%0 DATA
%A Giovanni, Forchini
%D 2017
%T Some properties of tests for possibly unidentified parameters
%U https://bridges.monash.edu/articles/Some_properties_of_tests_for_possibly_unidentified_parameters/5090212
%R 10.4225/03/5938aaa247730
%2 https://bridges.monash.edu/ndownloader/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−.