Impossible inference in econometrics: Theory and applications

Marinho Bertanha and Marcelo Moreira

Journal of Econometrics, 2020, vol. 218, issue 2, 247-270

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 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.

Keywords: Hypothesis tests; Confidence intervals; Weak identification; Regression discontinuity (search for similar items in EconPapers)
JEL-codes: C12 C14 C31 (search for similar items in EconPapers)
Date: 2020
References: Add references at CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304407620301366
Full text for ScienceDirect subscribers only

Related works:
Working Paper: Impossible Inference in Econometrics: Theory and Applications (2020)
Working Paper: Impossible inference in econometrics: theory and applications (2019)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:218:y:2020:i:2:p:247-270

DOI: 10.1016/j.jeconom.2020.04.016

Access Statistics for this article

Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

More articles in Journal of Econometrics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().