Scientific controls and sampling

I'm not sure I completely understand what Scott Sumner (or Mark Sadowski) is getting at in this post. You can't see the effect of fiscal policy if your sample has the same monetary policy (e.g. US states or EU member nations)? For reference, Sumner's description of monetary offset is laid out in the paper linked in this post. Basically, it says if fiscal policy increases AD, this will raise inflation which will cause the central bank to react to bring inflation back to target. In the long run, the AD boost is offset by monetary policy.

In the cases we are looking at (EU member nations), each has the same monetary authority (the ECB) so the monetary policy is an EU-wide aggregate while the fiscal policy is local to the member nations. While Sumner's model has a plausible mechanism for the ECB to offset the average fall in AD due to austerity, it wouldn't offset the relative fall between nations. The nations engaging in more austerity will be worse off than those engaging in less. This still makes Paul Krugman's point that austerity is bad.

On a more fundamental level, you'd think you'd want to control for monetary policy which means you'd want to have the same monetary policy in the sample population. If having the same monetary policy makes the effect you want to see unobservable, then how do you know the offset exists in the first place? A mysterious force counteracting another force resulting in no effect? It's like saying my glass of whisky here is experiencing a force to the right that is always counteracted by a force to the left [1] -- how did I ever know about either? 

Speaking of forces, I'd like to bring up the information transfer picture. It's actually a picture:

Depending on the current location of the economy in the space of monetary base (MB) and NGDP, the direction of the "force" due to fiscal shifts and monetary shifts range from almost parallel (a quantity theory economy) to orthogonal (a liquidity trap economy). In the former, you can have almost complete monetary offset. In the latter, monetary policy isn't even pushing in the right direction (it has no projection along the NGDP axis). This goes back to Krugman's sample and Sadowski's "unskewed" version: if the countries are all in a liquidity trap, then you're going to see the effects of austerity. If you're not, then monetary policy would have offset the fall in AD from the recession in the first place an no austerity would've been necessary (and if it had been tried it would have been offset).

[1] Well, it actually is from air pressure -- but we know about that from different experiments. Which is kind of my point.