[MUSIC].
In other modules we've talked about things like regression analysis and experiments to
learn about causality.
Why don't we just stop there, why isn't that all we need to know?
Well, experiments require treatments to be randomly assigned to units, that's often not
the case.
Regression analysis requires us to measure every possible confounder, that's often impossible.
So what do we do if we can do an experiment and can't use regression analysis?
Next, we're going to talk about something called instrumental variables analysis.
It's one of the oldest and most important ways for learning about causality using observational
data.
Now it's pretty complicated so pay really close attention.
There are six steps involved in doing instrumental variables analysis.
Step one, we observe a variable, called the instrument, that is correlated with the outcome
variable.
So remember we've got our outcome variable: the variable we are trying to affect.
We've got our treatment variable: the variable that we are interested in learning the effect
of the treatment on the outcome.
Now we have a third variable called the instrument, and when we look at our data it seems to be
that the instrument is correlated with the outcome, so units that have higher outcome
levels of the outcome variable tend to have higher levels of the instrument for example,
or maybe it's negatively correlated, units with higher values of the outcome variable
tend to have negative values of the instrument.
Step two, we assume that the instrument does not have a causal effect on the outcome variable,
so the correlation that we see between the instrument and the outcome is not because
the instrument has a causal effect on the outcome variable.
Instead, that correlation is picking up the effect of some confounding variable.
Step three, we assume that the instrument does have a causal effect on the treatment
variable.
So in step two, we assume the instrument does not have a causal effect on the outcome but
it does have a causal effect on the treatment.
Step four, we assume that the instrument is randomly assigned to units or is as-if randomly
assigned.
Step five, because of step four, the causal effect of the instrument on the treatment
variable is their correlation in the data.
So, here we're thinking of a new randomized experiment where we randomly assign the instrument
to people and I want to know what's the causal effect of the instrument on the treatment
variable.
So because I randomly assigned it, I know that whatever correlation I see between the
instrument and the treatment in the data is the causal effect of the instrument on the
treatment.
Step six, since the instrument is randomly assigned by step four, it is not correlated
with any other possible confounder except for the treatment.
So where does that leave us?
We've got this variable called the instrument that's correlated with the outcome.
The instrument doesn't have a causal effect on the outcome, so this correlation is not
necessarily picking a causal effect of the instrument.
It's got to be picking up the causal effect of a confounder.
The instrument does have a causal effect on the treatment, so we might be picking up the
causal effect of the treatment on the outcome in this correlation here, but it could be
something else.
But now the instrument's randomly assigned and because of that it can't be correlated
with any other confounders except the treatment.
So we've ruled out all possible explanations for the correlation between the instrument
and the outcome except one: that there is a causal effect of the treatment on the outcome
and that's what we are trying to get at, that is the essence of instrumental variables analysis.
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