Errors-in-variables models: a generalized functions approach

Identi…cation in errors-in-variables regression models was recently extended to wide models classes by S. Schennach (Econometrica, 2007) (S) via use of generalized functions. In this paper the problems of nonand semiparametric identi…cation in such models are re-examined. Nonparametric identi…cation holds under weaker assumptions than in (S); the proof here does not rely on decomposition of generalized functions into ordinary and singular parts, which may not hold. Conditions for continuity of the identi…cation mapping are provided and a consistent nonparametric plug-in estimator for regression functions in the L1space constructed. Semiparametric identi…cation via a …nite set of moments is shown to hold for classes of functions that are explicitly The support of the Social Sciences and Humanities Research Council of Canada (SSHRC), the Fonds québecois de la recherche sur la société et la culture (FRQSC) is gratefully acknowledged. The author thanks participants in the Cowles Foundation conference, the UK ESG, CEA 2009 and Stats in the Chateau meetings and P.C.B.Phillips, X. Chen and Denis Nekipelov for illuminating discussions and suggestions. An anonymous referee provided a very thorough report containing many important points and suggestions. The remaining errors are all mine.