%0 Journal Article %A Forchini, Giovanni %D 2017 %T Some properties of tests for possibly unidentified parameters %U https://bridges.monash.edu/articles/journal_contribution/Some_properties_of_tests_for_possibly_unidentified_parameters/5090212 %R 10.4225/03/5938aaa247730 %2 https://ndownloader.figshare.com/files/8628169 %K Similar tests %K Consistent tests %K Identification %K 2005 %K monash:7437 %K Weak instruments %K 1959.1/42244 %X 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−. %I Monash University