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 mitigate this problem. However, we show that in general the smoothness assumptions cannot be confirmed empirically . In response, we treat the structural function as partially identified and construct a consistent estimator of the identified set  under bounds on the degree of misspecification.  Our proposed technique is a practical alternative to standard NPIV estimation and allows the researcher to make meaningful inferences about the structural function when  misspecification cannot ruled out. The method is easy to implement and computationally light. The first stage resembles that of sieve minimum-distance estimation, and the second stage requires numerical solution of a linear programming problem. In contrast to existing methods our second stage does not require that the researcher choose any penalty function, penalty parameter nor a particular dimension of a sieve space. To compare our method to existing approaches we present an empirical application based on Horowitz (2011)  .
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 .
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mitigate this
reduce the severity of the
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we show that in general the smoothness assumptions cannot be confirmed empirically
if the smoothness conditions are too strong then imposing them imparts bias
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and robust confidence bands
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The set estimator can interpreted as error bounds on a point estimator and used to perform sensitivity analysis.
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NPIV estimation
methods
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some
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The method
Our procedure
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requires numerical solution of a linear programming problem. In contrast to existing methods our second stage does not require that the researcher choose any penalty function, penalty parameter nor a particular dimension of a sieve space. To compare our method to existing approaches we present an empirical application based on
is formulated as a linear program. We apply our methods to the empirical setting of Blundell et al. (2007) and
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who estimate shape-invariant Engel curves