Working Paper: NBER ID: w15301
Authors: Alberto Abadie; Guido W. Imbens
Abstract: Propensity score matching estimators (Rosenbaum and Rubin, 1983) are widely used in evaluation research to estimate average treatment effects. In this article, we derive the large sample distribution of propensity score matching estimators. Our derivations take into account that the propensity score is itself estimated in a first step, prior to matching. We prove that first step estimation of the propensity score affects the large sample distribution of propensity score matching estimators. Moreover, we derive an adjustment to the large sample variance of propensity score matching estimators that corrects for first step estimation of the propensity score. In spite of the great popularity of propensity score matching estimators, these results were previously unavailable in the literature.
Keywords: No keywords provided
JEL Codes: C13; C14
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Estimator matching on the estimated propensity score (C51) | Bias and coverage rates of confidence intervals (C46) |
| Estimator matching on the true propensity score (C51) | Variances and bias of estimates (C51) |
| Estimation of the propensity score (C51) | Large sample distribution of matching estimators (C51) |
| First-step estimation process (C51) | Variance of matching estimators (C51) |
| Matching on the estimated propensity score (C52) | Asymptotic variance of matching estimators (C51) |
| Using estimated scores (C13) | Properties of matching estimators (C51) |