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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

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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.

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Bibliographic Info

Paper provided by Department of Economics, University of Bristol, UK in its series The Centre for Market and Public Organisation with number 11/266.

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Length: 31 pages
Date of creation: Aug 2011
Date of revision:
Handle: RePEc:bri:cmpowp:11/266

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Keywords: Structural Mean Models; Multiple Instrumental Variables; Generalised Method of Moments; Mendelian Randomisation; Local Average Treatment Effects;

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  1. Joshua D. Angrist, 2000. "Estimation of Limited-Dependent Variable Models with Dummy Endogenous Regressors: Simple Strategies for Empirical Practice," NBER Technical Working Papers 0248, National Bureau of Economic Research, Inc.
  2. 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.
  3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  4. 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.
  5. 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.
  6. 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.
  7. Pierre Chaussé, . "Computing Generalized Method of Moments and Generalized Empirical Likelihood with R," Journal of Statistical Software, American Statistical Association, vol. 34(i11).
  8. 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.
  9. 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.
  10. 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.
  11. 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.
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