Before revision:  We propose a partial identification approach that allows a researcher to explicitly and transparently examine this trade-off and make inferences about the structural function that are valid under a small failure of instrumental validity. We construct a simple, consistent estimator of the identified set .
After revision:  We propose a partial identification approach to estimation in NPIV models. We provide a point estimator that minimizes the worst-case asymptotic bias and error-bounds that explicitly account for some degree of misspecification .