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The Confidence Interval Method for Selecting Valid Instrumental Variables

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  • Frank Windmeijer
  • Xiaoran Liang
  • Fernando P Hartwig
  • Jack Bowden

Abstract

We propose a new method, the conÂ…dence interval (CI) method, to select valid instruments from a set of potential instruments that may contain invalid ones, for instrumental variables estimation of the causal effect of an exposure on an outcome. Invalid instruments are such that they fail the exclusion restriction and enter the model as explanatory variables. The CI method is based on the conÂ…dence intervals of the per instrument causal effects estimates. Each instrument speciÂ…fic causal effect estimate is obtained whilst treating all other instruments as invalid. The CI method selects the largest group with all conÂ…dence intervals overlapping with each other as the set of valid instruments. Under a plurality rule, we show that the resulting IV, or two-stage least squares (2SLS) estimator has oracle properties, meaning that it has the same limiting distribution as the oracle 2SLS estimator with the set of invalid instruments known. This result is the same as for the hard thresholding with voting (HT) method of Guo et al. (2018). Unlike the HT method, the number of instruments selected as valid by the CI method is guaranteed to be monotonically decreasing for decreasing values of the tuning parameter, which determines the width of the conÂ…dence intervals. For the CI method, we can therefore use a downward testing procedure based on the Sargan test for overidentifying restrictions. We Â…find in a simulation design similar to that of Guo et al. (2018) better properties for the CI method based estimation and inference than for the HT method and in an application of the effect of BMI on blood pressure that the CI method is better able to detect invalid instruments.

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  • Frank Windmeijer & Xiaoran Liang & Fernando P Hartwig & Jack Bowden, 2019. "The Confidence Interval Method for Selecting Valid Instrumental Variables," Bristol Economics Discussion Papers 19/715, School of Economics, University of Bristol, UK.
    • Handle: RePEc:bri:uobdis:19/715
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    References listed on IDEAS

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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. 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.
    3. Zijian Guo & Hyunseung Kang & T. Tony Cai & Dylan S. Small, 2018. "Confidence intervals for causal effects with invalid instruments by using two‐stage hard thresholding with voting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(4), pages 793-815, September.
    4. Newey, Whitney K & West, Kenneth D, 1987. "Hypothesis Testing with Efficient Method of Moments Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(3), pages 777-787, October.
    5. Frank Windmeijer & Helmut Farbmacher & Neil Davies & George Davey Smith, 2019. "On the Use of the Lasso for Instrumental Variables Estimation with Some Invalid Instruments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(527), pages 1339-1350, July.
    6. Donald W. K. Andrews, 1999. "Consistent Moment Selection Procedures for Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 67(3), pages 543-564, May.
    7. Paul S. Clarke & Frank Windmeijer, 2012. "Instrumental Variable Estimators for Binary Outcomes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1638-1652, December.
    8. von Hinke, Stephanie & Davey Smith, George & Lawlor, Debbie A. & Propper, Carol & Windmeijer, Frank, 2016. "Genetic markers as instrumental variables," Journal of Health Economics, Elsevier, vol. 45(C), pages 131-148.
    9. A. Belloni & D. Chen & V. Chernozhukov & C. Hansen, 2012. "Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain," Econometrica, Econometric Society, vol. 80(6), pages 2369-2429, November.
    10. Frank Windmeijer, 2019. "Two-stage least squares as minimum distance," The Econometrics Journal, Royal Economic Society, vol. 22(1), pages 1-9.
    11. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    12. Hyunseung Kang & Anru Zhang & T. Tony Cai & Dylan S. Small, 2016. "Instrumental Variables Estimation With Some Invalid Instruments and its Application to Mendelian Randomization," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 132-144, March.
    13. Imbens, Guido W., 2014. "Instrumental Variables: An Econometrician's Perspective," IZA Discussion Papers 8048, Institute of Labor Economics (IZA).
    14. Adam E. Locke & Bratati Kahali & Sonja I. Berndt & Anne E. Justice & Tune H. Pers & Felix R. Day & Corey Powell & Sailaja Vedantam & Martin L. Buchkovich & Jian Yang & Damien C. Croteau-Chonka & Tonu , 2015. "Genetic studies of body mass index yield new insights for obesity biology," Nature, Nature, vol. 518(7538), pages 197-206, February.
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    Cited by:

    1. Liang, X.; & Sanderson, E.; & Windmeijer, F.;, 2022. "Selecting Valid Instrumental Variables in Linear Models with Multiple Exposure Variables: Adaptive Lasso and the Median-of-Medians Estimator," Health, Econometrics and Data Group (HEDG) Working Papers 22/22, HEDG, c/o Department of Economics, University of York.
    2. Cavicchioli, Maddalena, 2023. "Statistical analysis of Markov switching vector autoregression models with endogenous explanatory variables," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    3. Biewen, Martin & Fitzenberger, Bernd & Seckler, Matthias, 2020. "Counterfactual quantile decompositions with selection correction taking into account Huber/Melly (2015): An application to the German gender wage gap," Labour Economics, Elsevier, vol. 67(C).
    4. Nicolas Apfel & Julia Hatamyar & Martin Huber & Jannis Kueck, 2024. "Learning control variables and instruments for causal analysis in observational data," Papers 2407.04448, arXiv.org.
    5. 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.
    6. Nicolas Apfel & Helmut Farbmacher & Rebecca Groh & Martin Huber & Henrika Langen, 2022. "Detecting Grouped Local Average Treatment Effects and Selecting True Instruments," Papers 2207.04481, arXiv.org, revised Oct 2023.
    7. Yiqi Lin & Frank Windmeijer & Xinyuan Song & Qingliang Fan, 2022. "On the instrumental variable estimation with many weak and invalid instruments," Papers 2207.03035, arXiv.org, revised Dec 2023.
    8. Nicolas Apfel & Frank Windmeijer, 2022. "The Falsification Adaptive Set in Linear Models with Instrumental Variables that Violate the Exclusion or Conditional Exogeneity Restriction," Papers 2212.04814, arXiv.org, revised Apr 2024.
    9. Nicolas Apfel, 2019. "Relaxing the Exclusion Restriction in Shift-Share Instrumental Variable Estimation," Papers 1907.00222, arXiv.org, revised Jul 2022.

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    Keywords

    Causal inference; Instrumental variables; Invalid instruments;
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