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Instrumental Variable Estimators for Binary Outcomes

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  • Paul Clarke
  • Frank Windmeijer

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Abstract

The estimation of exposure effects on study outcomes is almost always complicated by non-random exposure selection - even randomised controlled trials can be affected by participant non-compliance. If the selection mechanism is non-ignorable then inferences based on estimators that fail to adjust for its effects will be misleading. Potentially consistent estimators of the exposure effect can be obtained if the data are expanded to include one or more instrumental variables (IVs). An IV must satisfy core conditions constraining it to be associated with the exposure, and indirectly (but not directly) associated with the outcome through this association. Here we consider IV estimators for studies in which the outcome is represented by a binary variable. While work on this problem has been carried out in statistics and econometrics, the estimators and their associated identifying assumptions have existed in the separate domains of structural models and potential outcomes with almost no overlap. In this paper, we review and integrate the work in these areas and reassess the issues of parameter identification and estimator consistency. Identification of maximum likelihood estimators comes from strong parametric modelling assumptions, with consistency depending on these assumptions being correct. Our main focus is on three semi-parametric estimators based on the generalised method of moments, marginal structural models and structural mean models (SMM). By inspecting the identifying assumptions for each method, we show that these estimators are inconsistent even if the true model generating the data is simple, and argue that this implies that consistency is obtained only under implausible conditions. Identification for SMMs can also be obtained under strong exposure-restricting design constraints that are often appropriate for randomised controlled trials, but not for observational studies. Finally, while estimation of local causal parameters is possible if the selection mechanism is monotonic, not all SMMs identify a local parameter.

Suggested Citation

  • Paul Clarke & Frank Windmeijer, 2009. "Instrumental Variable Estimators for Binary Outcomes," The Centre for Market and Public Organisation 09/209, Department of Economics, University of Bristol, UK.
  • Handle: RePEc:bri:cmpowp:09/209
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. repec:bla:jorssa:v:180:y:2017:i:2:p:569-586 is not listed on IDEAS
    3. Laing, Timothy, 2015. "Rights to the forest, REDD+ and elections: Mining in Guyana," Resources Policy, Elsevier, vol. 46(P2), pages 250-261.
    4. repec:ags:stataj:196675 is not listed on IDEAS
    5. 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.
    6. 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, Department of Economics, University of Bristol, UK.
    7. 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.
    8. 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.
    9. 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. 0(Number 1), pages 1-15, March.
    10. Stephan, Gesine & van den Berg, Gerard & Homrighausen, Pia, 2016. "Randomizing information on a targeted wage support program for older workers: A field experiment," Annual Conference 2016 (Augsburg): Demographic Change 145487, Verein für Socialpolitik / German Economic Association.
    11. Maarten J. Bijlsma & Ben Wilson, 2017. "A new approach to understanding the socio-economic determinants of fertility over the life course," MPIDR Working Papers WP-2017-013, Max Planck Institute for Demographic Research, Rostock, Germany.

    More about this item

    Keywords

    Econometrics; Generalized methods of moments; Parameter identification; Marginal structural models; Structural mean models; Structural models;

    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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