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

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

Research output: Contribution to journalArticle (Academic Journal)peer-review

29 Citations (Scopus)
318 Downloads (Pure)


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, and 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.
Original languageEnglish
Pages (from-to)1339-1350
Number of pages12
JournalJournal of the American Statistical Association
Issue number527
Early online date13 Nov 2018
Publication statusPublished - 25 Sep 2019

Structured keywords

  • ECON Econometrics
  • ECON CEPS Data


  • causal inference
  • instrumental variables estimation
  • invalid instruments
  • Lasso
  • Mendelian randomisation


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