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Since Interest_in_Acme is unobservable, the average causal effect of Loyalty Club Membership on Spend is unidentifiable. However, there is an important exception to that rule, that is if Interest_in_A …

DAG 1: In the first case, you rely on a very special case where the average causal effect (ACE) can be estimated. … The $C \rightarrow E1$ in the second DAG doesn't mean much. In our intervention (on both exposures), we are setting both $E1$ and $C$. …

There are two valid sets to close the backdoor paths $\{Z_4, Z_1\}$ and $\{Z_2, Z_1\}$ To understand why, I will walk through my thought process. First, $Z_1$ requires being conditioned on, since it …

we can also replace the direct $Y \rightarrow R_Y$ instead with a unobserved variable $U$ linking $Y$ and $R_Y$ I highly recommend the below source for the application of missing data in the causal DAG …

So, I take the perspective that we should phrase the assumptions like, "exchangeability with positivity". My reasoning follows a similar line to what you state above: exchangeability is only well-defi …