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Research Publications

Working papers

Working papers from the Federal Reserve Bank of Dallas are preliminary drafts circulated for professional comment.

2026

No. 2601

Weak Instrument Bias in Impulse Response Estimators

Daniel J. Lewis and Karel Mertens

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.

DOI: https://doi.org/10.24149/wp2601

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