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Instrumental variables estimation and inference in the presence of many exogenous regressors

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  • Stanislav Anatolyev

    (New Economic School)

Abstract

We consider a standard instrumental variables model contaminated by the presence of a large number of exogenous regressors. In an asymptotic framework where this number is proportional to the sample size, we study the impact of their ratio on the validity of existing estimators and tests. When the instruments are few, the inference using the conventional 2SLS estimator and associated t and J statistics, as well as the Anderson-Rubin and Kleibergen tests, is still valid. When the instruments are many, the LIML estimator remains consistent, but the presence of many exogenous regressors changes its asymptotic variance. Moreover, the conventional bias correction of the 2SLS estimator is no longer appropriate. We provide asymptotically correct versions of bias correction for the 2SLS estimator, derive its asymptotically correct variance estimator, extend the Hansen-Hausman-Newey LIML variance estimator to the case of many exogenous regressors, and propose asymptotically valid modi cations of the J overidenti cation tests based on the LIML and bias corrected 2SLS estimators.

Suggested Citation

  • Stanislav Anatolyev, 2012. "Instrumental variables estimation and inference in the presence of many exogenous regressors," Working Papers w0162, Center for Economic and Financial Research (CEFIR).
    • Handle: RePEc:cfr:cefirw:w0162
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    References listed on IDEAS

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    Cited by:

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    3. Eric Gautier & Christiern Rose, 2022. "Fast, Robust Inference for Linear Instrumental Variables Models using Self-Normalized Moments," Papers 2211.02249, arXiv.org, revised Nov 2022.
    4. Tiziano Arduini & Eleonora Patacchini & Edoardo Rainone, 2014. "Identification and Estimation of Outcome Response with Heterogeneous Treatment Externalities," EIEF Working Papers Series 1407, Einaudi Institute for Economics and Finance (EIEF), revised Sep 2014.
    5. Daniel A. Broxterman & William D. Larson, 2020. "An empirical examination of shift‐share instruments," Journal of Regional Science, Wiley Blackwell, vol. 60(4), pages 677-711, September.
    6. Anatolyev, Stanislav & Sølvsten, Mikkel, 2023. "Testing many restrictions under heteroskedasticity," Journal of Econometrics, Elsevier, vol. 236(1).
    7. Michal Kolesár & Raj Chetty & John Friedman & Edward Glaeser & Guido W. Imbens, 2015. "Identification and Inference With Many Invalid Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 474-484, October.
    8. Zhenhong Huang & Chen Wang & Jianfeng Yao, 2023. "A specification test for the strength of instrumental variables," Papers 2302.14396, arXiv.org.
    9. Kirill S. Evdokimov & Michal Kolesár, 2018. "Inference in Instrumental Variable Regression Analysis with Heterogeneous Treatment Effects," Working Papers 2018-16, Princeton University. Economics Department..
    10. Muhammad Qasim, 2024. "A weighted average limited information maximum likelihood estimator," Statistical Papers, Springer, vol. 65(5), pages 2641-2666, July.
    11. Kolesár, Michal, 2018. "Minimum distance approach to inference with many instruments," Journal of Econometrics, Elsevier, vol. 204(1), pages 86-100.
    12. Paul Goldsmith-Pinkham & Isaac Sorkin & Henry Swift, 2020. "Bartik Instruments: What, When, Why, and How," American Economic Review, American Economic Association, vol. 110(8), pages 2586-2624, August.
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    14. Helmut Farbmacher & Rebecca Groh & Michael Muhlegger & Gabriel Vollert, 2024. "Revisiting the Many Instruments Problem using Random Matrix Theory," Papers 2408.08580, arXiv.org.

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    More about this item

    Keywords

    instrumental variables regression; many instruments; many exogenous regressors; 2SLS estimator; LIML estimator; bias correction; t test; J test; AndersonRubin test; Kleibergen test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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