IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2210.07680.html

Conditional Likelihood Ratio Test with Many Weak Instruments

Author

Listed:
  • Sreevidya Ayyar
  • Yukitoshi Matsushita
  • Taisuke Otsu

Abstract

This paper extends validity of the conditional likelihood ratio (CLR) test developed by Moreira (2003) to instrumental variable regression models with unknown error variance and many weak instruments. In this setting, we argue that the conventional CLR test with estimated error variance loses exact similarity and is asymptotically invalid. We propose a modified critical value function for the likelihood ratio (LR) statistic with estimated error variance, and prove that this modified test achieves asymptotic validity under many weak instrument asymptotics. Our critical value function is constructed by representing the LR using four statistics, instead of two as in Moreira (2003). A simulation study illustrates the desirable properties of our test.

Suggested Citation

  • Sreevidya Ayyar & Yukitoshi Matsushita & Taisuke Otsu, 2022. "Conditional Likelihood Ratio Test with Many Weak Instruments," Papers 2210.07680, arXiv.org.
    • Handle: RePEc:arx:papers:2210.07680
    as

    Download full text from publisher

    File URL: https://arxiv.org/pdf/2210.07680
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    3. Donald W. K. Andrews & Marcelo J. Moreira & James H. Stock, 2006. "Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression," Econometrica, Econometric Society, vol. 74(3), pages 715-752, May.
    4. 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.
    5. Moreira, Humberto & Moreira, Marcelo J., 2019. "Optimal two-sided tests for instrumental variables regression with heteroskedastic and autocorrelated errors," Journal of Econometrics, Elsevier, vol. 213(2), pages 398-433.
    6. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Anna Mikusheva & Liyang Sun, 2024. "Weak identification with many instruments," The Econometrics Journal, Royal Economic Society, vol. 27(2), pages -28.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sreevidya Ayyar & Yukitoshi Matsushita & Taisuke Otsu, 2022. "Conditional likelihood ratio test with many weak instruments," STICERD - Econometrics Paper Series 624, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. 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.
    3. Guilhem Bascle, 2008. "Controlling for endogeneity with instrumental variables in strategic management research," Post-Print hal-00576795, HAL.
    4. Wang, Wenjie & Doko Tchatoka, Firmin, 2018. "On Bootstrap inconsistency and Bonferroni-based size-correction for the subset Anderson–Rubin test under conditional homoskedasticity," Journal of Econometrics, Elsevier, vol. 207(1), pages 188-211.
    5. Antoine, Bertille & Lavergne, Pascal, 2023. "Identification-robust nonparametric inference in a linear IV model," Journal of Econometrics, Elsevier, vol. 235(1), pages 1-24.
    6. Keisuke Hirano & Jack R. Porter, 2015. "Location Properties of Point Estimators in Linear Instrumental Variables and Related Models," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 720-733, December.
    7. Bertille Antoine & Pascal Lavergne, 2020. "Identification-Robust Nonparametric Interference in a Linear IV Model," Discussion Papers dp20-03, Department of Economics, Simon Fraser University.
    8. 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.
    9. Wang, Wenjie, 2021. "Wild Bootstrap for Instrumental Variables Regression with Weak Instruments and Few Clusters," MPRA Paper 106227, University Library of Munich, Germany.
    10. Joel L. Horowitz, 2018. "Non-Asymptotic Inference in Instrumental Variables Estimation," Papers 1809.03600, arXiv.org.
    11. 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.
    12. Imbens, Guido W., 2014. "Instrumental Variables: An Econometrician's Perspective," IZA Discussion Papers 8048, IZA Network @ LISER.
    13. Sheng Wang & Hyunseung Kang, 2022. "Weak‐instrument robust tests in two‐sample summary‐data Mendelian randomization," Biometrics, The International Biometric Society, vol. 78(4), pages 1699-1713, December.
    14. Isaiah Andrews & Timothy B. Armstrong, 2017. "Unbiased instrumental variables estimation under known first‐stage sign," Quantitative Economics, Econometric Society, vol. 8(2), pages 479-503, July.
    15. Wang, Wenjie & Zhang, Yichong, 2024. "Wild bootstrap inference for instrumental variables regressions with weak and few clusters," Journal of Econometrics, Elsevier, vol. 241(1).
    16. Marcellino, Massimiliano & Kapetanios, George & Khalaf, Lynda, 2015. "Factor based identification-robust inference in IV regressions," CEPR Discussion Papers 10390, Centre for Economic Policy Research.
    17. Murray Michael P., 2017. "Linear Model IV Estimation When Instruments Are Many or Weak," Journal of Econometric Methods, De Gruyter, vol. 6(1), pages 1-22, January.
    18. Wang, Wenjie & Kaffo, Maximilien, 2016. "Bootstrap inference for instrumental variable models with many weak instruments," Journal of Econometrics, Elsevier, vol. 192(1), pages 231-268.
    19. repec:bla:ecorec:v:91:y:2015:i::p:1-24 is not listed on IDEAS
    20. Dennis Lim & Wenjie Wang & Yichong Zhang, 2022. "A Conditional Linear Combination Test with Many Weak Instruments," Papers 2207.11137, arXiv.org, revised Apr 2023.
    21. Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91(S1), pages 1-24, June.

    More about this item

    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:arx:papers:2210.07680. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: arXiv administrators (email available below). General contact details of provider: https://arxiv.org/ .

    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.