Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/211095
Authors: 
Bertanha, Marinho
Moreira, Marcelo J.
Year of Publication: 
2019
Series/Report no.: 
cemmap working paper No. CWP02/19
Abstract: 
This paper studies models in which hypothesis tests have trivial power, that is, power smaller than size. This testing impossibility, or impossibility type A, arises when any alternative is not distinguishable from the null. We also study settings where it is impossible to have almost surely bounded confidence sets for a parameter of interest. This second type of impossibility (type B) occurs under a condition weaker than the condition for type A impossibility: the parameter of interest must be nearly unidentifi ed. Our theoretical framework connects many existing publications on impossible inference that rely on different notions of topologies to show models are not distinguishable or nearly unidentifi ed. We also derive both types of impossibility using the weak topology induced by convergence in distribution. Impossibility in the weak topology is often easier to prove, it is applicable for many widely-used tests, and it is useful for robust hypothesis testing. We conclude by demonstrating impossible inference in multiple economic applications of models with discontinuity and time-series models.
Subjects: 
hypothesis tests
confidence intervals
weak identification
regression discontinuity
JEL: 
C12
C14
C31
Document Type: 
Working Paper

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