IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/hal-00591732.html
   My bibliography  Save this paper

High-dimensional instrumental variables regression and confidence sets

Author

Listed:
  • Eric Gautier

    () (TSE - Toulouse School of Economics - UT1 - Université Toulouse 1 Capitole - CNRS - Centre National de la Recherche Scientifique - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales)

  • Alexandre Tsybakov

    () (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - ENSAE ParisTech - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique, ENSAE ParisTech - École Nationale de la Statistique et de l'Administration Économique)

  • Christiern Rose

    () (University of Queensland [Brisbane])

Abstract

This article considers inference in linear models with K regressors, some or many could be endogenous, and L instruments. L can range from less than K to any order smaller than an exponential in the sample size and K is arbitrary. For moderate K, identification robust confidence sets are obtained by solving a hierarchy of semidefinite programs. For larger K, we propose the STIV estimator. The analysis of its error uses sensitivity characteristics which are sharper than those in the literature on sparsity. Data-driven bounds on them and robust confidence sets are obtained by solving K linear programs. Results on rates of convergence, variable selection, and confidence sets which "adapt" to the sparsity are given. We generalize our approach to models with approximation errors, systems, endogenous instruments, and two-stage for confidence bands for vectors of linear functionals and functions. The application is to a demand system with many endogenous regressors.

Suggested Citation

  • Eric Gautier & Alexandre Tsybakov & Christiern Rose, 2018. "High-dimensional instrumental variables regression and confidence sets," Working Papers hal-00591732, HAL.
  • Handle: RePEc:hal:wpaper:hal-00591732
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00591732v5
    as

    Download full text from publisher

    File URL: https://hal.archives-ouvertes.fr/hal-00591732v5/document
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jerry A. Hausman & Whitney K. Newey & Tiemen Woutersen & John C. Chao & Norman R. Swanson, 2012. "Instrumental variable estimation with heteroskedasticity and many instruments," Quantitative Economics, Econometric Society, vol. 3(2), pages 211-255, July.
    2. Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, vol. 16(06), pages 797-834, December.
    3. 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.
    4. Amemiya, Takeshi, 1974. "The nonlinear two-stage least-squares estimator," Journal of Econometrics, Elsevier, vol. 2(2), pages 105-110, July.
    5. Alastair R. Hall & Fernanda P. M. Peixe, 2003. "A Consistent Method for the Selection of Relevant Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 22(3), pages 269-287, January.
    6. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    7. Okui, Ryo, 2011. "Instrumental variable estimation in the presence of many moment conditions," Journal of Econometrics, Elsevier, vol. 165(1), pages 70-86.
    8. Caner, Mehmet, 2009. "Lasso-Type Gmm Estimator," Econometric Theory, Cambridge University Press, vol. 25(01), pages 270-290, February.
    Full references (including those not matched with items on IDEAS)

    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:hal:wpaper:hal-00591732. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.