I read from the following slides on observational studies, pg. 16, Observational Studies, Keio,
that given:
$$ ATE ≡ E[Y_i(1) − Y_i(0)] $$
They pose the following question: Can we identify the $ATE$ when $D_i$ is not randomized? Here, $D_i \in \{0,1\}$ is the treatment assignment variable.
I am wondering what it means by identification in this context. I understand generally that identification in models refers to the fact that the data alludes to only a single set of parameters, which something like a mixture model does not adhere to. In the context above, if $D_i$ is not randomized, what will the "multiple" sets of parameters referring to the same data be?