Ignorability

Treatment assignment is independent of the Potential-Outcomes, possibly after conditioning on covariates $X$: $\{Y_t,Y_c\}\perp S\mid X$. When it holds, comparing treated and control units (within strata of $X$) identifies the average Causal-Estimand. Randomization guarantees ignorability unconditionally; observational designs must assume it given observed covariates. Strong ignorability (Rosenbaum & Rubin, 1983) is this conditional-independence condition plus Overlap — the pair needed for identification by adjustment.

The assignment-mechanism view that makes this precise is developed in Rubin1977-AssignmentOnCovariate and the Bayesian treatment of Rubin1978-BayesianCausalEffects.

Relied on by

PSM and regression adjustment directly; RCT obtains it by design.

Referenced by

Rubin1977-AssignmentOnCovariate (assignment on observed $X$), Rubin1978-BayesianCausalEffects (ignorable mechanisms), Rubin1974-EstimatingCausalEffects (implicit, nonrandomized case), Holland1986-StatisticsAndCausalInference.

Credibility-revolution pass (selection-on-observables / exogeneity control strategy): AngristKrueger1999-EmpiricalStrategiesLaborEconomics, Meyer1995-NaturalAndQuasiExperiments.

Method-buildout pass (2026-06-17) — the identifying assumption of the PSM literature (Imbens2004-NonparametricATEReview, Imbens2015-MatchingMethodsInPractice, CaliendoKopeinig2008-PSMImplementationGuidance, SmithTodd2005-ReconcilingPSMEvidence); the SCM factor-model rationale (AbadieEtAl2010-SyntheticControlMethods, AbadieEtAl2015-ComparativePoliticsSCM); program-evaluation surveys (AbadieCattaneo2018-EconometricMethodsProgramEvaluation, ImbensWooldridge2009-ProgramEvaluation); and the sequential-ignorability assumptions of mediation (Keele2015-CausalMediationAnalysis, VanderWeele2016-MediationAnalysis).

New-papers pass (2026-07-04): ArkhangelskyImbens2024-FixedEffectsGeneralizedMundlak (group unconfoundedness, strengthened to conditioning on group-level balancing scores).