IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v33y2017i05p1046-1080_00.html

Asymptotic Size Of Kleibergen’S Lm And Conditional Lr Tests For Moment Condition Models

Author

Listed:
  • Andrews, Donald W.K.
  • Guggenberger, Patrik

Abstract

An influential paper by Kleibergen (2005, Econometrica 73, 1103–1123) introduces Lagrange multiplier (LM) and conditional likelihood ratio-like (CLR) tests for nonlinear moment condition models. These procedures aim to have good size performance even when the parameters are unidentified or poorly identified. However, the asymptotic size and similarity (in a uniform sense) of these procedures have not been determined in the literature. This paper does so.This paper shows that the LM test has correct asymptotic size and is asymptotically similar for a suitably chosen parameter space of null distributions. It shows that the CLR tests also have these properties when the dimension p of the unknown parameter θ equals 1. When p ≥ 2, however, the asymptotic size properties are found to depend on how the conditioning statistic, upon which the CLR tests depend, is weighted. Two weighting methods have been suggested in the literature. The paper shows that the CLR tests are guaranteed to have correct asymptotic size when p ≥ 2 when the weighting is based on an estimator of the variance of the sample moments, i.e., moment-variance weighting, combined with the Robin and Smith (2000, Econometric Theory 16, 151–175) rank statistic. The paper also determines a formula for the asymptotic size of the CLR test when the weighting is based on an estimator of the variance of the sample Jacobian. However, the results of the paper do not guarantee correct asymptotic size when p ≥ 2 with the Jacobian-variance weighting, combined with the Robin and Smith (2000, Econometric Theory 16, 151–175) rank statistic, because two key sample quantities are not necessarily asymptotically independent under some identification scenarios.Analogous results for confidence sets are provided. Even for the special case of a linear instrumental variable regression model with two or more right-hand side endogenous variables, the results of the paper are new to the literature.

Suggested Citation

  • Andrews, Donald W.K. & Guggenberger, Patrik, 2017. "Asymptotic Size Of Kleibergen’S Lm And Conditional Lr Tests For Moment Condition Models," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1046-1080, October.
    • Handle: RePEc:cup:etheor:v:33:y:2017:i:05:p:1046-1080_00
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0266466616000347/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. Purevdorj Tuvaandorj, 2021. "Robust Permutation Tests in Linear Instrumental Variables Regression," Papers 2111.13774, arXiv.org, revised Jul 2024.
    2. Stépahne Auray & Nicolas Lepage-Saucier & Purevdorj Tuvaandor, 2018. "Doubly Robust GMM Inference and Differentiated Products Demand Models," Working Papers 2018-13, Center for Research in Economics and Statistics.
    3. Frank Kleibergen & Zhaoguo Zhan, 2025. "Double robust inference for continuous updating GMM," Quantitative Economics, Econometric Society, vol. 16(1), pages 295-327, January.
    4. Phillips, Peter C.B. & Gao, Wayne Yuan, 2017. "Structural inference from reduced forms with many instruments," Journal of Econometrics, Elsevier, vol. 199(2), pages 96-116.
    5. Tetsuya Kaji, 2019. "Theory of Weak Identification in Semiparametric Models," Papers 1908.10478, arXiv.org, revised Aug 2020.
    6. Muyang Ren, 2025. "Extrapolating LATE with Weak IVs," Papers 2512.23854, arXiv.org.
    7. Martínez-Iriarte, Julián & Sun, Yixiao & Wang, Xuexin, 2020. "Asymptotic F tests under possibly weak identification," Journal of Econometrics, Elsevier, vol. 218(1), pages 140-177.
    8. Cheng, Xu, 2015. "Robust inference in nonlinear models with mixed identification strength," Journal of Econometrics, Elsevier, vol. 189(1), pages 207-228.
    9. Kleibergen, Frank & Kong, Lingwei, 2025. "Identification robust inference for the risk premium in term structure models," Journal of Econometrics, Elsevier, vol. 248(C).
    10. 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.
    11. Steven T. Berry & Philip A. Haile, 2021. "Foundations of Demand Estimation," NBER Working Papers 29305, National Bureau of Economic Research, Inc.
    12. Hugo Kruiniger, 2025. "Uniform Quasi ML based inference for the panel AR(1) model," Papers 2508.20855, arXiv.org, revised Dec 2025.
    13. Andrews, Donald W.K. & Cheng, Xu & Guggenberger, Patrik, 2020. "Generic results for establishing the asymptotic size of confidence sets and tests," Journal of Econometrics, Elsevier, vol. 218(2), pages 496-531.
    14. Aragón, Edilean Kleber da Silva Bejarano & Galvão, Ana Beatriz, 2023. "Shock-based inference on the Phillips curve with the cost channel," Economic Modelling, Elsevier, vol. 126(C).
    15. Chaudhuri, Saraswata & Renault, Eric, 2020. "Score tests in GMM: Why use implied probabilities?," Journal of Econometrics, Elsevier, vol. 219(2), pages 260-280.
    16. Gregory Cox, 2022. "Weak Identification in Low-Dimensional Factor Models with One or Two Factors," Papers 2211.00329, arXiv.org, revised Mar 2024.
    17. Marcelo J. Moreira & Geert Ridder & Mahrad Sharifvaghefi, 2026. "Power Bounds and Efficiency Loss for Asymptotically Optimal Tests in IV Regression," Papers 2603.21004, arXiv.org.
    18. Gregory Fletcher Cox, 2020. "Weak Identification with Bounds in a Class of Minimum Distance Models," Papers 2012.11222, arXiv.org, revised Oct 2025.
    19. Don S. Poskitt, 2020. "On GMM Inference: Partial Identification, Identification Strength, and Non-Standard," Monash Econometrics and Business Statistics Working Papers 40/20, Monash University, Department of Econometrics and Business Statistics.

    More about this item

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

    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:33:y:2017:i:05:p:1046-1080_00. 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.