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Jackknife Instrumental Variable Estimation with Heteroskedasticity

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  • P.A. Bekker
  • F. Crudu

Abstract

We present a new genuine jackknife estimator for instrumental variable inference with unknown heteroskedasticity. It weighs observations such that many- instruments consistency is guaranteed while the signal component in the data is maintained. We show that this results in a smaller signal component in the many- instruments asymptotic variance when compared to estimators that neglect a part of the signal to achieve consistency. Both many-instruments and many-weak- instruments asymptotic distributions are derived using high-level assumptions that allow for the simultaneous presence of weak and strong instruments for different explanatory variables. Standard errors are formulated compactly. We review briefly known estimators and show in particular that our symmetric jackknife estimator performs well when compared to the HLIM and HFUL estimators of Hausman et al. in Monte Carlo experiments.

Suggested Citation

  • P.A. Bekker & F. Crudu, 2013. "Jackknife Instrumental Variable Estimation with Heteroskedasticity," Working Paper CRENoS 201313, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    • Handle: RePEc:cns:cnscwp:201313
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    Citations

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    Cited by:

    1. Crudu, Federico & Mellace, Giovanni & Sándor, Zsolt, 2021. "Inference In Instrumental Variable Models With Heteroskedasticity And Many Instruments," Econometric Theory, Cambridge University Press, vol. 37(2), pages 281-310, April.
    2. 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.
    3. Qingliang Fan & Zijian Guo & Ziwei Mei, 2022. "A Heteroskedasticity-Robust Overidentifying Restriction Test with High-Dimensional Covariates," Papers 2205.00171, arXiv.org, revised May 2024.
    4. Wang, Wenjie & Kaffo, Maximilien, 2016. "Bootstrap inference for instrumental variable models with many weak instruments," Journal of Econometrics, Elsevier, vol. 192(1), pages 231-268.
    5. Tom Boot & Johannes W. Ligtenberg, 2023. "Identification- and many instrument-robust inference via invariant moment conditions," Papers 2303.07822, arXiv.org, revised Sep 2023.
    6. Zhenhong Huang & Chen Wang & Jianfeng Yao, 2023. "A specification test for the strength of instrumental variables," Papers 2302.14396, arXiv.org.
    7. Bekker, Paul & Wansbeek, Tom, 2016. "Simple many-instruments robust standard errors through concentrated instrumental variables," Economics Letters, Elsevier, vol. 149(C), pages 52-55.
    8. Crudu, Federico & Neri, Laura & Tiezzi, Silvia, 2018. "Family Ties and Children Obesity in Italy," MPRA Paper 90360, University Library of Munich, Germany, revised 15 Oct 2018.
    9. Meijer, Erik & Spierdijk, Laura & Wansbeek, Tom, 2017. "Consistent estimation of linear panel data models with measurement error," Journal of Econometrics, Elsevier, vol. 200(2), pages 169-180.
    10. Murray Michael P., 2017. "Linear Model IV Estimation When Instruments Are Many or Weak," Journal of Econometric Methods, De Gruyter, vol. 6(1), pages 1-22, January.
    11. Mohammed S. Y. Omran & Mohammad A. A. Zaid & Aladdin Dwekat, 2021. "The relationship between integrated reporting and corporate environmental performance: A green trial," Corporate Social Responsibility and Environmental Management, John Wiley & Sons, vol. 28(1), pages 427-445, January.
    12. Morales-Oñate, Víctor & Crudu, Federico & Bevilacqua, Moreno, 2021. "Blockwise Euclidean likelihood for spatio-temporal covariance models," Econometrics and Statistics, Elsevier, vol. 20(C), pages 176-201.
    13. Johannes W. Ligtenberg, 2023. "Inference in IV models with clustered dependence, many instruments and weak identification," Papers 2306.08559, arXiv.org, revised Mar 2024.
    14. Kolesár, Michal, 2018. "Minimum distance approach to inference with many instruments," Journal of Econometrics, Elsevier, vol. 204(1), pages 86-100.
    15. Tom Boot & Didier Nibbering, 2024. "Inference on LATEs with covariates," Papers 2402.12607, arXiv.org.

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    More about this item

    Keywords

    Instrumental Variables; Heteroskedasticity; Many Instruments; Jackknife;
    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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