Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies
Reference: Rubin, D. B. (1974). Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies. Journal of Educational Psychology 66(5): 688–701. October 1974. APA PsycNet record (DOI 10.1037/h0037350) · ERIC index entry · See also Rubin’s later book with Imbens, Causal Inference for Statistics, Social, and Biomedical Sciences (Cambridge UP 2015) for the canonical textbook statement.
Summary
Rubin’s 1974 paper is the founding statement of the potential-outcomes framework (a.k.a. the Rubin causal model) — the alternative to Pearl’s graphical apparatus that has dominated statistics, econometrics, and biomedical inference. The central move: rather than thinking of causation in terms of mechanisms or structural equations, define a causal effect counterfactually. For each unit i and each treatment level t, posit a potential outcome Yᵢ(t) — the outcome unit i would have exhibited under treatment t. The unit-level causal effect of treatment t versus control c is Yᵢ(t) − Yᵢ(c). The fundamental problem of causal inference is that only one of Yᵢ(t) and Yᵢ(c) is ever observed for any single unit — the other is counterfactual. Causal inference is then statistical inference about the unobserved counterfactual.
The framework’s payoff comes from clarifying the role of randomization. Under random assignment to treatment, observed and counterfactual outcomes are exchangeable: the distribution of Yᵢ(t) in the treated group equals the distribution that would have obtained in the control group had they been treated. The average treatment effect (ATE) E[Y(t) − Y(c)] is then estimable as the simple difference in group means. The framework also clarifies what observational data lets us do: under stated ignorability (a.k.a. conditional exchangeability, no unmeasured confounders) and positivity assumptions, the ATE is identifiable by covariate adjustment — the same calculation Pearl’s backdoor adjustment formula yields, derived from the counterfactual side. Subsequent work (Rosenbaum–Rubin propensity scores 1983, matching, Imbens–Angrist instrumental-variables 1994) builds out the estimation toolbox.
The framework is now the dominant language of causal inference in applied statistics. For CBCL / CIVeX, knowing both languages matters: a CIVeX certificate may be written in either graphical or potential-outcomes notation, and the verifier may need to translate between them. The formal equivalence is established by Pearl–Bareinboim 2009 and Pearl 2010: any non-parametric causal effect expressible in one framework is expressible in the other under translation; the languages differ in ergonomics (graphs make assumptions visually inspectable; potential outcomes make assumptions algebraically inspectable) rather than expressive power. The paper is the place to cite to acknowledge the other half of the causal toolkit.
Key Ideas
- Potential outcomes: for each unit
i and treatment level t, posit Yᵢ(t) — the outcome unit i would exhibit under t. Both Yᵢ(treated) and Yᵢ(control) are well-defined, but only one is observed for any given unit.
- Unit-level causal effect:
Yᵢ(t) − Yᵢ(c). Defined for each unit, even though typically unobservable.
- Fundamental problem of causal inference: only one potential outcome per unit is observable. Causal inference is statistical inference about the unobserved counterfactual.
- SUTVA (Stable Unit-Treatment Value Assumption): implicit in defining
Yᵢ(t) as a function of unit and treatment only — (i) no interference between units, and (ii) no multiple versions of treatment. SUTVA violations (peer effects, network spillovers, treatment heterogeneity) require explicit extension.
- Ignorability / Conditional Exchangeability:
(Y(t), Y(c)) ⫫ T | X — given covariates X, treatment assignment is independent of potential outcomes. The non-graphical statement of “no unmeasured confounders”.
- Positivity / Common Support:
0 < P(T = t | X = x) < 1 for all x in the support. Required for ATE identification — must have some chance of either treatment at every covariate level.
- Randomization: random assignment of
T independent of (Y(t), Y(c)) makes ignorability hold without conditioning. The methodological justification for randomized experiments.
- Average Treatment Effect (ATE):
E[Y(t) − Y(c)]. The standard target estimand. Identifiable under ignorability + positivity by standardization (covariate adjustment), which yields the same formula as Pearl’s backdoor adjustment.
- Successors: propensity score (Rosenbaum–Rubin 1983), matching, instrumental variables (Imbens–Angrist 1994), the Local Average Treatment Effect (LATE), doubly-robust estimation, the entire modern econometric/biostatistical causal-inference toolbox.
Connections
Conceptual Contribution
- Claim: Causal effects can be defined and estimated by positing potential outcomes
Yᵢ(t) for each unit-treatment pair and treating causal inference as statistical inference about unobserved counterfactuals. Random assignment guarantees identifiability of average effects without further assumptions; observational data require ignorability (no unmeasured confounders) and positivity (common support).
- Mechanism: For each unit
i and treatment level t, define Yᵢ(t) as the outcome i would exhibit under t. The fundamental problem: only one Yᵢ(t) is observed per unit. Define the unit-level effect Yᵢ(t) − Yᵢ(c) and population estimands (ATE, ATT). Identify the ATE under random assignment without further assumption; under observational data with measured covariates X, identify under ignorability (Y(t), Y(c)) ⫫ T | X and positivity. Estimate by direct standardization, propensity-score adjustment, matching, or instrumental variables when assumptions fail.
- Concepts introduced/used: Potential Outcomes, Rubin Causal Model, Counterfactual, SUTVA, Ignorability, Positivity, Average Treatment Effect, Propensity Score (later), Instrumental Variable (later), Fundamental Problem of Causal Inference.
- Stance: foundational technical paper.
- Relates to: The complementary framework to Pearl 1995 / <em>Causality</em> 2000 — the same causal effects in different notation. Pearl–Bareinboim 2009 and Pearl 2010 establish formal mappings between the two; ignorability + positivity in the Rubin language correspond to the existence of an admissible covariate set in the Pearl backdoor sense. The languages differ in ergonomics: graphs make assumptions visually inspectable; potential outcomes make assumptions algebraically inspectable and integrate naturally with regression-based estimation. The 1974 paper is the seed; the canonical textbook statement is Imbens–Rubin 2015. For CBCL / CIVeX, the framework provides the other half of the causal toolkit: a CIVeX certificate may state its identification claim in either potential-outcomes or graphical language, and the verifier may need to translate. Knowing both is part of the technical literacy required for serious causal-claim verification. Shpitser–Pearl 2006’s completeness on the graphical side has no equally clean counterpart on the potential-outcomes side — the practical computational ground favours graphs.