ON THE COMPLETENESS CONDITION IN NONPARAMETRIC INSTRUMENTAL PROBLEMS

The notion of completeness between two random elements has been considered recently to provide identification in nonparametric instrumental problems. This condition is quite abstract, however, and characterizations have been obtained only in special cases. This paper considers a nonparametric model between the two variables with an additive separability and a large support condition. In this framework, different versions of completeness are obtained, depending on which regularity conditions are imposed. This result allows one to establish identification in an instrumental nonparametric regression with limited endogenous regressor, a case where the control variate approach breaks down.