Correcting for misclassied binary regressors using instrumental variables

Estimators that exploit an instrumental variable to correct for misclassification in a binary regressor typically assume that the misclassification rates are invariant across all values of the instrument. We show that this assumption is invalid in routine empirical settings. We derive a new estimator that is consistent when misclassification rates vary across values of the instrumental variable. In cases where identification is weak, our moments can be combined with bounds to provide a confidence set for the parameter of interest.