IDEAS home Printed from https://ideas.repec.org/p/ifs/cemmap/05-19.html
   My bibliography  Save this paper

Generalised Anderson-Rubin statistic based inference in the presence of a singular moment variance matrix

Author

Listed:
  • Nicky L. Grant

    (Institute for Fiscal Studies)

  • Richard J. Smith

    (Institute for Fiscal Studies)

Abstract

The particular concern of this paper is the construction of a confidence region with pointwise asymptotically correct size for the true value of a parameter of interest based on the generalized Anderson-Rubin (GAR) statistic when the moment variance matrix is singular. The large sample behaviour of the GAR statistic is analysed using a Laurent series expansion around the points of moment variance singularity. Under a condition termed first order moment singularity the GAR statistic is shown to possess a limiting chi-square distribution on parameter sequences converging to the true parameter value. Violation, however, of this condition renders the GAR statistic unbounded asymptotically. The paper details an appropriate discretisation of the parameter space to implement a feasible GAR-based confidence region that contains the true parameter value with pointwise asymptotically correct size. Simulation evidence is provided that demonstrates the efficacy of the GAR-based approach to moment-based inference described in this paper.

Suggested Citation

  • Nicky L. Grant & Richard J. Smith, 2019. "Generalised Anderson-Rubin statistic based inference in the presence of a singular moment variance matrix," CeMMAP working papers CWP05/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:05/19
    as

    Download full text from publisher

    File URL: https://www.ifs.org.uk/uploads/cemmap/wps/CWP051919.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Andrews, Donald W.K. & Cheng, Xu, 2013. "Maximum likelihood estimation and uniform inference with sporadic identification failure," Journal of Econometrics, Elsevier, vol. 173(1), pages 36-56.
    Full references (including those not matched with items on IDEAS)

    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. Young-Joo Kim & Myung Hwan Seo, 2017. "Is There a Jump in the Transition?," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 241-249, April.
    2. Jean-Marie Dufour & Joachim Wilde, 2018. "Weak identification in probit models with endogenous covariates," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(4), pages 611-631, October.
    3. Kadilli, Anjeza & Krishnakumar, Jaya, 2022. "Smooth Transition Simultaneous Equation Models," Journal of Economic Dynamics and Control, Elsevier, vol. 145(C).
    4. Andrews, Donald W.K. & Cheng, Xu, 2013. "Maximum likelihood estimation and uniform inference with sporadic identification failure," Journal of Econometrics, Elsevier, vol. 173(1), pages 36-56.
    5. Khalaf, Lynda & Urga, Giovanni, 2014. "Identification robust inference in cointegrating regressions," Journal of Econometrics, Elsevier, vol. 182(2), pages 385-396.
    6. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2011. "Inference on Treatment Effects After Selection Amongst High-Dimensional Controls," Papers 1201.0224, arXiv.org, revised May 2012.
    7. Gregory Cox, 2022. "A Generalized Argmax Theorem with Applications," Papers 2209.08793, arXiv.org.
    8. Chen, Feiyan & Ding, Feng & Alsaedi, Ahmed & Hayat, Tasawar, 2017. "Data filtering based multi-innovation extended gradient method for controlled autoregressive autoregressive moving average systems using the maximum likelihood principle," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 53-67.
    9. Andrews, Donald W.K. & Cheng, Xu, 2014. "Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure," Econometric Theory, Cambridge University Press, vol. 30(2), pages 287-333, April.
    10. 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.
    11. Chen, Xiaohong & Ponomareva, Maria & Tamer, Elie, 2014. "Likelihood inference in some finite mixture models," Journal of Econometrics, Elsevier, vol. 182(1), pages 87-99.
    12. Jean-Marie Dufour & Emmanuel Flachaire & Lynda Khalaf & Abdallah Zalghout, 2020. "Identification-Robust Inequality Analysis," Cahiers de recherche 03-2020, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    13. D’Amour, Alexander & Ding, Peng & Feller, Avi & Lei, Lihua & Sekhon, Jasjeet, 2021. "Overlap in observational studies with high-dimensional covariates," Journal of Econometrics, Elsevier, vol. 221(2), pages 644-654.
    14. Ruoyao Shi & Zhipeng Liao, 2018. "An Averaging GMM Estimator Robust to Misspecification," Working Papers 201803, University of California at Riverside, Department of Economics.
    15. Bera Anil K. & Doğan Osman & Bilias Yannis & Yoon Mann J. & Taşpınar Süleyman, 2020. "Adjustments of Rao’s Score Test for Distributional and Local Parametric Misspecifications," Journal of Econometric Methods, De Gruyter, vol. 9(1), pages 1-29, January.
    16. Tiemen M. Woutersen & John Ham, 2013. "Calculating confidence intervals for continuous and discontinuous functions of parameters," CeMMAP working papers 23/13, Institute for Fiscal Studies.
    17. Khalaf, Lynda & Lin, Zhenjiang, 2021. "Projection-based inference with particle swarm optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 128(C).
    18. Jui-Chung Yang & Ke-Li Xu, 2013. "Estimation and Inference under Weak Identi cation and Persistence: An Application on Forecast-Based Monetary Policy Reaction Function," 2013 Papers pya307, Job Market Papers.
    19. Gregory Cox, 2020. "Weak Identification with Bounds in a Class of Minimum Distance Models," Papers 2012.11222, arXiv.org, revised Dec 2022.
    20. Cheng, Xu, 2015. "Robust inference in nonlinear models with mixed identification strength," Journal of Econometrics, Elsevier, vol. 189(1), pages 207-228.

    More about this item

    Keywords

    Laurent series expansion; moment indicator; parameter sequences; singular moment matrix;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • 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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:ifs:cemmap:05/19. 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: Emma Hyman (email available below). General contact details of provider: https://edirc.repec.org/data/cmifsuk.html .

    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.