STICERD Econometrics Seminar Series
Theory of Weak Identification in Semiparametric Models
Testuya Kaji (University of Chicago)
Thursday 21 March 2019 14:00 - 15:30
Due to the onging coronavirus outbreak, many of our seminars and public events this year will continue as online seminars. Please check our website listings and Twitter feed @STICERD_LSE for updates.
About this event
We provide general formulation of weak identiﬁcation in semiparametric models and a novel eﬃciency concept. Weak identiﬁcation occurs when a parameter is weakly regular, i.e., when it depends on the score asymptotically. When this happens, consistent or equivariant estimation is shown to be impossible. We then show that behind every weakly regular parameter there exists an underlying parameter that is regular and fully characterizes the weakly regular parameter. While this parameter is not unique, concepts of suﬃciency and minimality help pin down the desirable choice. If the estimation of minimal suﬃcient underlying parameters is ineﬃcient, it introduces noise in the corresponding estimation of weakly regular parameters, whence we can improve the estimators by local asymptotic Rao-Blackwellization. We call an estimator weakly eﬃcient if it attains an asymptotic distribution that does not admit such improvement. We demonstrate in heteroskedastic linear IV models that popular estimators can be improved under some conditions.
STICERD Econometrics seminars are held on Thursdays in term time at 14.00-15.30, ONLINE, unless specified otherwise.
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