Instrumental variable estimates of causal effects can be biased when using many instruments that are only weakly
associated with the exposure. We describe several techniques to reduce this bias and estimate corrected standard errors. We present our findings using a simulation study and an empirical application. For the latter, we
estimate the effect of height on lung function, using genetic variants as instruments for height. Our simulation
study demonstrates that, using many weak individual variants, two-stage least squares (2SLS) is biased, whereas
the limited information maximum likelihood (LIML) and the continuously updating estimator (CUE) are unbiased and have accurate rejection frequencies when standard errors are corrected for the presence of many weak
instruments. Our illustrative empirical example uses data on 3631 children from England. We used 180 genetic
variants as instruments and compared conventional ordinary least squares estimates with results for the 2SLS,
LIML, and CUE instrumental variable estimators using
