Endogenous binary choice models with median restrictions: A comment

Hong and Tamer [Hong, H. and Tamer, E. (2003). Endogenous binary choice model with median restrictions. Economics Letters, 80 219-225] provide a sufficient condition for identification of a binary choice model with endogenous regressors. For a special case of their model, we show that this condition essentially requires that the endogenous regressor is degenerate conditional on the instrument with positive probability. Moreover, under weak assumptions, we show that this condition fails to rule out any possible value for the coefficient on the endogenous regressor.