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Inference in instrumental variables models with heteroskedasticity and many instruments

Author

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  • Federico Crudu
  • Giovanni Mellace
  • Zsolt Sándor

Abstract

This paper proposes novel inference procedures for instrumental variable models in the presence of many, potentially weak instruments that are robust to the presence of heteroskedasticity. First, we provide an Anderson-Rubin-type test for the entire parameter vector that is valid under assumptions weaker than previously proposed Anderson-Rubin-type tests. Second, we consider the case of testing a subset of para- meters under the assumption that a consistent estimator for the parameters not under test exists. We show that under the null the proposed statistics have Gaussian limiting distributions and derive alternative chi square approximations. An extensive simulation study shows the competitive finite sample properties in terms of size and power of our procedures. Finally, we provide an empirical application using college proximity instruments to estimate the returns to education.

Suggested Citation

  • Federico Crudu & Giovanni Mellace & Zsolt Sándor, 2020. "Inference in instrumental variables models with heteroskedasticity and many instruments," Department of Economics University of Siena 821, Department of Economics, University of Siena.
  • Handle: RePEc:usi:wpaper:821
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    References listed on IDEAS

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    Cited by:

    1. Dennis Lim & Wenjie Wang & Yichong Zhang, 2022. "A Conditional Linear Combination Test with Many Weak Instruments," Papers 2207.11137, arXiv.org, revised Apr 2023.
    2. Anatolyev, Stanislav & Sølvsten, Mikkel, 2023. "Testing many restrictions under heteroskedasticity," Journal of Econometrics, Elsevier, vol. 236(1).
    3. Manu Navjeevan, 2023. "An Identification and Dimensionality Robust Test for Instrumental Variables Models," Papers 2311.14892, arXiv.org.
    4. Johannes W. Ligtenberg, 2023. "Inference in IV models with clustered dependence, many instruments and weak identification," Papers 2306.08559, arXiv.org, revised Mar 2024.
    5. Tom Boot & Didier Nibbering, 2024. "Inference on LATEs with covariates," Papers 2402.12607, arXiv.org.
    6. Matsushita, Yukitoshi & Otsu, Taisuke, 2024. "A jackknife Lagrange multiplier test with many weak instruments," LSE Research Online Documents on Economics 116392, London School of Economics and Political Science, LSE Library.
    7. Max-Sebastian Dov`i, 2021. "Inference on the New Keynesian Phillips Curve with Very Many Instrumental Variables," Papers 2101.09543, arXiv.org, revised Mar 2021.
    8. Max-Sebastian Dovì & Anders Bredahl Kock & Sophocles Mavroeidis, 2024. "A Ridge-Regularized Jackknifed Anderson-Rubin Test," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(3), pages 1083-1094, July.
    9. Chao, John C. & Swanson, Norman R. & Woutersen, Tiemen, 2023. "Jackknife estimation of a cluster-sample IV regression model with many weak instruments," Journal of Econometrics, Elsevier, vol. 235(2), pages 1747-1769.
    10. Lim, Dennis & Wang, Wenjie & Zhang, Yichong, 2024. "A conditional linear combination test with many weak instruments," Journal of Econometrics, Elsevier, vol. 238(2).
    11. Anna Mikusheva & Liyang Sun, 2023. "Weak Identification with Many Instruments," Papers 2308.09535, arXiv.org, revised Jan 2024.
    12. Johannes W. Ligtenberg & Tiemen Woutersen, 2024. "Multidimensional clustering in judge designs," Papers 2406.09473, arXiv.org.
    13. Tom Boot & Johannes W. Ligtenberg, 2023. "Identification- and many instrument-robust inference via invariant moment conditions," Papers 2303.07822, arXiv.org, revised Sep 2023.
    14. Christis Katsouris, 2023. "Optimal Estimation Methodologies for Panel Data Regression Models," Papers 2311.03471, arXiv.org, revised Nov 2023.

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    More about this item

    Keywords

    Instrumental variables; heteroskedasticity; many instruments; jackknife; inference;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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