in addition to the three core instrumental variables assumptions,
relevance exclusion and [UNKNOWN], we are gonna make one extra assumption
that there are no defiers in the population.
So among all the four logically
possible kinds of people, one of them just doesn't exist, they just
aren't any defiers.
Everyone is either an always taker, never taker or a complier, nobody
is a defier.
So this is an assumption, in some cases it might hold in some cases
it might not.
What if some cases where it might hold?
Well, randomized experiment where the treatment is only available if you
are assigned to receive treatment is a very credible case where the
no defiers assumption holds.
So what do I mean? Well suppose that a new drug is invented and
we are doing an experiment to see what the effects
of this new drug are.
So we are gonna randomly assign some people to receive the new drug
and some people to not.
If you are assigned to not receive the drug then there is no way
you can possibly get the drug and take it.
So it's simply impossible for you to be a defier, because a
defier is somebody who when they assigned not to receive treatment
somehow receives treatment anyway.
That's just not possible in this case.
Now it's also not possible by the way to be an always taker, because
an always taker is somebody who always gets the treatment regardless
of whether they are assigned to or not.
Saying again if you're not assigned treatment then you can't actually
receive the drug.
Now by the way, the reason we could still have non-compliance here
is that even though you're assigned to receive the drug, you might
take it home, put it on your night stand but you might not actually
take it.
So that's somebody
who doesn't comply with their treatment.
So we can still have never takers, these are people who are assigned
to receive treatment, they get the drug, they bring it home but
they don't physically take it and compliers, people who when they're
assigned to get treated, they take the drug home and they actually
do take it.
So this is a case where the No defiers assumption makes sense.
But in general we don't have to actually rule out always takers
like happened in the previous example.
So to see this, let's look at an equivalent way of seeing the no
defier assumption.
It's called the Monotonicity Assumption.
Now this assumption says that treatment assignment will only push
people into receiving treatment.
That is, treatment assignment just makes people more likely to receive
treatment, it does not make them less likely to receive treatment.
So it's never
going to take people who would have received treatment
regardless and then change their opinion and say, well now that
I'm assigned to receive treatment, I'm not going to actually get
treated, that's what a defier does.
So this is a different way of viewing the no defiers assumption
and it's equivalent.
So one situation where this makes sense is when the instrument lowers
the cost of getting treatment.
So typically we think that if you lower the cost of doing something
then people are going to be more likely to do it.
They're not gonna say now that the cost is lower I'm gonna stop
doing it even though I was before when the cost was higher.
So a more concrete example let's look at a situation where researchers
wanted to look at the effect of using mosquito bed nets on whether
people get malaria in a developing country.
So what they did is randomly assign households to either get a free
bed net
or not, so they were gonna show up at some people's households
and give them a free bed net.
Some other people, they just went and showed at their house.
Now they can't force people to actually use the bed net, to hang
it above their bed and sleep under it, but they can give it to them,
so some people may not comply with treatment.
They may receive the free bed net and throw them in a corner and
not use it or maybe they'll sell it to somebody and spend the money
on something else.
So those people don't comply.
But it's very unlikely that when a household receives bed nets,
free bed nets from experimenters that they then go around their
house and take down any bed nets that they were using before, that's
exactly what a defier does.
A defier is someone who when there assigned to get treatment, so
they get a free bed net they don't use it.
But when they don't get a free bed net so when the experimenter
doesn't show up at their door, they actually do have bed nets hanging
in their beds and they used them.
So in
this case probably there aren't any defiers in the population
and so the notifiers assumption makes sense.
Now in a layer module we'll see exactly how we use the no defiers
assumption, to learn the local average treatment effect from our
data.
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