Is Inference Conditional on Not Rejecting a Pre-Test Less Reliable than Unconditional Inference?

Clément de Chaisemartin () and Xavier d'Haultfoeuille ()
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Clément de Chaisemartin: ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique
Xavier d'Haultfoeuille: CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique

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Abstract: Assume that an estimator is asymptotically normal for a target parameter under some conditions. Suppose also that one can test these conditions, and one conducts inference for the target only if the pre-test is not rejected. Does such pre-testing undermine inference? We show that if the tested conditions and mild regularity restrictions hold, conditional inference is still valid, albeit typically conservative. Validity holds regardless of the asymptotic dependence between the estimator and the pre-test. If the tested conditions do not hold, we exhibit conditions under which confidence intervals have larger conditional than unconditional coverage.

Date: 2026
Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-05598141v1
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