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.