Binary misclassification and identification in regression models

We study a regression model with a binary explanatory variable that is subject to misclassification errors. The regression coefficient is then only partially identified. We derive several results that relate different assumptions about the misclassification probabilities and the conditional variances to the size of the identified set.

► The coefficient of a binary misclassified regressor is partially identified. ► Restricting the misclassification probability reduces the size of the identified set. ► With symmetric misclassification and homoscedasticity the coefficient is identified.