Instrumental Variables Estimation with Some Invalid Instruments and its Application to Mendelian Randomization∗

Instrumental variables have been widely used for estimating the causal effect be-tween exposure and outcome. Conventional estimation methods require complete knowledge about all the instruments ’ validity; a valid instrument must not have a direct effect on the outcome and not be related to unmeasured confounders. Often, this is impractical as highlighted by Mendelian randomization studies where genetic markers are used as instruments and complete knowledge about instruments ’ validity is equivalent to complete knowledge about the involved genes ’ functions. In this paper