Impossible inference in econometrics: Theory and applications

By Marinho Bertanha, Marcelo J. Moreira. 2016

29 citations recorded by the source corpus.

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 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 unidentified. 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 unidentified. 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.

Subfields: Economics and Econometrics, Statistics and Probability

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Citations in the corpus

The hardness of conditional independence testing and the generalised covariance measure (2018, background): “On the other hand, it is known that if a problem is untestable, the convex closure of the null must contain the alternative [31], [8], Theorem 5 and Corollary 1, resp.”
Testing continuity of a density via g-order statistics in the regression discontinuity design (2018, result): “This framework is similar to the one in Canay and Kamat (2018), who in turn exploit results from Canay, Romano and Shaikh (2017). It is worth noting that the hypothesis we test, the test statistic, the critical value, and most of the formal arguments are different from those in Canay and Kamat (2018”