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Instrumental Variable Estimators for Binary Outcomes

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  • Paul Clarke
  • Frank Windmeijer

Abstract

Instrumental variables (IVs) can be used to construct estimators of exposure effects on the outcomes of studies affected by non-ignorable selection of the exposure. Estimators which fail to adjust for the effects of non-ignorable selection will be biased and inconsistent. Such situations commonly arise in observational studies, but even randomised controlled trials can be affected by non-ignorable participant non-compliance. In this paper, we review IV estimators for studies in which the outcome is binary. Recent work on identification is interpreted using an integrated structural modelling and potential outcomes framework, within which we consider the links between different approaches developed in statistics and econometrics. The implicit assumptions required for bounding causal effects and point-identification by each estimator are highlighted and compared within our framework. Finally, the implications for practice are discussed.

Suggested Citation

  • Paul Clarke & Frank Windmeijer, 2010. "Instrumental Variable Estimators for Binary Outcomes," The Centre for Market and Public Organisation 10/239, The Centre for Market and Public Organisation, University of Bristol, UK.
    • Handle: RePEc:bri:cmpowp:10/239
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    Cited by:

    1. Luke Keele & Dylan Small & Richard Grieve, 2017. "Randomization-based instrumental variables methods for binary outcomes with an application to the ‘IMPROVE’ trial," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(2), pages 569-586, February.
    2. Marra Giampiero & Radice Rosalba, 2017. "A joint regression modeling framework for analyzing bivariate binary data in R," Dependence Modeling, De Gruyter, vol. 5(1), pages 268-294, December.
    3. 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.
    4. Tom M. Palmer & Roland R. Ramsahai & Vanessa Didelez & Nuala A. Sheehan, 2011. "Nonparametric bounds for the causal effect in a binary instrumental-variable model," Stata Journal, StataCorp LP, vol. 11(3), pages 345-367, September.
    5. Geneletti, Sara & Baio, Gianluca & O'Keeffe, Aidan & Ricciardi, Federico, 2019. "Bayesian modelling for binary outcomes in the regression discontinuity design," LSE Research Online Documents on Economics 100096, London School of Economics and Political Science, LSE Library.
    6. Laing, Timothy, 2015. "Rights to the forest, REDD+ and elections: Mining in Guyana," Resources Policy, Elsevier, vol. 46(P2), pages 250-261.
    7. Paul Clarke & Frank Windmeijer, 2009. "Identification of Causal Effects on Binary Outcomes Using Structural Mean Models," The Centre for Market and Public Organisation 09/217, The Centre for Market and Public Organisation, University of Bristol, UK.
    8. Johannes Jarke-Neuert & Grischa Perino & Henrike Schwickert, 2023. "Free riding in climate protests," Nature Climate Change, Nature, vol. 13(11), pages 1197-1202, November.
    9. Katherine Bobroske & Michael Freeman & Lawrence Huan & Anita Cattrell & Stefan Scholtes, 2022. "Curbing the Opioid Epidemic at Its Root: The Effect of Provider Discordance After Opioid Initiation," Management Science, INFORMS, vol. 68(3), pages 2003-2015, March.
    10. Ming-Yueh Huang & Kwun Chuen Gary Chan, 2024. "Adaptive Reduction of Curse of Dimensionality in Nonparametric Instrumental Variable Estimation," Mathematics, MDPI, vol. 13(1), pages 1-20, December.
    11. Davies, Neil & Dickson, Matt & Smith, George Davey & Windmeijer, Frank & van den Berg, Gerard J., 2019. "The Causal Effects of Education on Adult Health, Mortality and Income: Evidence from Mendelian Randomization and the Raising of the School Leaving Age," IZA Discussion Papers 12192, Institute of Labor Economics (IZA).
    12. Kitagawa, Toru, 2021. "The identification region of the potential outcome distributions under instrument independence," Journal of Econometrics, Elsevier, vol. 225(2), pages 231-253.
    13. Moler-Zapata, S.; & Grieve, R.; & Basu, A.; & O'Neill, S.;, 2022. "How does a local Instrumental Variable Method perform across settings with instruments of differing strengths? A simulation study and an evaluation of emergency surgery," Health, Econometrics and Data Group (HEDG) Working Papers 22/18, HEDG, c/o Department of Economics, University of York.
    14. Chuhui Li & Donald S. Poskitt & Frank Windmeijer & Xueyan Zhao, 2022. "Binary outcomes, OLS, 2SLS and IV probit," Econometric Reviews, Taylor & Francis Journals, vol. 41(8), pages 859-876, September.
    15. Maarten J. Bijlsma & Ben Wilson, 2017. "Modelling the socio-economic determinants of fertility: a mediation analysis using the parametric g-formula," MPIDR Working Papers WP-2017-013, Max Planck Institute for Demographic Research, Rostock, Germany.
    16. 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.
    17. Menon, Seetha, 2014. "Unfinished lives: the effect of domestic violence on neonatal & infant mortality," ISER Working Paper Series 2014-27, Institute for Social and Economic Research.
    18. Jarke-Neuert, Johannes & Perino, Grischa & Schwickert, Henrike, 2021. "Free-Riding for Future: Field Experimental Evidence of Strategic Substitutability in Climate Protest," SocArXiv sh6dm, Center for Open Science.
    19. Taylor, Amy E. & Davies, Neil M. & Ware, Jennifer J. & VanderWeele, Tyler & Smith, George Davey & Munafò, Marcus R., 2014. "Mendelian randomization in health research: Using appropriate genetic variants and avoiding biased estimates," Economics & Human Biology, Elsevier, vol. 13(C), pages 99-106.
    20. Myoung‐jae Lee, 2021. "Instrument residual estimator for any response variable with endogenous binary treatment," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(3), pages 612-635, July.
    21. Berhanu, Wassie, 2011. "Recurrent shocks, poverty traps and the degradation of pastoralists’ social capital in southern Ethiopia," African Journal of Agricultural and Resource Economics, African Association of Agricultural Economists, vol. 6(01), pages 1-15, March.
    22. Ditte Nørbo Sørensen & Torben Martinussen & Eric Tchetgen Tchetgen, 2019. "A causal proportional hazards estimator under homogeneous or heterogeneous selection in an IV setting," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(4), pages 639-659, October.
    23. Stephan, Gesine & van den Berg, Gerard & Homrighausen, Pia, 2016. "Randomizing information on a targeted wage support program for older workers: A field experiment," VfS Annual Conference 2016 (Augsburg): Demographic Change 145487, Verein für Socialpolitik / German Economic Association.
    24. Robert Carroll & Chris Metcalfe & Sarah Steeg & Neil M Davies & Jayne Cooper & Nav Kapur & David Gunnell, 2016. "Psychosocial Assessment of Self-Harm Patients and Risk of Repeat Presentation: An Instrumental Variable Analysis Using Time of Hospital Presentation," PLOS ONE, Public Library of Science, vol. 11(2), pages 1-13, February.
    25. Goeun Lee & Myoung-jae Lee, 2023. "Regression Discontinuity for Binary Response and Local Maximum Likelihood Estimator to Extrapolate Treatment," Evaluation Review, , vol. 47(2), pages 182-208, April.

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    More about this item

    Keywords

    bounds; causal inference; generalized method of moments; local average treatment effects; marginal structural models; non-compliance; parameter identification; potential outcomes; structural mean models; structural models;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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