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On the Use of the Lasso for Instrumental Variables Estimation with Some Invalid Instruments

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  • Frank Windmeijer
  • Helmut Farbmacher
  • Neil Davies
  • George Davey Smith

Abstract

We investigate the behaviour of the Lasso for selecting invalid instruments in linear instrumental variables models for estimating causal effects of exposures on outcomes, as proposed recently by Kang, Zhang, Cai and Small (2016, Journal of the American Statistical Association). Invalid instruments are such that they fail the exclusion restriction and enter the model as explanatory variables. We show that for this setup, the Lasso may not consistently select the invalid instruments if these are relatively strong. We propose a median estimator that is consistent when less than 50% of the instruments are invalid, but its consistency does not depend on the relative strength of the instruments, or their correlation structure. We show that this estimator can be used for adaptive Lasso estimation, with the resulting estimator having oracle properties. The methods are applied to a Mendelian randomisation study to estimate the causal effect of BMI on diastolic blood pressure, using data on individuals from the UK Biobank, with 96 single nucleotide polymorphisms as potential instruments for BMI.

Suggested Citation

  • Frank Windmeijer & Helmut Farbmacher & Neil Davies & George Davey Smith, 2016. "On the Use of the Lasso for Instrumental Variables Estimation with Some Invalid Instruments," Bristol Economics Discussion Papers 16/674, Department of Economics, University of Bristol, UK, revised 08 Aug 2017.
  • Handle: RePEc:bri:uobdis:16/674
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    References listed on IDEAS

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    Cited by:

    1. 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, Department of Economics, University of Bristol, UK.
    2. Nicolas Apfel, 2019. "Relaxing the Exclusion Restriction in Shift-Share Instrumental Variable Estimation," Papers 1907.00222, arXiv.org, revised Dec 2019.
    3. Prosper Dovonon & Firmin Doko Tchatoka & Michael Aguessy, 2019. "Relevant moment selection under mixed identification strength," School of Economics Working Papers 2019-04, University of Adelaide, School of Economics.
    4. Guber, Raphael, 2018. "Instrument Validity Tests with Causal Trees: With an Application to the Same-sex Instrument," MEA discussion paper series 201805, Munich Center for the Economics of Aging (MEA) at the Max Planck Institute for Social Law and Social Policy.
    5. Christoph Breunig & Enno Mammen & Anna Simoni, 2018. "Ill-posed Estimation in High-Dimensional Models with Instrumental Variables," Papers 1806.00666, arXiv.org.
    6. Byunghoon Kang, 2018. "Higher Order Approximation of IV Estimators with Invalid Instruments," Working Papers 257105320, Lancaster University Management School, Economics Department.

    More about this item

    Keywords

    causal inference; instrumental variables estimation; invalid instruments; Lasso; Mendelian randomisation.;

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