IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v37y2021i2p281-310_3.html

Inference In Instrumental Variable Models With Heteroskedasticity And Many Instruments

Author

Listed:
  • Crudu, Federico
  • Mellace, Giovanni
  • Sándor, Zsolt

Abstract

This paper proposes novel inference procedures for instrumental variable models in the presence of many, potentially weak instruments that are robust to the presence of heteroskedasticity. First, we provide an Anderson–Rubin-type test for the entire parameter vector that is valid under assumptions weaker than previously proposed Anderson–Rubin-type tests. Second, we consider the case of testing a subset of parameters under the assumption that a consistent estimator for the parameters not under test exists. We show that under the null, the proposed statistics have Gaussian limiting distributions and derive alternative chi-square approximations. An extensive simulation study shows the competitive finite sample properties in terms of size and power of our procedures. Finally, we provide an empirical application using college proximity instruments to estimate the returns to education.

Suggested Citation

  • Crudu, Federico & Mellace, Giovanni & Sándor, Zsolt, 2021. "Inference In Instrumental Variable Models With Heteroskedasticity And Many Instruments," Econometric Theory, Cambridge University Press, vol. 37(2), pages 281-310, April.
    • Handle: RePEc:cup:etheor:v:37:y:2021:i:2:p:281-310_3
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S026646662000016X/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Other versions of this item:

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dennis Lim & Wenjie Wang & Yichong Zhang, 2022. "A Conditional Linear Combination Test with Many Weak Instruments," Papers 2207.11137, arXiv.org, revised Apr 2023.
    2. Anatolyev, Stanislav & Sølvsten, Mikkel, 2023. "Testing many restrictions under heteroskedasticity," Journal of Econometrics, Elsevier, vol. 236(1).
    3. Manu Navjeevan, 2023. "An Identification and Dimensionality Robust Test for Instrumental Variables Models," Papers 2311.14892, arXiv.org, revised Dec 2024.
    4. Qu Feng & Sombut Jaidee & Wenjie Wang, 2025. "Robust Inference with High-Dimensional Instruments," Papers 2506.23834, arXiv.org.
    5. Johannes W. Ligtenberg, 2023. "Inference in clustered IV models with many and weak instruments," Papers 2306.08559, arXiv.org, revised Oct 2025.
    6. Tom Boot & Didier Nibbering, 2024. "Inference on LATEs with covariates," Papers 2402.12607, arXiv.org, revised Nov 2024.
    7. Matsushita, Yukitoshi & Otsu, Taisuke, 2024. "A jackknife Lagrange multiplier test with many weak instruments," LSE Research Online Documents on Economics 116392, London School of Economics and Political Science, LSE Library.
    8. Max-Sebastian Dov`i, 2021. "Inference on the New Keynesian Phillips Curve with Very Many Instrumental Variables," Papers 2101.09543, arXiv.org, revised Mar 2021.
    9. 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.
    10. Chao, John C. & Swanson, Norman R. & Woutersen, Tiemen, 2023. "Jackknife estimation of a cluster-sample IV regression model with many weak instruments," Journal of Econometrics, Elsevier, vol. 235(2), pages 1747-1769.
    11. Lim, Dennis & Wang, Wenjie & Zhang, Yichong, 2024. "A conditional linear combination test with many weak instruments," Journal of Econometrics, Elsevier, vol. 238(2).
    12. Luther Yap, 2024. "Inference with Many Weak Instruments and Heterogeneity," Papers 2408.11193, arXiv.org, revised Apr 2025.
    13. Wenze Li, 2025. "An Empirical Comparison of Weak-IV-Robust Procedures in Just-Identified Models," Papers 2506.18001, arXiv.org.
    14. Anna Mikusheva & Liyang Sun, 2024. "Weak identification with many instruments," The Econometrics Journal, Royal Economic Society, vol. 27(2), pages -28.
    15. Johannes W. Ligtenberg & Tiemen Woutersen, 2024. "Multidimensional clustering in judge designs," Papers 2406.09473, arXiv.org.
    16. Doko Tchatoka, Firmin & Wang, Wenjie, 2025. "Identification-Robust Two-Stage Bootstrap Tests with Pretesting for Exogeneity," MPRA Paper 125017, University Library of Munich, Germany.
    17. Eleonora Brandimarti, 2025. "Self-Selection, University Courses and Returns to Advanced Degrees," Papers 2511.09260, arXiv.org.
    18. Hongwei Shi & Xinyu Zhang & Xu Guo & Baihua He & Chenyang Wang, 2025. "Testing overidentifying restrictions on high-dimensional instruments and covariates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 77(2), pages 331-352, April.
    19. Tom Boot & Johannes W. Ligtenberg, 2023. "Identification- and many moment-robust inference via invariant moment conditions," Papers 2303.07822, arXiv.org, revised Oct 2025.
    20. Dennis Lim & Wenjie Wang & Yichong Zhang, 2024. "A Dimension-Agnostic Bootstrap Anderson-Rubin Test For Instrumental Variable Regressions," Papers 2412.01603, arXiv.org, revised Sep 2025.
    21. Christis Katsouris, 2023. "Optimal Estimation Methodologies for Panel Data Regression Models," Papers 2311.03471, arXiv.org, revised Nov 2023.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cup:etheor:v:37:y:2021:i:2:p:281-310_3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/ect .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.