  The instrumental variable method is widely used in the health and social
sciences for identification and estimation of causal effects in the presence of
potentially unmeasured confounding. In order to improve efficiency, multiple
instruments are routinely used, leading to concerns about bias due to possible
violation of the instrumental variable assumptions. To address this concern, we
introduce a new class of g-estimators that are guaranteed to remain consistent
and asymptotically normal for the causal effect of interest provided that a set
of at least $\gamma$ out of $K$ candidate instruments are valid, for
$\gamma\leq K$ set by the analyst ex ante, without necessarily knowing the
identities of the valid and invalid instruments. We provide formal
semiparametric efficiency theory supporting our results. Both simulation
studies and applications to the UK Biobank data demonstrate the superior
empirical performance of our estimators compared to competing methods.
