Robustness of binary choice models to conditional heteroscedasticity

•Probit/Logit MLE with misspecified conditional heteroscedasticity is analyzed.•The MLE's probability limit is a positive scalar multiple of the true parameter.•Bounds are given on the scalar.•Predictions based on the estimator are unaffected by the misspecification.• t-tests can be used inspite of the misspecification.

We show that when the true data generating process of a large class of binary choice models contains conditional heteroscedasticity, predictions based on the misspecified MLE in which conditional heteroscedasticity is ignored, are unaffected by the misspecification.