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Estimating Structural Mean Models with Multiple Instrumental Variables using the Generalised Method of Moments

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  • Paul S. Clarke
  • Tom M. Palmer
  • Frank Windmeijer

Abstract

Instrumental variables analysis using genetic markers as instruments is now a widely used technique in epidemiology and biostatistics. As single markers tend to explain only a small proportion of phenotypical variation, there is increasing interest in using multiple genetic markers to obtain more precise estimates of causal parameters. Structural mean models (SMMs) are semi-parametric models that use instrumental variables to identify causal parameters, but there has been little work on using these models with multiple instruments, particularly for multiplicative and logistic SMMs. In this paper, we show how additive, multiplicative and logistic SMMs with multiple discrete instrumental variables can be estimated efficiently using the generalised method of moments (GMM) estimator, how the Hansen J-test can be used to test for model mis-specification, and how standard GMM software routines can be used to fit SMMs. We further show that multiplicative SMMs, like the additive SMM, identify a weighted average of local causal effects if selection is monotonic. We use these methods to reanalyse a study of the relationship between adiposity and hypertension using SMMs with two genetic markers as instruments for adiposity. We find strong effects of adiposity on hypertension, but no evidence of unobserved confounding.

Suggested Citation

  • Paul S. Clarke & Tom M. Palmer & Frank Windmeijer, 2011. "Estimating Structural Mean Models with Multiple Instrumental Variables using the Generalised Method of Moments," The Centre for Market and Public Organisation 11/266, The Centre for Market and Public Organisation, University of Bristol, UK.
    • Handle: RePEc:bri:cmpowp:11/266
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    References listed on IDEAS

    as
    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. James Robins & Andrea Rotnitzky, 2004. "Estimation of treatment effects in randomised trials with non-compliance and a dichotomous outcome using structural mean models," Biometrika, Biometrika Trust, vol. 91(4), pages 763-783, December.
    3. Todd, Petra, 2001. "Estimations of Limited Dependent Variable Models with Dummy Endogenous Regressors: Simple Strategies for Empirical Practice: Comment," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 25-27, January.
    4. Angrist, Joshua D, 2001. "Estimations of Limited Dependent Variable Models with Dummy Endogenous Regressors: Simple Strategies for Empirical Practice," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 2-16, January.
    5. Chaussé, Pierre, 2010. "Computing Generalized Method of Moments and Generalized Empirical Likelihood with R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 34(i11).
    6. Tan, Zhiqiang, 2010. "Marginal and Nested Structural Models Using Instrumental Variables," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 157-169.
    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. S. Vansteelandt & E. Goetghebeur, 2003. "Causal inference with generalized structural mean models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(4), pages 817-835, November.
    9. Moffitt, Robert A, 2001. "Estimations of Limited Dependent Variable Models with Dummy Endogenous Regressors: Simple Strategies for Empirical Practice: Comment," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 20-23, January.
    10. Angrist, Joshua D, 2001. "Estimations of Limited Dependent Variable Models with Dummy Endogenous Regressors: Simple Strategies for Empirical Practice: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 27-28, January.
    11. Mark J. Van Der Laan & Alan Hubbard & Nicholas P. Jewell, 2007. "Estimation of treatment effects in randomized trials with non‐compliance and a dichotomous outcome," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 463-482, June.
    12. Imbens, Guido W, 2001. "Estimations of Limited Dependent Variable Models with Dummy Endogenous Regressors: Simple Strategies for Empirical Practice: Comment," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 17-20, January.
    13. Mullahy, John, 2001. "Estimations of Limited Dependent Variable Models with Dummy Endogenous Regressors: Simple Strategies for Empirical Practice: Comment," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 23-25, January.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Structural Mean Models; Multiple Instrumental Variables; Generalised Method of Moments; Mendelian Randomisation; Local Average Treatment Effects;
    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
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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