He has an extended criticism here. I'll sum up my position in this way: Krugman persuades successfully, he does not prove successfully. Proof is hard in macroeconomics. Unlike Bob, who in prior posts directly challenged me, Krugman obviously never mentions me. I'm going to make this distinction between plausible persuasion and successful proof more strenuously to a guy that specifically engages me. But since he seems to want me to call Krugman out, I'm happy to say that he hasn't really "proven" anything - there are lots of stories that are consistent with the evidence he provides. But he is definitely persuasive.
On the one hand, we should know very clearly the difference between these two things. Epistemological quibbles can really lead scientists astray. Scientists are in the business of rigorous persuasion. Mathematicians and logicians are in the business of proof. Now - with that understanding that proof is hard, a little casualness with words like "prove" and "falsify" is fine, I think - so long as we know what is meant. Epistemologists don't own these words, after all. My concern with some a priorists among economists is that not only do they use the language of "proof" and "falsification" - they also seem to think it should be used and understood in the same way that logician or mathematician uses or understands it.
Anyway - that's all a digression, but it's a digression that frames the issue. Ultimately, if you mention me by name in a post of course I'm going to engage you directly. I'm also in the business of persuasion - I'm happy to clarify that Krugman should know that when he says "prove" he means "persuade" or "justify". But I think he makes a good persuasive case, so of course I'm not going to spend scarce blogging time addressing it - even though Bob is right and I've never denied he's right on this point. I'd rather address people who (1.) don't make a persuasive case, and (2.) go further by mistaking their attempted persuasion as an attempted proof, and (3.) actually mention me by name.