# #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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