Short and Simple Confidence Intervals when the Directions of Some Effects are Known

Philipp Ketz and Adam McCloskey
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Philipp Ketz: PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

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Abstract: We provide adaptive confidence intervals on a parameter of interest in the presence of nuisance parameters when some of the nuisance parameters have known signs. The confidence intervals are adaptive in the sense that they tend to be short at and near the points where the nuisance parameters are equal to zero. We focus our results primarily on the practical problem of inference on a coefficient of interest in the linear regression model when it is unclear whether or not it is necessary to include a subset of control variables whose partial effects on the dependent variable have known directions (signs). Our confidence intervals are trivial to compute and can provide significant length reductions relative to standard confidence intervals in cases for which the control variables do not have large effects. At the same time, they entail minimal length increases at any parameter values. We prove that our confidence intervals are asymptotically valid uniformly over the parameter space and illustrate their length properties in an empirical application to a factorial design field experiment and a Monte Carlo study calibrated to the empirical application.

Keywords: Confidence intervals; Adaptive inference; Uniform inference; Sign restrictions; Boundary problems (search for similar items in EconPapers)
Date: 2023
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Published in Review of Economics and Statistics, 2023, ⟨10.1162/rest_a_01297⟩

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Related works:
Working Paper: Short and Simple Confidence Intervals When the Directions of Some Effects Are Known (2024)
Working Paper: Short and Simple Confidence Intervals When the Directions of Some Effects Are Known (2024)
Working Paper: Short and Simple Confidence Intervals when the Directions of Some Effects are Known (2023)
Working Paper: Short and Simple Confidence Intervals when the Directions of Some Effects are Known (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:pseptp:halshs-03957242

DOI: 10.1162/rest_a_01297

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