Before revision:  An arbitrarily small deviation from instrumental validity can lead to large asymptotic bias for many NPIV estimators. Imposing strong smoothness conditions on the structural function may reduce the severity of the problem .
After revision:  An arbitrarily small deviation from instrumental validity can lead to large asymptotic bias for a broad class of estimators. The problem is mitigated if strong restrictions on the structural function may reduce the severity of the problem .