Randomized Experiments with Ambiguous Record Linkage

Randomized experiments are often linked to administrative data to measure outcomes, but coarse identifiers can leave multiple administrative records consistent with each experimental unit. We show that unbiased estimation of the sample average treatment effect is possible without resolving these ambiguous links or specifying an outcome model. Our key linkage requirement is that the true administrative outcome is contained among the candidate outcomes for each experimental unit. We characterize the precision cost of linkage ambiguity and study two complementary ways to mitigate it: regression adjustment and reweighting based on observed linkage characteristics. We establish finite-sample and asymptotic properties of these estimators and develop valid randomization-based and large-sample inference.