"Could it be that the time series covers a long era in which for the most part the Federal Reserve is trying to manage aggregate demand and so offsetting any effects of fiscal policy on aggregate demand, while the cross section covers just an unusual short period during which central banks have lost their traction and their ability to engage in monetary offset?"
Yes definitely! In fact I'd be even more optimistic than that. Fiscal policy is endogenous to macroeconomic conditions so in addition to the particularly weak monetary offset these days I'd imagine periods in the Davies et al. series - if properly identified - would show better results for fiscal policy too. Certainly I'm not saying that scatterplots are just a mess that we can't make sense of (more on this below). He continues...
"I don't think it is that you have to believe Krugman's scatterplot or Davies's--I think that both are true, valid, important, and pose tests that any theory that we are not going to reject must pass."
Yes to true, valid, and important. It's the tests that I'm concerned about. Let me put it this way, for most of the applications we deal with for a theory to pass a scatterplot test you can't have just a theory. You have to have a theory plus a set of other ideas about what's going on in a world that's very complex, endogenous, etc. Now if you wanted to you could call your theory plus all these other ideas (e.g.., that for the Davies time span the monetary offset was operating normally, etc.) the "theory" but this very quickly degenerates into either cobbling on assumptions to make it work or a wide range of different theories consistent with the same data. And that gets us right to the problem I pointed out - where some people will be siding with Krugman and some with Davies. Instead I'm just suggesting we consider it true, valid, and important, but not a good test of theory.
"And I don't understand the aversion to scatterplots: in the end it is all scatterplots--albeit with an argument for paying attention to some pieces of the identifying variance underlying the scatter plot and not others..."
This is another great chance to re-emphasize my point. I do not have an aversion to scatterplots. I just put one together today for a DHHS project. I have an aversion to treating scatterplots as if they present a prima facie case for most economic theories.