# Dangling epsilons

Whenever I look at an estimation equation like this:

from this paper, I wonder what’s in that dangling epsilon term. In this equation we have Y’s on the left hand side. And I think to myself, “what kinds of things produce Y’s (or changes in Y’s)”. Now, Y is GDP and from my intro macro class I remember things like K’s and L’s produce Y’s. So given there’s no L’s and K’s in the equation, they must be in the dangling epsilon.

Changes in labor and capital are in the error term, but this is only a problem if changes in these factors of production are correlated with the other variables on the right hand side that aren’t in the error term.

Ah-oh.

It seems to me changes in labor and capital are correlated with changes in government expenditures (and military expenditures in particular… after all, the military is the worlds biggest employer). So while this paper claims to show the effect of military expenditures on output, it really shows that military expenditures create jobs and attract capital (they have an IV but as far as I can tell it doesn’t address this issue).

But can we salvage the overall message of the paper? Isn’t creating jobs and attracting capital exactly what we’re trying to do with fiscal stimulus? Yes, but not if it means that labor and capital is coming from other States. GDP is increasing in the States that have more military expenditures but is necessarily decreasing in the States that are losing workers and capital. Because these two effects cancel each other out, the “true” fiscal multiplier is less than the 1.5 estimated by this paper.

## 5 thoughts on “Dangling epsilons”

1. JZing says:

Equation (1) is in per-capita terms, so the estimate will be biased upwards if the laborers attracted by government military spending exhibit above-average productivity.

2. theobot1000 says:

Nice catch. This is why I like your ‘blog- simple, intuitive, good economics. The underlying problem is simple- an undergraduate can spot it. A good reminder that getting the really basic stuff right still matters, irrespective of the level of mathematical sophistication of our models or empirical set-ups.

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