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 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.
We would like to thank Dan Black, Andreas Hagemann, Gary Solon, Jeff Wooldridge, and seminar participants at the University of Chicago Harris School, the University of Michigan Labor Lunch, Michigan State University, the 2019 Society of Labor Economists meetings, and the Michigan-Michigan State-Western University Labo(u)r Day Conference for helpful comments and suggestions. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.