Fundamental Problem of Causal Inference

Holland’s (1986) name for the core obstacle: it is impossible to observe both $Y_t(u)$ and $Y_c(u)$ on the same unit, so the individual-level causal effect can never be directly observed. Causal inference is therefore an exercise in substituting something observable for the unobservable.

Holland frames two responses:

• Scientific solution — invoke homogeneity/invariance assumptions (e.g. the same unit measured at another time stands in for the counterfactual).
• Statistical solution — give up on the individual effect and estimate the average causal effect $\tau =E(Y_t-Y_c)$ over a population, using design (especially Randomization) to make $E(Y_t)$ and $E(Y_c)$ recoverable from different units.

Relied on by

Every identification strategy is a particular way of solving this problem.

Referenced by

Holland1986-StatisticsAndCausalInference (origin / names it); Rubin1978-BayesianCausalEffects and Rubin1980-RandomizationAnalysis develop the same obstacle as a missing-data problem.