Nonparametric instrumental variables estimators are highly sensitive to the failure of instrumental validity. 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 . However, if the smoothness conditions are too strong then imposing them imparts bias. In response, we treat the structural function as partially identified and construct a consistent estimator of the identified set and robust confidence bands under bounds on the degree of misspecification. The set estimator can interpreted as error bounds on a point estimator and used to perform sensitivity analysis. Our proposed technique is a practical alternative to standard methods and allows the researcher to make meaningful inferences about the structural function when some misspecification cannot ruled out. Our procedure is easy to implement and computationally light. The first stage resembles that of sieve minimum-distance estimation, and the second stage is formulated as a linear program . We apply our methods to the empirical setting of Blundell et al. (2007) and Horowitz (2011) who estimate shape-invariant Engel curves.
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.
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We show that nonparametric
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the failure of instrumental validity. An
misspecification: an
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many NPIV estimators. Imposing strong smoothness conditions
a broad class of estimators. The problem is mitigated if strong restrictions
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may reduce the severity of the problem
are imposed in estimation
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smoothness conditions are too strong
true function does not obey the restrictions,
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In response, we treat the structural function as partially identified and construct a consistent estimator of the identified set and robust confidence bands under bounds on the degree of misspecification. The set estimator can interpreted as error bounds on a point estimator and used to perform sensitivity analysis. Our proposed technique is a practical alternative to standard methods and allows the researcher to make meaningful
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
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when some misspecification cannot ruled out. Our procedure is easy to implement and computationally light. The first stage resembles that of sieve minimum-distance estimation, and the second stage is formulated as a linear program
that are valid under a small failure of instrumental validity. We construct a simple, consistent estimator of the identified set
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