New possibilities in identification of binary choice models with fixed effects

We study the identification of binary choice models with fixed effects. We propose a condition called sign saturation and show that this condition is sufficient for identifying the model. In particular, this condition can guarantee identification even when all the regressors are bounded, including multiple discrete regressors. We also establish that without this condition, the model is not identified unless the error distribution belongs to a special class. Moreover, we show that sign saturation is also essential for identifying the sign of treatment effects. Finally, we introduce a measure for sign saturation and develop tools for its estimation and inference.