It's very good to see DeLong more skeptical of local multiplier studies than he has been in the past (at least as I've read him in the past). Regular readers know I'm not a particularly big fan of these studies.
There are two big things to keep on the radar with empirical multiplier studies: (1.) endogeneity of the fiscal decision, and (2.) crowding out. We do careful studies in the first place (and not just scatterplots of government spending on growth, like Krugman often shows) because fiscal policy is endogenous. We also do empirical studies (rather than just relying on theory) because of concerns about crowding out, which dull the impact of fiscal policy. Whenever you read a multiplier study, you need to ask yourself "does this adjust for the endogeneity of fiscal policy?" and "does this show me the full impact of crowding out?". If the answer to the first question is "no" the estimate is going to be biased down, and if the answer to the second question is "no" then it's going to be biased up.
Then all sorts of other problems like demand spillovers can enter the picture, but those are the really major issues.
Local multiplier studies usually do a good job at the first question. One of my big concerns is the second question. Federal military spending is financed by taxes that fall on the entire country or by borrowing that falls on national credit markets. Any crowding out will be common to all observations, which means that it will be differenced out. So crowding out - the major reason why we don't just draw a Keynesian cross and call it a day - the reason why we like to measure what the multiplier actually is - is taken out of the picture in most local multiplier studies by design. That's really not good. DeLong puts it this way:
"Third, consider a permanent increase in government purchases in one
region financed by taxes on all regions. Under a full Ricardian régime,
such a permanent increase in spending will have no effect at all on
demand and output: public demand rises, and private demand falls by the
same amount. However, the public demand will be concentrated in the one
region where the spending takes place. That region will thereafter have a
higher relative intensity of economic activity, and ultimately more
factors of production will choose to locate there.
Yet a local multiplier study would then show a considerable multiplier in both the short and the long run."
So this suggests that the local multiplier estimates are biased upward - that the multiplier is actually smaller than suggested.
But wait! The other thing that comes into the picture in any local study is spillovers. The U.S. is an open market and there's a considerable amount of interstate commerce. While differencing out the crowding out makes the multiplier biased upward, the spillovers make the multiplier an underestimate.
So it seems to me there are a lot of problems with local multipliers.
One reason DeLong always likes them is that they hold monetary policy constant. Normally you'd wonder why that's a good thing. Monetary policy is not held constant, so why do we like an estimate that holds it constant?? The reason, of course, is the whole zero lower bound issue. Maybe, but don't we all agree that the Fed is not out of ammo? Don't we all agree that while there are problems with working through the interest rate channel it can still work through inflation and expectations? So the whole "holding monetary policy constant" issue doesn't seem especially important to me.
I still think the best studies are the national studies that look for good exogenous variation in fiscal policy. I used to put the work of both the Romers and Barro and Redlick in this class, but lately I've had some internal conflict over how well identified the Barro and Redlick work really is (I hope to write up a note on that sometime this summer). The Romers take care of the endogeneity problem, and they take account of crowding out, and there's no attenuation of the estimate due to spillovers. Good empirical multiplier work is extremely hard to come by, but it seems to me the Romers offer the gold standard here, rather than the local studies.
While I'm doing the macroeconomic track, I doubt I'll ever be a hot-shot macroeconomist. Still, my dream paper would be to do a kickass multiplier study that really nails the endogeneity problem (without introducing other problems). That is very hard and therefore very impressive stuff.