Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 221 / 1 / a / Solution

Causal identification means that $\mathbb{E}[Y(a_1,a_2)]$ is uniquely determined by the observed joint distribution of $(A_1,X,A_2,Y)$ under the causal assumptions. Equivalently, it admits an identifying formula containing only observed-data probabilities and conditional expectations.

The G-computation formula for this two-stage treatment isThe first factor is the observed mean outcome after the specified treatment history and intermediate value; the second averages over the intermediate-variable distribution generated after the first treatment.