New possibilities in identification of binary choice models with fixed effects

We study the identification of binary choice models with fixed effects. We provide a condition called sign saturation and show that this condition is sufficient for the identification of the model. In particular, we can guarantee identification even when all the regressors are bounded, including multiple discrete regressors. We also show that without this condition, the model is not identified unless the error distribution belongs to a special class. The same sign saturation condition is also essential for identifying the sign of treatment effects. A test is provided to check the sign saturation condition and can be implemented using existing algorithms for the maximum score estimator.