Errors-in-Variables Models : A Generalized Functions Approach

Generalized functions are a powerful tool for examining errors-in-variables models, since they extend consideration to wide modelclasses. Schennach (Econometrica, 2007) - (S) applies this approach to prove identification in a general class of models. Here the problems addressed in (S) are revisited because various features of the generalized functions approach need to be clari?ed. The nonparametric identification theorem in (S) applies less generally than claimed (e.g. disallowing functions with fractional power growth) by relying on decomposition of generalized functions into ordinary and singular parts which may not hold. This paper highlights the issues of importance in applying generalized functions and provides the general nonparametric identification result relating it to possibility of estimation.