Weak Instrument Bias in Impulse Response Estimators

Daniel Lewis and Karel Mertens

No 20990, CEPR Discussion Papers from Centre for Economic Policy Research

Abstract: We approximate the finite-sample distribution of impulse response function (IRF) estimators that are just-identified with a weak instrument using the conventional local-to-zero asymptotic framework. Since the distribution lacks a mean, we assess bias using the mode and conclude that researchers prioritizing robustness against weak instrument bias should favor vector autoregressions (VARs) over local projections (LPs). Existing testing procedures are ill-suited for assessing weak instrument bias in IRF estimates, and we propose a novel simple test based on the usual first-stage F-statistic. We investigate instrument strength in several applications from the literature, and discuss to what extent structural parameters must be restricted ex-ante to reject meaningful bias due to weak identification.

Keywords: Local projections; Vector autoregressions; Instrumental variables; Weak instruments; Impulse responses; dynamic causal effects (search for similar items in EconPapers)
JEL-codes: C32 C36 (search for similar items in EconPapers)
Date: 2026-01
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