Estimation of Average Treatment Effects With Misclassification

This paper considers identification and estimation of the marginal effect of a mismeasured binary regressor in a nonparametric regression, or the conditional average effect of a binary treatment or policy on some outcome where treatment may be misclassified. Misclassification probabilities and the true probability of treatment are also nonparametrically 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. The identifying assumption is existence of a variable that affects the decision to treat (the binary regressor) and satisfies some conditional independence assumptions. This variable could be an instrument or a second mismeasure of treatment. Estimation is either ordinary GMM or a proposed local GMM, which can be used generally to nonparametrically estimate functions based on conditional moment restrictions. An empirical application estimating returns to schooling is provided.