Propensity Score

The conditional probability of treatment given covariates, $e(X)=\mathrm{Pr}(D=1\mid X)$ (Rosenbaum & Rubin, 1983). Its key property is that it is a balancing score: if treatment is ignorable given $X$, it is also ignorable given the scalar $e(X)$, so conditioning on the propensity score alone removes covariate bias and collapses a high-dimensional matching problem to one dimension. Used via matching, subclassi- fication/blocking, or inverse-probability weighting. It does not weaken the identifying assumptions — it still requires Ignorability and Overlap ($0<e(X)<1$); the score is only known when assignment is controlled, and otherwise must be estimated.

Relied on by

PSM and weighting estimators (selection-on-observables designs); the propensity-score DiD of Abadie2005-SemiparametricDiD.

Referenced by

• CaliendoKopeinig2008-PSMImplementationGuidance, Imbens2015-MatchingMethodsInPractice, Imbens2004-NonparametricATEReview, SmithTodd2005-ReconcilingPSMEvidence
• ArkhangelskyImbens2024-FixedEffectsGeneralizedMundlak (group-level balancing scores generalize the Rosenbaum–Rubin balancing property to grouped data)