Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 221 / 2 / i / Solution

The no unmeasured confounding assumption is the conditional exchangeability statementAlso assume consistency of potential outcomes, no interference between units, and positivity in causal inference, in particular $\mathbb{P}(A=0\mid X)>0$ on the covariate support of treated units. ThenThe first treated potential outcome equals the observed treated mean by consistency. Moreover,Subtracting proves the displayed identification formula for the average treatment effect on the treated.