[MUSIC] Panel data has a long history, and unfortunately it's just riddled with confusing
terminology, jargon, and concepts.
So let's talk about these.
But before we do that, keep in mind that the main way we use panel data to learn about
causality is the same as we've already discussed before, like with the death penalty example.
That's not going to change, it's just the particular statistical, and technical details,
and jargon that comes up.
So let's move on to this.
Well, there's a bunch of different statistical techniques for actually computing these causal
effects.
One of them is called the Differences-in-Differences Estimator.
It's just what we did in the death penalty example.
Another one's called the Fixed Effects Estimator, and that's just a slightly different way of
implementing these ideas.
Another one is called the First Differences Estimator.
Again, it's just a little bit of a difference in how this statistics works.
Now, another thing you might hear of is called the Random Effects Estimator.
Now this actually is different than the fixed effects estimator, and the first differences
estimator, all these other things that use panel data.
And that's because, for the random effects estimator, it doesn't use the time dimension
of our data in any important way.
In fact, for the random effects estimator, you could throw out all of your data except
for one time period, and you'd still get a correct estimate.
So what's the hitch?
Well, the problem is, the random effects estimator uses the assumption that it's not just changes
in levels of unobserved variables that don't systematically vary across the treatment and
control group, but actually the levels themselves also don't vary systematically across treatment
and control group.
And that was the same assumption we used in doing a randomized experiment, for example.
So the random effects estimator is saying that actually we do have something like a
randomized experiment.
It just so happens that we also have data over time, and it turns out that when you
have data over time, you can get more precise estimates.
So your confidence intervals can be smaller.
So the random effects estimator, as used in econometrics, doesn't use this differences-in-differences
style idea to get identification.
It's more of a randomized experiment thing, so it's really just trying to get more precise
estimates.
So it doesn't use the time dimension.
That's the key difference in econometrics that lays between the random effects estimator
and what we've focused on in talking about panel data.
Now remember, though, that the term random effects and fixed effects actually don't have
a completely agreed upon meaning, so they mean different things to different people.
So you should be careful and always check that whenever you are reading a paper or talking
to somebody that you are both on the same page and you understand what you're talking
about.
Now another thing that can come up in panel data is something called Dynamic Effects.
This is a situation where your outcome variable yesterday affects the value of your outcome
variable today.
So think about unemployment.
Say your outcome variable is whether you're unemployed today or not.
Well, whether you were unemployed yesterday may affect whether you're unemployed today,
for various reasons.
Maybe employers are afraid of hiring people who've been unemployed for a long time, or
maybe your skills actually degrade over time as you're sitting around and not working,
so it makes you less likely to find a job because you actually don't have as many skills
as a few years ago, if you are unemployed for that long.
Now these are also called Lagged Effects, which just mean that the effect of a value
of a variable today lingers around for a while or “lags around.”
So it affects something in the future.
Another jargon you'll hear is that panel data studies are called Short T Studies.
So by that we mean that there aren't many years in the data set, or there aren't that
many time periods.
So capital T is often used to denote the number of time periods in your data.
And usually in a panel data study, there's not that many you say 2 years, 3 years, 4
years maybe 10 years.
So we call this a short T situation or short T study.
This is to contrast panel data studies with Time Series Studies, where we often had data
over many decades, or maybe even centuries.
That's called a Long T Study, where we have data over many, many time periods.
So this is just some extra jargon you'll hear in describing what a study is about.
So keep in mind all of this jargon, it can really be confusing, but the key takeaway
is the difference-in-differences type identification idea.
That's what underlying how panel data can let us learn about causality.
[MUSIC].