economize on the use of money. But that is a completely different story, and it does not create a "no man's land."