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Asymptotics Of Diagonal Elements Of Projection Matrices Under Many Instruments/Regressors

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  • Anatolyev, Stanislav
  • Yaskov, Pavel

Abstract

This article sheds light on the asymptotic behavior of diagonal elements of projection matrices associated with instruments or regressors under many instrument/regressor asymptotics. When the diagonal elements do not exhibit variation asymptotically, certain results in the many instrument/regressor literature lead to elegant solutions and conclusions. We establish conditions when this happens, provide relevant examples, and analyze instrument designs, for which this property does or does not hold.

Suggested Citation

  • Anatolyev, Stanislav & Yaskov, Pavel, 2017. "Asymptotics Of Diagonal Elements Of Projection Matrices Under Many Instruments/Regressors," Econometric Theory, Cambridge University Press, vol. 33(3), pages 717-738, June.
    • Handle: RePEc:cup:etheor:v:33:y:2017:i:03:p:717-738_00
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    Cited by:

    1. Kaffo, Maximilien & Wang, Wenjie, 2017. "On bootstrap validity for specification testing with many weak instruments," Economics Letters, Elsevier, vol. 157(C), pages 107-111.
    2. Hyunseok Jung & Xiaodong Liu, 2023. "Testing for Peer Effects without Specifying the Network Structure," Papers 2306.09806, arXiv.org, revised Mar 2024.
    3. Dörnemann, Nina & Dette, Holger, 2023. "Fluctuations of the diagonal entries of a large sample precision matrix," Statistics & Probability Letters, Elsevier, vol. 198(C).
    4. Max-Sebastian Dov`i & Anders Bredahl Kock & Sophocles Mavroeidis, 2022. "A Ridge-Regularised Jackknifed Anderson-Rubin Test," Papers 2209.03259, arXiv.org, revised Nov 2023.
    5. Byunghoon Kang, 2018. "Higher Order Approximation of IV Estimators with Invalid Instruments," Working Papers 257105320, Lancaster University Management School, Economics Department.
    6. Pavel Yaskov, 2018. "LLN for Quadratic Forms of Long Memory Time Series and Its Applications in Random Matrix Theory," Journal of Theoretical Probability, Springer, vol. 31(4), pages 2032-2055, December.
    7. Dörnemann, Nina, 2023. "Likelihood ratio tests under model misspecification in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    8. Zhenhong Huang & Chen Wang & Jianfeng Yao, 2023. "A specification test for the strength of instrumental variables," Papers 2302.14396, arXiv.org.
    9. Boot, Tom, 2023. "Joint inference based on Stein-type averaging estimators in the linear regression model," Journal of Econometrics, Elsevier, vol. 235(2), pages 1542-1563.
    10. Zhenhong Huang & Chen Wang & Jianfeng Yao, 2023. "Assessing the strength of many instruments with the first-stage F and Cragg-Donald statistics," Papers 2302.14423, arXiv.org.
    11. Richard, Patrick, 2019. "Residual bootstrap tests in linear models with many regressors," Journal of Econometrics, Elsevier, vol. 208(2), pages 367-394.

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