Causal Inference (Rubin)

Causal inference under the Rubin potential-outcomes framework defines effects counterfactually: the potential outcomes of an individual under treatment $T=1$ and control $T=0$ are $Y(1)$ and $Y(0)$, and the average treatment effect is

$\text{ATE} = \mathbb{E}[Y(1) - Y(0)]$;

observed data reveal only one potential outcome per individual, so estimating the ATE requires an ignorability (no unmeasured confounding) assumption.

impact evaluation when online experiments are infeasible or already over, ex-post attribution for recommendation systems and growth strategies; interviews typically probe confounders vs colliders, the full propensity-score matching (PSM) pipeline, and classic correlation ≠ causation examples.

correlation is not causation — a confounder $X$ affecting both $T$ and $Y$ manufactures spurious correlation, while conditioning on a collider introduces selection bias (Berkson's paradox); the propensity score $e(x) = P(T=1 \mid x)$ compresses high-dimensional covariates into a one-dimensional balancing score, and PSM proceeds as: ① fit $e(x)$ by logistic regression ② match or weight on the score ③ estimate $\hat{\text{ATE}} = \bar{Y}_1 - \bar{Y}_0$ on matched samples ④ check balance; unlike direct regression on $X$, it is more robust to model misspecification when covariates are high-dimensional and overlap is limited.

Define ATE under potential outcomes. Why can't observed data estimate it directly?

Confounders vs colliders? Why does conditioning on a collider introduce bias?

Role of the propensity score and the full four-step PSM pipeline?

Give a correlation ≠ causation example and state the ignorability assumption.

PSM vs direct regression adjustment: pros and cons? How to run balance checks?