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One Instrument to Rule Them All: The Bias and Coverage of Just-ID IV

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  • Joshua Angrist
  • Michal Kolesár

Abstract

We revisit the finite-sample behavior of just-identified instrumental variables (IV) estimators, arguing that in most microeconometric applications, just-identified IV bias is negligible and the usual inference strategies likely reliable. Three widely-cited applications are used to explain why this is so. We then consider pretesting strategies of the form t1 > c, where t1 is the first-stage t-statistic, and the first-stage sign is given. Although pervasive in empirical practice, pretesting on the first-stage F-statistic exacerbates bias and distorts inference. We show, however, that median bias is both minimized and roughly halved by setting c = 0, that is by screening on the sign of the estimated first stage. This bias reduction is a free lunch: conventional confidence interval coverage is unchanged by screening on the estimated first-stage sign. To the extent that IV analysts sign-screen already, these results strengthen the case for a sanguine view of the finite-sample behavior of just-ID IV.

Suggested Citation

  • Joshua Angrist & Michal Kolesár, 2021. "One Instrument to Rule Them All: The Bias and Coverage of Just-ID IV," NBER Working Papers 29417, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:29417
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    Cited by:

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    3. Zachrisson, Henrik Daae & Dearing, Eric & Borgen, Nicolai T. & Sandsør, Astrid Marie Jorde & Karoly, Lynn A., 2021. "Zachrisson et al 2021 ECEC Achievement," EdArXiv zrctw, Center for Open Science.
    4. Moler-Zapata, S.; & Grieve, R.; & Basu, A.; & O'Neill, S.;, 2022. "How does a local Instrumental Variable Method perform across settings with instruments of differing strengths? A simulation study and an evaluation of emergency surgery," Health, Econometrics and Data Group (HEDG) Working Papers 22/18, HEDG, c/o Department of Economics, University of York.
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    6. Joshua D. Angrist, 2022. "Empirical Strategies in Economics: Illuminating the Path From Cause to Effect," Econometrica, Econometric Society, vol. 90(6), pages 2509-2539, November.
    7. Van de Sijpe, Nicolas & Windmeijer, Frank, 2023. "On the power of the conditional likelihood ratio and related tests for weak-instrument robust inference," Journal of Econometrics, Elsevier, vol. 235(1), pages 82-104.
    8. Keane, Michael & Neal, Timothy, 2023. "Instrument strength in IV estimation and inference: A guide to theory and practice," Journal of Econometrics, Elsevier, vol. 235(2), pages 1625-1653.
    9. Bensch, Gunther & Ankel-Peters, Jörg & Vance, Colin, 2023. "Spotlight on Researcher Decisions – Infrastructure Evaluation, Instrumental Variables, and Specification Screening," VfS Annual Conference 2023 (Regensburg): Growth and the "sociale Frage" 277703, Verein für Socialpolitik / German Economic Association.
    10. Jeffrey Clemens & Philip G. Hoxie & Stan Veuger, 2022. "Was Pandemic Fiscal Relief Effective Fiscal Stimulus? Evidence from Aid to State and Local Governments," NBER Working Papers 30168, National Bureau of Economic Research, Inc.
    11. Isaiah Andrews & Anna Mikusheva, 2022. "GMM is Inadmissible Under Weak Identification," Papers 2204.12462, arXiv.org, revised May 2023.
    12. Ankel-Peters, Jörg & Vance, Colin & Bensch, Gunther, 2022. "Spotlight on researcher decisions – Infrastructure evaluation, instrumental variables, and first-stage specification screening," OSF Preprints sw6kd, Center for Open Science.

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    More about this item

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation
    • J08 - Labor and Demographic Economics - - General - - - Labor Economics Policies

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