Theory of Weak Identification in Semiparametric Models

We provide general formulation of weak identification in semiparametric models and an efficiency concept. Weak occurs when a parameter is weakly regular, that is, it locally homogeneous degree zero. When this happens, consistent or equivariant estimation shown to be impossible. then show there exists underlying regular fully characterizes the parameter. While not unique, concepts sufficiency minimality help pin down desirable one. If minimal sufficient parameters inefficient, introduces noise corresponding parameters, whence we can improve estimators by local asymptotic Rao–Blackwellization. call estimator efficient if does admit such improvement. New are presented linear IV nonlinear regression models. Simulation model demonstrates how 2SLS optimal improved.