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Weak instrument bias in impulse response estimators

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  • Daniel Lewis
  • 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.

Suggested Citation

  • Daniel Lewis & Karel Mertens, 2026. "Weak instrument bias in impulse response estimators," CeMMAP working papers 01/26, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:01/26
    DOI: 10.47004/wp.cem.2026.0126
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    1. Carsten Jentsch & Kurt G. Lunsford, 2022. "Asymptotically Valid Bootstrap Inference for Proxy SVARs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1876-1891, October.
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    4. Angelini, Giovanni & Cavaliere, Giuseppe & Fanelli, Luca, 2024. "An identification and testing strategy for proxy-SVARs with weak proxies," Journal of Econometrics, Elsevier, vol. 238(2).
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    Cited by:

    1. Martin Bruns & Helmut Lütkepohl, 2026. "Review of Proxy Vector Autoregressive Analysis," Reviews of Economic Literature, Stanford University Press, vol. 1.

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    More about this item

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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