Some properties of tests for possibly unidentified parameters
journal contributionposted on 08.06.2017 by Forchini, Giovanni
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It is well known that confidence intervals for weakly identified parameters are unbounded with positive probability (e.g. Dufour, Econometrica 65, pp. 1365-1387 and Staiger and Stock, Econometrica 65, pp. 557-586), and that the asymptotic risk of their estimators is unbounded (Pötscher, Econometrica 70, pp.1035-1065). In this note we extend these “impossibility results” and show that uniformly consistent tests for weakly identified parameters do not exist. We also show that all similar tests of size 1/2α< concerning possibly unidentified parameters have type II error probability that can be as large as 1α−.