Correcting for Misclassified 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 this assumption is invalid in routine empirical settings. We derive a new estimator which allows misclassification rates to vary across values of the instrumental variable. Our key identifying assumption, that the sum of misclassification rates remains constant across instrument values, follows from the empirical examples we present. We also show this assumption can be relaxed using moment inequalities that arise from our model. We demonstrate the usefulness of our estimator through Monte Carlo simulations and a re-analysis of the extent to which Medicaid eligibility crowds out other forms of health insurance. Correcting for measurement error substantially reduces estimates of crowd out and the extent to which Medicaid eligibility lowers the share of the uninsured.