We show that nonparametric instrumental variables  estimators are highly sensitive to misspecification: 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 are imposed in estimation. However, if the true function does not obey the restrictions , then imposing them imparts bias. Therefore, there is a trade-off between the sensitivity to invalid instruments and bias from imposing excessive restrictions. 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 . We apply our methods to the empirical setting of Blundell et al. (2007) and Horowitz (2011) to estimate shape-invariant Engel curves.
We show that nonparametric instrumental variables (NPIV) estimators are highly sensitive to misspecification: an arbitrarily small deviation from instrumental validity can lead to large asymptotic bias for a broad class of estimators. One can mitigate the problem by placing strong restrictions on the structural function in estimation. However, if the true function does not obey the restrictions then imposing them imparts bias. Therefore, there is a trade-off between the sensitivity to invalid instruments and bias from imposing excessive restrictions. In light of this trade-off 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 . We apply our methods to the empirical setting of Blundell et al. (2007) and Horowitz (2011) to estimate shape-invariant Engel curves.
A
(NPIV)
R
The problem is mitigated if
One can mitigate the problem by placing
D
are imposed
D
,
R
We
In light of this trade-off we
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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
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