[MUSIC] So causal effects may differ from person to person because people are different.
What that means is there's a distribution of causal effects in the population.
So some people may have a positive effect, some people may have a negative effect.
Now the best case scenario for learning about causality is that we learn the unit level
causal effects for every single person.
So for example, you go to the doctor you have some problem.
He's got a medication he can give you.
If he knows your unit level effect, he will give you the medication if it's positive,
he won't give it to you if it's negative.
We can make individual treatment decisions perfectly based on everybody's unit level
causal effect.
Now if we knew the distribution of causal effects, meaning we know every causal effect
for everybody, we could learn a bunch of interesting numbers, like the percentage of people who
have positive treatment effect.
That would say how many people benefit from having Medicaid, for example, or how many
people benefit from a particular drug.
Now as I mentioned before, the problem is we fundamentally cannot learn unit level causal
effects because we don't see the same person both having treatment and not having treatment.
So typically, trying to learn the unit level causal effect for everybody is just out of
the question, so we just can't do it.
Now, even learning about the distribution of causal effects - which says maybe we don't
know exactly who has the positive effect, who has the negative effect, but we know that
most people have a positive effect, for example - that's also often too much to ask for, and
very difficult to get.
It can be done, but it typically requires many assumptions and is difficult to do.
So what people often settle for is something called the Average Treatment Effect.
The average treatment effect is simply you take up everybody in the population, all your
people, and you look at their unit level causal effects.
That's a number, you write it down on a list, you do that for everybody and then you just
take the average of all of those numbers.
That's the average effect.
Now, that's sometimes a good summary of the overall effect of treatment, but sometimes
looking at just averages isn't necessarily a good thing.
So for example, here I've got this comic for an app called TornadoGuard, what does this
app do?
Well, it plays a loud alert sound when there is a tornado warning in your area.
Well the average star rating four stars out of five - looks pretty good.
Let's look at the distribution of star ratings.
Well, the first guy says, “Five stars.
Good user interface, many alert choices.”
That's nice.
Second person says, “Five stars.
Runs great, doesn't crash.”
Pretty good.
Third person says, “Five stars.
I like how you can set it to multiple locations.”
Okay.
Fourth person, “One star.
App did not warn me about tornado.”
So in some cases you don't necessarily want to be satisfied with the average.
You want to know things about the distribution or the extremes, the maximum causal effect,
the minimum causal effect.
But those are more difficult to get than the average.
So that's why we are going to start from there.
So let’s think about average treatment effects.
So, say we treat everybody.
We give everybody Medicaid.
Then we're going to observe everybody's outcome under the treatment.
So we observe everybody's cholesterol when they have Medicaid.
Now, the average of everybody's outcome in that case is called the Average Outcome Under
The Policy.
Now suppose we do the opposite, okay.
Here we are just doing a hypothetical to get a better understanding of what this definition
is.
So I suppose that we didn't treat anybody.
We don't give anybody Medicaid, then we observe their outcomes.
We observe cholesterol for everybody, and we just take the average cholesterol.
Well that average is called the Average Outcome Without The Policy, and the average treatment
effect is just the difference between the Average Outcome Under The Policy and the Average
Outcome Without The Policy.
That's it.
That's all it is, and that actually is equivalent to the definition I gave earlier that you
take the individual unit causal effects, and you just write them down for every person
and then you take the average of that.
That also will give you the average treatment effect.
So, let's suppose that larger values are better of the outcome.
So for example, GDP: let's suppose that we want more GDP.Then a typical interpretation
of the average treatment effect is that a positive average treatment effect means that
the policy is good.
It means that on average, the treatment effects increase the outcomes.
Because remember, the average treatment effect is the difference between the average with
the policy, and the average without the policy.
So if that difference is positive, it means the outcomes are larger on average with the
policy than they are without the policy.
So if bigger outcomes are better, then a positive average treatment effect means the public
policy is good.
And conversely, a negative average treatment effect means the treatment is bad.
And a zero or very close to zero average treatment effect means the policy has no effect.
That's the typical interpretation for the average treatment effect.
But remember what I mentioned earlier, it's an average so everyone has a different treatment
effect.
Some people are positive, some people are negative, possibly maybe everyone is positive,
that would be nice.
So these distributional features, we should also keep in mind, as I said, that's difficult
to get, so that's why people often focus on the average treatment effect.
[MUSIC].