Estimation of Average Treatment Effects With Misclassification

This paper provides conditions for identification and estimation of the conditional or unconditional average effect of a binary treatment or policy on a scalar outcome in models where treatment may be misclassified. Misclassification probabilities and the true probability of treatment are also identified. Misclassification occurs when treatment is measured with error, that is, some units are reported to have received treatment when they actually have not, and vice versa. Conditional outcomes, treatment probabilities, and misclassification probabilities are nonparametric. The identifying assumption is the existence of a variable that affects the decision to treat and satisfies some conditional independence assumptions. This variable could be an instrument or a second mismeasure of treatment. Estimation takes the form of either ordinary GMM or a local GMM that is proposed, which can be used generally to nonparametrically estimate functions from conditional moment restrictions