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

Paul Clarke, Tom Palmer and Frank Windmeijer

The Centre for Market and Public Organisation from The Centre for Market and Public Organisation, University of Bristol, UK

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.

Keywords: Structural Mean Models; Multiple Instrumental Variables; Generalised Method of Moments; Mendelian Randomisation; Local Average Treatment Effects (search for similar items in EconPapers)
JEL-codes: C13 C14 C26 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2011-08
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Related works:
Working Paper: Estimating structural mean models with multiple instrumental variables using the generalised method of moments (2012)
Working Paper: Estimating structural mean models with multiple instrumental variables using the generalised method of moments (2011)
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