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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). The authors 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, they prove that this condition is testable. They finally show that their strategy can also be applied to the identification of generalized Roy models.
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