3
$\begingroup$

Assume, we have the following:

$Y$- outcome

$D$- exposure

$U$- unobserved confounder

$V$- instrumental variable.

Assume there are no observed confounders.

Can we check the assumption of exclusion restriction by running a regression of $Y$ on $D$ and $V$ and testing if the coefficient associated with $V$ is 0? The rational is all the effects of $V$ on $Y$ has to go through $D$ so once $D$ is controlled, there should be no effect of $V$.

$\endgroup$
3
$\begingroup$

Can we check the assumption of exclusion restriction by running a regression of Y on D and V and testing if the coefficient associated with V is 0?

No, you can't. It's easy to see why visually. Consider the DAG below, representing your set up:

enter image description here

Your proposal is to regress $Y$ on $D$ and $V$ and check if the coefficient of $V$ is zero. But look what happens if you condition $D$:

enter image description here

That is, even though you have blocked the directed path $V \rightarrow D \rightarrow Y$, you now opened the path $V \rightarrow D \leftarrow U \rightarrow Y$ (represented in red)! The treatment, in this case, acts as a collider, and conditioning on it opens the mentioned spurious path.

Thus, we should not expect the regression coefficient of $Y$ on $V$ conditional on $D$ to be zero even if $V$ is a valid instrument.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.