*Bounty: 100*

*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.