In the textbook "Causal Inference for Statistics" by Rubin and Imbens, the following argument is made on pg. 39:
"In part of this text we view our sample of size N as a random sample from an infinite super-population. In that case we employ slightly different formulations of the restric- tions on the assignment mechanism. Sampling from the super-population generates a joint sampling distribution on the quadruple of unit-level variables (Yi(0), Yi(1), Wi, Xi), i = 1, . . . , N. More explicitly, we assume the (Yi(0), Yi(1), Wi, Xi) are independently and identically distributed draws from a distribution indexed by a global parameter."
I am wondering why the bolded portion is needed to be assumed. In the context of observational studies what happens if 1) we have dependence, and 2) if the tuple is not jointly identically distributed.
Is this a general assumption that can be relaxed? Where do we really need it? Specifically:
1) What happens if we have dependence?
2) What happens if they are NOT identically distributed?