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Inference with many instruments: When is Anderson–Rubin test still useful?

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  • Doko Tchatoka, Firmin
  • Ma, Yuguo

Abstract

This paper re-evaluates the Anderson–Rubin (AR) test’s performance in many-instrument settings. While previous work raised concerns about size distortions when the number of instruments grows with sample size, we demonstrate that such distortions primarily arise from using asymptotic approximations in settings where the underlying assumptions for their validity fail to hold. By contrast, implementing the AR test with exact F critical values yields accurate size control — even in high-dimensional settings where the number of instruments is close to the sample size. Monte Carlo simulations confirm these findings.

Suggested Citation

  • Doko Tchatoka, Firmin & Ma, Yuguo, 2025. "Inference with many instruments: When is Anderson–Rubin test still useful?," Economics Letters, Elsevier, vol. 257(C).
    • Handle: RePEc:eee:ecolet:v:257:y:2025:i:c:s0165176525005397
    DOI: 10.1016/j.econlet.2025.112702
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    1. Tatyana Deryugina & Garth Heutel & Nolan H. Miller & David Molitor & Julian Reif, 2019. "The Mortality and Medical Costs of Air Pollution: Evidence from Changes in Wind Direction," American Economic Review, American Economic Association, vol. 109(12), pages 4178-4219, December.
    2. Jean-Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 36(4), pages 767-808, November.
    3. Jean-Marie Dufour & Mohamed Taamouti, 2005. "Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments," Econometrica, Econometric Society, vol. 73(4), pages 1351-1365, July.
    4. Victor Chernozhukov & Christian Hansen & Martin Spindler, 2015. "Post-Selection and Post-Regularization Inference in Linear Models with Many Controls and Instruments," American Economic Review, American Economic Association, vol. 105(5), pages 486-490, May.
    5. Duncan Sheppard Gilchrist & Emily Glassberg Sands, 2016. "Something to Talk About: Social Spillovers in Movie Consumption," Journal of Political Economy, University of Chicago Press, vol. 124(5), pages 1339-1382.
    6. Hansen, Christian & Kozbur, Damian, 2014. "Instrumental variables estimation with many weak instruments using regularized JIVE," Journal of Econometrics, Elsevier, vol. 182(2), pages 290-308.
    7. Paul Goldsmith-Pinkham & Isaac Sorkin & Henry Swift, 2020. "Bartik Instruments: What, When, Why, and How," American Economic Review, American Economic Association, vol. 110(8), pages 2586-2624, August.
    8. Bhaven Sampat & Heidi L. Williams, 2019. "How Do Patents Affect Follow-On Innovation? Evidence from the Human Genome," American Economic Review, American Economic Association, vol. 109(1), pages 203-236, January.
    9. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
    10. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-681, May.
    11. Joshua D. Angrist & Alan B. Keueger, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(4), pages 979-1014.
    12. Anna Mikusheva & Liyang Sun, 2022. "Inference with Many Weak Instruments," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(5), pages 2663-2686.
    13. A. Belloni & D. Chen & V. Chernozhukov & C. Hansen, 2012. "Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain," Econometrica, Econometric Society, vol. 80(6), pages 2369-2429, November.
    14. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    15. Max-Sebastian Dovì & Anders Bredahl Kock & Sophocles Mavroeidis, 2024. "A Ridge-Regularized Jackknifed Anderson-Rubin Test," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(3), pages 1083-1094, July.
    16. Dufour, Jean-Marie, 2006. "Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics," Journal of Econometrics, Elsevier, vol. 133(2), pages 443-477, August.
    17. Andrews, Donald W.K. & Stock, James H., 2007. "Testing with many weak instruments," Journal of Econometrics, Elsevier, vol. 138(1), pages 24-46, May.
    18. Jean‐Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 36(4), pages 767-808, November.
    19. John C. Chao & Norman R. Swanson, 2005. "Consistent Estimation with a Large Number of Weak Instruments," Econometrica, Econometric Society, vol. 73(5), pages 1673-1692, September.
    20. Nicole Maestas & Kathleen J. Mullen & Alexander Strand, 2013. "Does Disability Insurance Receipt Discourage Work? Using Examiner Assignment to Estimate Causal Effects of SSDI Receipt," American Economic Review, American Economic Association, vol. 103(5), pages 1797-1829, August.
    21. Will Dobbie & Jacob Goldin & Crystal S. Yang, 2018. "The Effects of Pretrial Detention on Conviction, Future Crime, and Employment: Evidence from Randomly Assigned Judges," American Economic Review, American Economic Association, vol. 108(2), pages 201-240, February.
    22. Anatolyev, Stanislav & Gospodinov, Nikolay, 2011. "Specification Testing In Models With Many Instruments," Econometric Theory, Cambridge University Press, vol. 27(2), pages 427-441, April.
    23. Dufour, Jean-Marie & Taamouti, Mohamed, 2007. "Further results on projection-based inference in IV regressions with weak, collinear or missing instruments," Journal of Econometrics, Elsevier, vol. 139(1), pages 133-153, July.
    24. Ayyar, Sree & Matsushita, Yukitoshi & Otsu, Taisuke, 2025. "Conditional likelihood ratio test with many weak instruments," LSE Research Online Documents on Economics 127520, London School of Economics and Political Science, LSE Library.
    25. Chirok Han & Peter C. B. Phillips, 2006. "GMM with Many Moment Conditions," Econometrica, Econometric Society, vol. 74(1), pages 147-192, January.
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    Keywords

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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