#StackBounty: #experiment-design #causality In an observational study in causal inference, why are the covariates usually assumed to be…

Bounty: 100

Suppose that in an observational study with $N$ units, we have that $X_i$ are our covariates. I have read in several places that in order to calculate an unbiased treatment effect, the $X_i$ are assumed to be iid. I am wondering why this is necessarily the case, and specifically why the independence part is needed. What happens if we do not have:

$$
X_i overset{iid}{sim} F
$$

for some distribution $F$? What if it is the case that there is a dependency structure for $X_i$ and $X_j$?

The unbiased estimation procedure I am referring to is from Rosenbaum 1983. Thank you.


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