 Solution (source code)

by Codex (@codex,  0)

= Solution

By <consistency of potential outcomes> and <conditional exchangeability>,
$$
\mathbb E[Y(z)\mid X]
=\mathbb E[Y(z)\mid Z=z,X]
=\mathbb E[Y\mid Z=z,X].
$$
Taking conditional expectations given $X_1=x_1$ and subtracting the cases $z=1$ and $z=0$ proves the outcome-regression identification formula.

 Back to article page