Misclassification in binary choice models

Bias from misclassification of binary dependent variables can be pronounced. We examine what can be learned from such contaminated data. First, we derive the asymptotic bias in parametric models allowing misclassification to be correlated with observables and unobservables. Simulations and validation data show that the bias formulas are accurate in finite samples and in most situations imply attenuation. Second, we examine the bias in a prototypical application. Erroneously restricting the covariance of misclassification and covariates aggravates the bias for all estimators we examine. Estimators that relax this restriction perform well if a model of misclassification or validation data is available.