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Many Instruments And/Or Regressors: A Friendly Guide

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  • Stanislav Anatolyev

Abstract

This paper surveys the state of the art in the econometrics of regression models with many instruments or many regressors based on alternative – namely, dimension – asymptotics. We list critical results of dimension asymptotics that lead to better approximations of properties of familiar and alternative estimators and tests when the instruments and/or regressors are numerous. Then, we consider the problem of estimation and inference in the basic linear instrumental variables regression setup with many strong instruments. We describe the failures of conventional estimation and inference, as well as alternative tools that restore consistency and validity. We then add various other features to the basic model such as heteroskedasticity, instrument weakness, etc., in each case providing a review of the existing tools for proper estimation and inference. Subsequently, we consider a related but different problem of estimation and testing in a linear mean regression with many regressors. We also describe various extensions and connections to other settings, such as panel data models, spatial models, time series models, and so on. Finally, we provide practical guidance regarding which tools are most suitable to use in various situations when many instruments and/or regressors turn out to be an issue.

Suggested Citation

  • Stanislav Anatolyev, 2019. "Many Instruments And/Or Regressors: A Friendly Guide," Journal of Economic Surveys, Wiley Blackwell, vol. 33(2), pages 689-726, April.
    • Handle: RePEc:bla:jecsur:v:33:y:2019:i:2:p:689-726
    DOI: 10.1111/joes.12295
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    Cited by:

    1. Itchoko M.M. Mwa Ndjokou, Prince Piva Asaloko, 2024. "Empirical verification of the link between the digital divide and women's economic participation in Africa," European Journal of Comparative Economics, Cattaneo University (LIUC), vol. 21(1), pages 123-164, June.
    2. Anna Mikusheva & Mikkel S{o}lvsten, 2023. "Linear Regression with Weak Exogeneity," Papers 2308.08958, arXiv.org, revised Jan 2024.
    3. Wang, Wenjie, 2022. "Wild bootstrap test of overidentification with many instruments and heteroskedasticity," MPRA Paper 115168, University Library of Munich, Germany.
    4. Anatolyev, Stanislav & Sølvsten, Mikkel, 2023. "Testing many restrictions under heteroskedasticity," Journal of Econometrics, Elsevier, vol. 236(1).
    5. Kuanhao Jiang & Rajarshi Mukherjee & Subhabrata Sen & Pragya Sur, 2022. "A New Central Limit Theorem for the Augmented IPW Estimator: Variance Inflation, Cross-Fit Covariance and Beyond," Papers 2205.10198, arXiv.org, revised Oct 2022.
    6. Helmut Farbmacher & Rebecca Groh & Michael Muhlegger & Gabriel Vollert, 2024. "Revisiting the Many Instruments Problem using Random Matrix Theory," Papers 2408.08580, arXiv.org.
    7. Abhimanyu Gupta & Myung Hwan Seo, 2023. "Robust Inference on Infinite and Growing Dimensional Time‐Series Regression," Econometrica, Econometric Society, vol. 91(4), pages 1333-1361, July.
    8. Mayer, Alexander, 2020. "(Consistently) testing strict exogeneity against the alternative of predeterminedness in linear time-series models," Economics Letters, Elsevier, vol. 193(C).
    9. Carlos Velasco & Xuexin Wang, 2021. "Instrumental variable estimation via a continuum of instruments with an application to estimating the elasticity of intertemporal substitution in consumption," Working Papers 2024-09-06, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    10. Wang, Wenjie, 2020. "On Bootstrap Validity for the Test of Overidentifying Restrictions with Many Instruments and Heteroskedasticity," MPRA Paper 104858, University Library of Munich, Germany.
    11. Johannes W. Ligtenberg, 2023. "Inference in IV models with clustered dependence, many instruments and weak identification," Papers 2306.08559, arXiv.org, revised Mar 2024.
    12. Malvina Marchese & María Dolores Martínez-Miranda & Jens Perch Nielsen & Michael Scholz, 2024. "Robustifying and simplifying high-dimensional regression with applications to yearly stock return and telematics data," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 10(1), pages 1-16, December.
    13. Mayer, Alexander, 2022. "On the local power of some tests of strict exogeneity in linear fixed effects models," Econometrics and Statistics, Elsevier, vol. 24(C), pages 49-74.

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