in addition to the three core instrumental variables assumptions,
relevance exclusion and exogeneity we're gonna make one extra assumption,
that there are no defiers in the population.
So among all the four logically possible kinds people, one of them
just doesn't exist, there just aren't any defiers.
Everyone is either an always taker, never taker or a compiler, nobody
is a defier.
So, this is an assumption, in some cases it might hold, in some
cases it might not.
What are some cases where it might hold?
Well randomized experiments where the treatment is only available
if you're assigned to receive treatment is a very credible case
where the no defiiers assumption holds.
So what do I mean?
Well suppose that a new drug is invented and we're doing an experiment
to see what the effects of
this new drug are.
So we're gonna randomly assign some people to receive the new drug
and some people to not.
If you're 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 are 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 are
assigned to get treated, they take the drug home and they actually
do take it.
So is a case 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 monitosity 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.
going to take people who would have receive treatment
regardless and then change their option and say well now that I'm
assigned to receive treatment I'm not going 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 are not going to say the cost is lower I'm gonna stop
doing it even though I was before when the cost was higher.
So in more concrete example, let's look at a situation where some
researchers wanted to look at the effect of using mosquitoes bed
nets on whether people get malaria in a developing country.
So what they did is randomly assign households to either 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 wouldn't show up to 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 a free bed net, and throw it in the corner, and
not use it or then 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 a bed net
a free bed net from the 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 they are assigned to get treatment,
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 no defiers assumption makes sense.
Now in a later 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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