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Can someone please explain how to read the unconfoundedness assumption. I'm unable to understand the symbols specifically the upside down "T".


Generally, that "upside down T" indicates orthogonality or independence (or unconfoundedness?) and I would interpret that notation as saying that the random vector $(Y_i(0), Y_i(1))$ is (conditionally) independent of the random variable $W$ given $X_i$, or more verbosely, conditioned on knowledge of $X_i$. If the random variables are jointly continuous and thus have joint densities, we can write

$$f_{Y_i(0), Y_i(1), W \mid X_i = x}(y_0,y_1, w \mid X_i = x) = f_{Y_i(0), Y_i(1) \mid X_i = x}(y_0,y_1, \mid X_i = x)f_{W \mid X_i = x}(w \mid X _i= x)$$ telling us that the conditional pdf of $Y_i(0), Y_i(1), W$ given $X_i=x$ factors into the product of the conditional pdf of $Y_i(0), Y_i(1)$ given $X_i=x$ and the conditional pdf of $W$ given $X_i=x$ and this factorization holds for all values $x$ that $X_i$ might take on. It is worth keeping in mind that conditional independence does not imply unconditional independence. It is not necessarily the case that $f_{Y_i(0), Y_i(1), W}(y_0,y_1, w)$ factors into the product $f_{Y_i(0), Y_i(1)}(y_0,y_1)f_{W}(w)$.

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