Weak Instrument Robust Simultaneous Confidence Bands for Impulse Response Functions

Daniel Lewis and Yatheesan Selvakumar

No 22124, CEPR Discussion Papers from Centre for Economic Policy Research

Abstract: Empirical researchers frequently make statements about the impacts of macroeconomic shocks at multiple horizons that require confidence bands that are simultaneously valid across those horizons, not just pointwise (for a single horizon). Increasing evidence suggests that available macroeconomic instruments are typically weak. We show that commonly-used simultaneous bands under strong identification can readily be adapted to be robust to weak instruments based on the Anderson and Rubin (1949) statistic. Our proposed sup-AR band is efficient amongst bands that control worst-case coverage. All robust bands considered are equivalent to their Wald counterparts under strong identification, at least asymptotically and under local alternatives. A simulation study demonstrates the advantages of the bands over the current default of projection methods. Simultaneously-valid robust inference continues to deliver economically meaningful conclusions in most applications considered; validity guarantees come at surprisingly low cost.

Keywords: Simultaneous inference; Confidence bands; Impulse response functions; Weak instruments; Robust inference (search for similar items in EconPapers)
JEL-codes: C32 C36 E32 E52 (search for similar items in EconPapers)
Date: 2026-11
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