[MUSIC] So far we've been talking about causality pretty informally, but if we're going to get
any quantitative measures of causal effects, we need to know what exactly do we mean by
causal effect?
So what is the causal effect of say, Medicaid on cholesterol, of having Medicaid on cholesterol?
Well, to answer that, think about one specific unit of analysis, namely, you.
Now what you're going to do is write down every single thing that could possibly affect
your cholesterol, including whether you have Medicaid or not.
Now we're going to define the causal effect of having Medicaid on your cholesterol as
the difference in your outcome, namely your cholesterol level, when you have Medicaid
minus when you don't have Medicaid, holding all those other variables constant, holding
all those other things that could possibly affect cholesterol the same.
That's the causal effect of having Medicaid on your cholesterol.
Now there's a few important points about this definition.
The first is it's a unit causal effect.
It's the causal effect for just you.
It's not the causal effect for everyone, not the causal effect for anybody else, just you.
The second important point is that the causal effect is a difference - holding all other
variables equal.
So what that means is that if we change the values of the other variables, and then look
at the same difference, we might get a different causal effect.
And that's called an Interaction.
So for example, the causal effect of having Medicaid may be zero if you have good eating
habits, or it may be positive if you have bad eating habits.
So if you have good eating habits, maybe you're just generally healthy, so it doesn't matter
whether you have health insurance through Medicaid or not.
But if you have bad eating habits, then maybe you are pretty unhealthy and it actually matters
whether you have health insurance, through Medicaid or not.
So that's called an Interaction Effect: the values of the other variables that we hold
fixed may affect the causal effect for you.
Now both of these points - the fact that it's a causal effect for just you, and the fact
that the other variables, the values of them, may interact with your treatment and cause
you to have a different causal effect depending on whether you have good eating habits or
bad eating habits - those both say that there's heterogeneity in causal effects.
So two people who are not identical might have different causal effects.
And moreover, the causal effect for the same person might be different if the other variables
change.
So basically all I'm saying is that people are different, and so their response to treatment
may be different.
Giving the same treatment to different people may cause different things to happen.
Now more abstractly, we envision there being two potential outcomes.
The outcome when you have Medicaid, and the outcome when you don't have Medicaid.
Now, in reality, we will never ever, ever, ever observe both outcomes, and that's just
because you can't simultaneously be on Medicaid and off Medicaid.
So this is sometimes called the Fundamental Problem of Causal Inference, and the reason
it's a problem is because if we did observe both outcomes — your outcome when you have
Medicaid and your outcome when you didn't have Medicaid — then learning causal effects
would be easy.
You just take the difference and that's your causal effect.
But unfortunately, we don't observe both, and that's a big problem.
And figuring out how to solve that is what we'll do in the rest of these modules.
[MUSIC].