This paper shows identification of a semiparametric binary choice model containing an endogenous regressor, when no outside instrumental variable is available. A simple estimator, an easy test for endogeneity, and an empirical application to US migration data are provided.

I propose a new estimator for cross-section semiparametric regressions containing unobserved binary random effects and apply it to alcohol consumption. The random effects (health consciousness) explain a significant proportion of otherwise unexplained variation in alcohol consumption. Education...