Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 221 / 1 / b / vii / Solution

None of the three coefficients has a causal interpretation. The $X_3$ coefficient is unavoidably confounded by unmeasured $U$. Conditioning on the collider $X_3$ opens paths through $U$ for both $X_1$ and $X_2$, so adding all measured regressors does not repair the bias.