[MUSIC] The key idea behind how we use panel data to get at causality was the Common Trends
Assumption.
If there's some unobserved confounder, it can differ in levels across the treatment
group and the control group, but the changes over time have to affect each group the same
on average.
Now, there's one very important, special case of this, and that's called a fixed effect
or an individual effect.
This is a variable that doesn't change over time.
So the idea here is that we can let the value of this unobserved variable be different in
the treatment group and in the control group.
But as long as the changes aren't systematic, which they aren't because by assumption, this
variable isn't changing over time, so the changes are always zero.
That's fine.
That's totally fine.
It doesn't violate the common trends assumption.
So we can allow for these unobserved fixed effects: variables that don't change over
time, but are systematically different across the treatment and control group.
So for example, let's look at the death penalty example.
Suppose that gun ownership wasn't changing over time, there were just some states that
had high gun ownership all the time, and some states that had low gun ownership for every
year, and nothing's changing, it's just the same.
So in this case, suppose that all the states that had the death penalty in 1977 were the
ones that had high gun ownership.
And all the states that didn't have the death penalty in 1977 were the ones that had low
gun ownership.
That's totally fine, because the common trends assumption is still satisfied.
The changes in gun ownership, which are zero - they're not going up, not going down - are
the same across groups, because they are not changing across groups.
So having these unobserved fixed effects is totally fine for panel data.
That's the key strength of why panel data is powerful for getting at causality.
We don't have to observe these unobserved fixed effects.
I don't have to have in my data set a number that tells me exactly how many guns there
are per state.
There's another example: let's think about the effect of being in a union on your wage.
Well, we usually think that people who are in unions might have higher skills overall
than people who aren't in unions.
So you can't just compare the average wage of union members with the average wage of
non-union members because there's this confounding variable: skill.
Skill might be systematically different between union members and non-union members.
So what are you going to do?
Well, if skills don't change over time, or they change in some way that affects union
members and non-union members equally, then we can use panel data to learn about the effect
of union membership on wages.
Now another thing to take way from this example that differs in the death penalty example
is that for the effect of union membership, the treatment status of different units doesn't
all change at the same time.
So for the death penalty example, we went from 1975, where the death penalty was illegal
everywhere, to 1977, where the death penalty was legal in some states.
So at one time period, a bunch of states changed their treatment status, and a bunch of other
states didn't.
Now with unions, some people are going to be joining and leaving the union at every
different time period, so there's no way to cleanly split up your data into “everyone
is in a union in one time period and nobody is in a union in the other time period,”
or something like that.
It's fine.
I can still apply this difference-in-differences style idea to learn about causal effects.
[MUSIC].