Misclassified Regressors in Binary Choice Models

This paper examines the effect of mismeasured discrete regressors in binary choice models. I examine plausible scenarios for the nature of the measurement error and discuss identifiability and estimation under various sets of semiparametric assumptions. Under a minimal set of assumptions, the model is only partially identified and I derive bounds for some of the parameters of interest. If the probability of misclassification is conditionally independent of the other regressors, the model is point identified and I propose a n consistent, asymptotically normal semiparametric two-step estimator under this set of conditions. If, however, the misclassification rates are not independent of the other regressors, further information is required. When an additional measurement on the mismeasured regressor is available I develop a n consistent, asymptotically normal estimator using the method of sieves without specifying the relationship between the probability of misclassification and the other explanatory variables. Monte Carlo simulations suggest good finite sample properties of the estimators and the method is illustrated with a study on the effect of unionization on the receipt of health benefits using data from the Current Population Survey. I would like to thank Han Hong, Bo Honoré and Elie Tamer for their tireless encouragement and advice. I have also benefited from discussions with Xiaohong Chen, Henry Farber and Ernst Schaumburg. I would also like to thank the participants in the Princeton Microeconometrics Reading Group