Impossible Inference in Econometrics: Theory and Applications

Marinho Bertanha, University of Notre Dame, IN Notre Dame, USA

will give a presentation on

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 in which it is impossible to have almost surely bounded condence 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 unidentied. Our theoretical framework connects many existing publications on impossible inference that rely on dierent notions of topologies to show models are not distinguishable or nearly unidenti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. (with Marcelo J. Moreira)