8.3 - Identification in Linear Setting

In this part of the Introduction to Causal Inference course, we show that instrumental variables allow us to identify the ATE if we make a linearity assumption. Please post questions in the YouTube comments section.

[michelspeiser]

It would be very useful to insert a concrete example here. What are typical instrumental variables?

[michelspeiser]

In which contexts is linearity a reasonable assumption concerning unobserved confounders?

[michelspeiser]

Can we really insert T_hat as a variable in the causal graph, when it is a deterministic function of Z?

[XplicitProject]

Around minute 9:00, you use the relevance assumption, which says that "Z has a causal effect on T". Can you show how that implies that Cov(T, Z) is not 0? I'm asking because I know there exist non independent random variables whose covariance is null.

[offon]

What happens if the instrument is not independent of confounders? Independence seems like a very strong assumption here.

[Grouahh]

Thanks for the clear explanation Brady.
I have a question regarding the 2SLS estimator. Am I correct to say that because we need to regress T on Z and then Y on T hat, the estimation of delta only depends on the effect on Z through T? If I rephrase, it means that from what I understand, the causal effect we estimate is only the causal effect from T to Y that is also a causal effect from Z to T. Is that right? So, an implication of that is if Z is poorly associated with T, then even though there is a huge causal effect from T to Y, we won't be able to estimate it? And even though Z is a good IV, there is always part of the causal effect from T to Y that is not taken into account (i.e. the part that is not flowing from Z to T). Therefore, in any way the 2SLS is less accurate than the Wald estimator in the binary setting?