Weak instrument robustsimultaneous confidence bands for impulse response functions

Daniel Lewis and Yatheesan Selvakumar

No 22/26, CeMMAP working papers from Institute for Fiscal Studies

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 worstcase 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.

Date: 2026-11-03
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Persistent link: https://EconPapers.repec.org/RePEc:azt:cemmap:22/26

DOI: 10.47004/wp.cem.2026.2226

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