  This paper proposes a closed-form linear IV estimator which allows endogenous
covariates to be weakly correlated or un-correlated but mean-dependent on
instruments. Identification rests on (1) a weak uncorrelatedness exclusion
restriction and (2) a weak relevance condition where covariates are
mean-dependent on instruments. The significant weakening of the relevance
condition does not come at the cost of a stronger exclusion restriction. The
estimator is root-n-consistent and asymptotically normal. Monte Carlo
simulations show the estimator exploits unknown forms of both monotone and
non-monotone identifying variation equally well, and it incurs less bias and
size distortion relative to conventional IV methods when instruments are weak.
An empirical example illustrates the practical usefulness of the estimator.
