unconfoundedness

Unconfoundedness, also called ignorability, is a foundational assumption in causal inference. In the potential outcomes framework, treatment T is assumed to be independent of the potential outcomes Y(0) and Y(1) conditional on a set of observed covariates X: (Y(0), Y(1)) ⟂ T | X. Under this assumption, causal effects can be identified from observational data by adjusting for X, since the treatment can be regarded as if randomly assigned within strata of X.

Identification and estimands: If unconfoundedness and common support hold (overlap: 0 < P(T=1|X=x) < 1 for all x in the support), the average treatment effect ATE can be identified as E[Y(1) - Y(0)] = E_X [ E(Y | T=1, X) - E(Y | T=0, X) ]. The average treatment effect on the treated (ATT) is E[Y(1) - Y(0) | T=1] = E_X [ E(Y | T=1, X) - E(Y | T=0, X) | T=1 ].

Estimation approaches include regression adjustment, matching on X or on the propensity score e(X) = P(T=1|X), inverse probability weighting, and doubly robust methods. These rely on the unconfoundedness assumption to yield unbiased or consistent estimates of causal effects from observational data.

Limitations: Unconfoundedness is not testable from the data alone and depends on correctly measuring and including all confounders. If important unobserved confounders exist, estimates may be biased. The overlap condition can also fail in practice, limiting identifiability.