Aim: To investigate the performance of semi-parametric methods for instrumental variable estimation (specificially the generalized method of moments, GMM, and structural mean models, SMM) with weak instruments.

Hypothesis: The use of weak instruments in a semi-parametric framework may lead to weak identification (that is, the optimization criterion for determining the value of the parameter estimates may be satisfied or nearly satisfied at multiple values of the parameters).

Methods: The performance of these estimators will be considered using simulated data as well as data from the ALSPAC study on the causal association of body mass index on the probability of early menarche using genetic variants associated with body mass index.

Exposure variable: Body mass index (measured at age 7.5).

Outcome variable: Early menarche (before 12 years). This variable has already been derived by RG.