[MUSIC] Now we're ready to start talking about the different ways we could actually learn
about causality.
And we're going to start with one of the oldest and best ways of doing it: experiments.
Now remember the definition of a unit level causal effect: it's the difference between
your outcome when you're treated and your outcome when you're not treated, holding all
of the variables fixed.
So the easiest way to learn about unit level causal effects is to find two units who have
every single variable exactly the same, except one of them is treated and one of them is
not treated.
Then you just look at the outcomes for the treated one, the outcome for the non-treated
one, you take the difference and you're done.
That's the idea behind the controlled experiments.
Now these are just the same things you see on TV infomercials where they are testing
paper towels, and they say “Here we have two paper towels.
Identical stains, but this one is our brand, and this one is that other brand, and look
at how better we are.”
That's just a controlled experiment.
So a little more serious example, here I have a picture of a plant growth chamber that they
have in places like the Chicago Botanical Gardens, where they use to do controlled experiments
on plants.
So suppose you want to know the effects of higher CO2 levels on plant growth, for example.
What you can do is you get two of these plant growth chambers, you take two genetically
equivalent plants, put one in one chamber, one in the other.
Then you set all the variables the same in both chambers using this control panel over
here.
You set things like the humidity level, the daylight level, etc., stuff like that, except
one variable you vary: CO2 level.
In one chamber, you put it low, in the other chamber you put it high.
Everything else is the same.
Then you wait for a while and you measure plant growth.
And since the plants are exactly the same and all the variables are the same, any differences
in growth can solely be attributed to differences in C02 levels.
So that's the controlled experiment.
Well, with these kinds of controlled experiments, you can in principle just have two observations:
one that's treated and one's that not treated.
In practice, you may want to observe a little bit more just because there is measurement
error in how you measure the outcomes or the treatment levels, CO2 for example, but as
far as causality is concerned, you only need one unit to be treated and one unit to not
be treated.
Now in social science, controlled experiments are basically impossible, and there are many
reasons for this.
The first being that measuring variables is very difficult in social science.
So there are lots of things like ability and effort and intelligence that are very, very
difficult to measure, and the idea behind a controlled experiment is to get two units
that are exactly the same in all variables.
But if you can't measure every variable, then how do you know whether two units are the
same?
Second, there are many, many, many variables that might matter in a social science setting,
and even if you could measure every one single of them, you probably are not going to be
able to find two people that are exactly identical in every way except for you're going to treat
one and you're not going to treat the other.
It's basically impossible.
And this is unlike in physical science like the plant growth chambers, where it's typically
known that only few variables matter for these things.
So basically controlled experiments are out, so what's the solution?
The solution is to do randomized experiments, which is what we will talk about next time.
[MUSIC].