I was talking with Bob Murphy last night about some of Scott Sumner's more strenuous claims. I for one have serious doubts about really declarative empirical claims about monetary or fiscal policy as it relates to the current depression (and I'm skeptical of a lot of historical empirical claims as well!). That goes for Konczal declaring a "natural experiment" as well as Sumner latching on every jobs report that comes out.
My point to Bob was that we need exogenous variation to get a handle on this. There is something of a case for exogenous cross-sectional variation. It's probably weak but it's probably there for a bright person to pull out (and many have tried). We don't have exogenous longitudinal variation in this crisis. That got me thinking about the exogenous variation we've used in the past to estimate multiplier, and that started to depress me about empirical macro.
The distinction between cross-sectional and longitudinal variation is a distinction between different data structures.
But an arguably more important distinction is between what we might call exogenous static and exogenous dynamic policy. In the New Keynesian (vs. the Old Keynesian) and the Market Monetarist (vs. the old Monetarist) or really just in the post-rational-expectations world a lot of the interesting policy effects are in the dynamics and in the impact of policy on expectations. So really if you want a meaningful policy multiplier you want not just to find exogenous policy variation - you want exogenous variation in peoples' expectations about future policy.
That is a very tall order, if you think about it. We usually think that peoples' expectations are affected because they know there is an intention on the part of policymakers to continue a particular policy. But the only reason why there would be such an intention is if there was cause for it (i.e., if the policy was not exogenous). This seems by its very nature a lot harder to me.
It's not impossible. One obvious example of trying to do this that comes to mind is Valerie Ramey's use of the "war news" variable in her work precisely to get at military spending that people expect to persist (I can't think of anyone that has been as explicit about the need for making this distinction as Ramey). If you think about the Romers' work on tax policy, these too are policies that people expect to persist (although I don't think they consider the distinction I make here quite so explicitly). So it's not hopeless, but it's a lot harder. Policy that changes easily (the spending side of fiscal policy or monetary policy) is going to be particularly hard to find exogenous dynamic variation, even though you may find creative ways to pick out exogenous static variation.
Maybe the way to go is to look for natural experiments, but of course natural experiments bring special circumstances. The Depression provides some good ones: FDR and gold for monetary policy and WWII for fiscal policy.