[MUSIC] Let's look at the results.
First, Angrist is going to split his analysis by Whites, with the results up here, and Non-Whites,
with the results down here.
Next he's going to look at three parts of your life.
The year immediately after you applied, which he labels During Service, then Transition
Years, few years later, and then finally after you've left the military if you joined right
here, which he calls After Service.
Furthermore, he's going to look at two different outcome variables: How much money you actually
make, which we saw in the previous graph, which he labels Earnings, and then whether
you are employed or not, which he labels Employment.
So finally he's going to look at five different ways of computing the effect of military service
on your earnings or whether you're employed, which are given in each of these five columns.
We are going to ignore these two columns here.
So in the first column he labels the Difference in Means.
This is what we saw in the previous graph.
This is just you take your two groups of people, for Whites who applied in 1982, you've got
two groups - the ones who enlisted in the military and the ones who didn't, and then
you look at the earnings of those two groups, take the difference, that's what you've got
here.
So here we see exactly what we saw on the previous graph: people who enlisted in the
military make more money.
The difference is positive.
So after service they make about $1200 more than people who didn't enlist in the military.
Same thing is true for non-whites, although they make significantly more compared to whites
than if they join the military, so about $2500 more after they've left the service.
So that's just the difference in means, and we already know that we might be worried about
the selection problem and these are not actually causal effects.
So following Angrist's identification strategy, he's going to use matching or regression to
control for other variables that might affect your earnings.
So let's see what he gets when he does that.
Here in the first column he's got the matching estimates.
And in the second - in the third column, he's got the regression estimates.
So now we see that after service we actually get a negative effect, so actually enlisting
in the military hurts your lifetime earnings, the complete opposite thing we see if we just
do the raw difference in means comparison.
And the same thing is true for the Transition Years, and During Service you make a little
bit more - these are for Whites.
For non-Whites however, we still see positive effects during service, we get a large $2100
effect.
For Transition Years about a $1000 effect, and then After Service, about $800 or $1000.
Now the reason these two columns are different is that they're both controlling for variables
in certain ways, but they are estimating slightly different average causal effects.
So we are getting a little different numbers, but there both have the same interpretation.
That these are the causal effects under the unconfoundedness assumption, whereas these
numbers are not causal.
So the main conclusion from just looking at these numbers is that joining the military
hurts your lifetime earnings for whites by this much, and for non-whites it helps their
lifetime earnings by this much, by about $1000 after service.
So one final thing before walking away and saying that we're done and we know what the
causal effects are, let's just double check and make sure that these estimates are actually
statistically significant, that we actually have a large enough sample size to conclude
that these are real effects.
So to do that, we're going to look at the confidence interval.
So let's look at the confidence interval for just this number here: -$197.20.
So this here, 70.5, is the estimated standard error, so we can use that to construct a 95%
confidence interval, which I've drawn right here.
Take our point estimate $197, minus 1.96 times the standard error, 70.5, then this upper
bound is the same thing except we add 1.96 times 70.5.
Doing the math we get this confidence interval, -$335 to - $59.
This interval does not contain zero, so we conclude that this effect, -$197, is actually
real.
So those are the main findings of Angrist’s study on the effect of military service on
lifetime earnings.
[MUSIC].