Statistics and Causal Inference

Causal Question / Estimand

What can a statistical model legitimately say about causation? The paper defines the unit-level causal effect as $Y_t(u)-Y_c(u)$ and, since that is unobservable, shifts the target to the population-level average causal effect $\tau =E(Y_t-Y_c)$ — the Causal-Estimand.

Identification Strategy

A conceptual paper, not an empirical one. Holland lays out “Rubin’s model” for causal inference (Potential-Outcomes) and argues that causal inference proceeds by solving the Fundamental-Problem-of-Causal-Inference one of two ways: the scientific solution (homogeneity/invariance assumptions substituting a known value for the missing counterfactual) or the statistical solution (use a population and design — especially Randomization — so that $E(Y_t)$ and $E(Y_c)$ are recoverable from different units, via $\tau =E(Y_t)-E(Y_c)$).

Key Assumptions

Potential-Outcomes, Randomization, SUTVA (population-level no-interference, implicit in the statistical solution), Ignorability (what the assignment mechanism $S$ must satisfy for observed group means to identify $\tau$).

Threats to Validity

n/a — theoretical contribution. The paper’s own caution: both solutions rest on untestable assumptions (homogeneity for the scientific route; the assignment mechanism for the statistical route), and conclusions are only as good as those.

Setting / Data

n/a — theoretical. Illustrative examples only (e.g. the light-switch room, a fourth grader’s arithmetic program).

Key Claims

• Coins the term “Rubin’s model” (the Rubin Causal Model) and traces the ideas to Rubin (1974) and back to Fisher.
• States the Fundamental Problem of Causal Inference: $Y_t(u)$ and $Y_c(u)$ cannot both be observed on the same unit, so the unit-level effect is never observed.
• Sharply separates the model for associational inference $(A,Y)$ from the model for causal inference $(S,Y_S)$ — association is “simply descriptive statistics,” causation is not.
• “No causation without manipulation”: only potentially manipulable treatments can be causes; attributes like race or gender cannot be causes in this framework.
• Emphasizes effects of causes over causes of effects as the place where statistics contributes most.

Connections

• Builds on: Rubin1974-EstimatingCausalEffects
• See also: Rubin1977-AssignmentOnCovariate, Rubin1978-BayesianCausalEffects, Rubin1980-RandomizationAnalysis, Foundations

Citation

Holland, P. W. (1986). Statistics and Causal Inference. Journal of the American Statistical Association, 81(396), 945–960. https://www.jstor.org/stable/2289064