Another look at the identification at infinity of sample selection models

It is often believed that without instrument, endogenous sample selection models are identified only if a covariate with a large support is available (see Chamberlain, 1986, and Lewbel, 2007). We propose a new identification strategy mainly based on the condition that the selection variable becomes independent of the covariates when the outcome, not one of the covariates, tends to infinity. No large support on the covariates is required. Moreover, we prove that this condition is testable. We finally show that our strategy can also be applied to the identification of generalized Roy models.