The commentary he provides here is actually better than similar commentary he's provided for similar scatterplots in the past. Several times in the post he mentions the prospect that the relationship is spurious, for example. And his claim is relatively limited - only that this shows that Keynesian arguments are not crazy. That's all good. But I still want to emphasize the perils of jumping on the scatterplot-as-prima-facie-case-for-theory bandwagon, particularly when the causality is so mucky.
The problem with this approach is that then you have to figure out what to do when Antony Davies, of the Mercatus Center (co-authoring with failed Virginia gubernatorial candidate Robert Sarvis) shows you this graph and presents it as a prima facie case against Keynesianism in 2012:
The axes are fundamentally the same with some minor tweaking (growth in real GDP per capita instead of real GDP, and federal spending share rather than federal spending). We can quibble about those tweaks (Krugmans are the more natural test of Keynesianism), but the big difference between the two graphs is that Davies's looks at the U.S. throughout it's history and Krugman's looks at a very short panel (so a little more than a cross section) of countries.
Now the difference between the two is interesting in its own right. Why is the (essentially) cross section Keynesian and the time series austerian? We can think up lots of reasonable stories for why, but if you put them together it also suggests that Krugman's scatterplot may be suffering from a case of Simpson's paradox, with most of the relationship he's interested in determined by variation between countries rather than within countries. That opens a big can of worms because then you have to ask, independent of any short-run policy decisions, why countries show so much variation and how much that variation can really tell us about short-run policy.
Antony Davies's graph of course has the same sorts of problems. The point is obviously not to defend his interpretation - I come down squarely on Krugman's side of all this in the end. The point is that using simple plots as prima facie cases for a scientific claim is bad practice, and opens you up to other people doing precisely the same thing and coming to precisely the opposite conclusion. How could you deconstruct Davies's argument without simultaneously deconstructing Krugman's? At the end of the day people will shake out into two groups: (1.) the people who know the problems these scatterplots pose are going to be unconvinced by both of them, and (2.) the people who don't know the problems and are going to be convinced perhaps by Krugman, but maybe by Davies - most likely whoever they agreed with in the first place.
I do think there's a role for graphs like this, and it's something that Krugman pointed out at the beginning of his post - simply informing people about the performance of different countries. I am not especially clued in to what's going on in Europe, for example. This sort of thing gives me a sense of one aspect of what's going on over there. But it shouldn't be used to defend Keynesianism.
Simon-Wren Lewis has a nice post up that does defend Keynesianism/ZLB problems from Sachs that does not rely on this stuff. He actually constructs a counterfactual to think about, which is precisely what's missing from the descriptive statistics Krugman and Davies have presented.