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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 confidence interval (CI) method, to select valid instruments from a larger set of potential instruments for instrumental variable (IV) estimation of the causal effect of an exposure on an outcome. Invalid instruments are such that they fail the exclusion conditions and enter the model as explanatory variables. The CI method is based on the CIs of the per instrument causal effects estimates and selects the largest group with all CIs overlapping with each other as the set of valid instruments. Under a plurality rule, we show that the resulting standard IV, or two‐stage least squares (2SLS) estimator has oracle properties. This result is the same as for the hard thresholding with voting (HT) method of Guo et al. (Journal of the Royal Statistical Society : Series B, 2018, 80, 793–815). 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. For the CI method, we can therefore use a downward testing procedure based on the Sargan (Econometrica, 1958, 26, 393–415) test for overidentifying restrictions and a main advantage of the CI downward testing method is that it selects the model with the largest number of instruments selected as valid that passes the Sargan test.

Suggested Citation

  • Frank Windmeijer & Xiaoran Liang & Fernando P. Hartwig & Jack Bowden, 2021. "The confidence interval method for selecting valid instrumental variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(4), pages 752-776, September.
    • Handle: RePEc:bla:jorssb:v:83:y:2021:i:4:p:752-776
    DOI: 10.1111/rssb.12449
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Xiaoran Liang & Eleanor Sanderson & Frank Windmeijer, 2022. "Selecting Valid Instrumental Variables in Linear Models with Multiple Exposure Variables: Adaptive Lasso and the Median-of-Medians Estimator," Papers 2208.05278, arXiv.org.
    4. Nicolas Apfel, 2019. "Relaxing the Exclusion Restriction in Shift-Share Instrumental Variable Estimation," Papers 1907.00222, arXiv.org, revised Jul 2022.
    5. 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.
    6. Zhaonan Qu & Yongchan Kwon, 2024. "Distributionally Robust Instrumental Variables Estimation," Papers 2410.15634, arXiv.org.
    7. 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).
    8. Cavicchioli, Maddalena, 2023. "Statistical analysis of Markov switching vector autoregression models with endogenous explanatory variables," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    9. 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.
    10. 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.

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