And I started having a lot of concerns with a multiplier estimate that I previously felt fine about (with the exception that it was averaged over a long time period and therefore was not an estimate of what we care about most: the multiplier in a recession). Despite all that, I always appreciated the identification strategy. Any empirical person can sympathize with a good, clean identification strategy.
Now I'm not nearly so sure. Military spending is not random. It's highly correlated with expectations about future output. Either you are responding to a threat to your output (or an ally's output), or you're an imperialist and you are responding to the prospect of getting more output.
I think this probably matters more than I had ever considered before. What I used to think was a decent instrument is, I am now thinking, a very, very bad instrument. Imagine what the second half of the twentieth century would be like if we let Germany and Japan be and normalized relations with them after they fought their fight. Forget the Holocaust and the racism for a minute. Think about a world where we have normalized relations with the Nazis, with Vichy France, and with a deteriorated (if not occupied) Britain. The world would be a very different place. God knows what the international monetary system would look like.
Anyway, these are the relevant counterfactuals and the output expectations given the decision not to go to war. It's precisely because of counterfactuals like this that there is such a strong correlation between military action and expectations about future output.
But that is really bad news for an attempt to use military spending as an instrument.
I feel like I should write these thoughts up in more detail.