Some Properties of Tests for Possibly Unidentified Parameters

Giovanni Forchini

No 21/05, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: 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 a < 1/2 concerning possibly unidentified parameters have type II error probability that can be as large as 1 - a.

Keywords: Similar tests; consistent tests; weak instruments; identification (search for similar items in EconPapers)
JEL-codes: C12 C30 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2005-09
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