Nonparametric instrumental variables (NPIV) estimators are highly sensitive to the failure of instrumental validity. We show that even an arbitrarily small deviation from full instrumental validity can lead to an arbitrarily large asymptotic bias for a broad class of NPIV estimators. Strong smoothness conditions on the structural function can mitigate this problem. Unfortunately, if the researcher allows for an arbitrarily small failure of instrumental validity then the failure of such a smoothness condition is generally not testable and in fact one cannot identify any upper bound on the magnitude of the failure. To address these problems we propose an alternative method in which the structural function is treated as partially identified . Under our procedure the researcher achieves robust confidence sets using a priori bounds on the deviation from instrumental validity and approximation error. Our procedure is based on the sieve-minimum distance method and has an added advantage in that it reduces the need to choose the size of the sieve space either directly or algorithmically. We also present a related method that allows the researcher to assess the sensitivity of their NPIV estimates to misspecification. This sensitivity analysis can inform the choice of sieve space in point estimation .
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) .
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Unfortunately, if the researcher allows for an arbitrarily small failure of instrumental validity then the failure of such a smoothness condition is generally not testable and in fact one cannot identify any upper bound on the magnitude of the failure. To address these problems we propose an alternative method in which
However, we show that in general the smoothness assumptions cannot be confirmed empirically. In response, we treat
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and construct a consistent estimator of the identified set under
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deviation from instrumental validity and approximation error. Our procedure is based on the sieve-minimum distance method and has an added advantage in that it reduces the need to choose the size of the sieve space either directly or algorithmically. We also present a related method that
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researcher to assess the sensitivity of their NPIV estimates to misspecification. This sensitivity analysis can inform the choice of sieve space in point estimation
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)