  The relevance condition of Integrated Conditional Moment (ICM) estimators is
significantly weaker than the conventional IV's in at least two respects: (1)
consistent estimation without excluded instruments is possible, provided
endogenous covariates are non-linearly mean-dependent on exogenous covariates,
and (2) endogenous covariates may be uncorrelated with but mean-dependent on
instruments. These remarkable properties notwithstanding, multiplicative-kernel
ICM estimators suffer diminished identification strength, large bias, and
severe size distortions even for a moderately sized instrument vector. This
paper proposes a computationally fast linear ICM estimator that better
preserves identification strength in the presence of multiple instruments and a
test of the ICM relevance condition. Monte Carlo simulations demonstrate a
considerably better size control in the presence of multiple instruments and a
favourably competitive performance in general. An empirical example illustrates
the practical usefulness of the estimator, where estimates remain plausible
when no excluded instrument is used.
