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Nonparametric Instrumental Variables Estimation Under Misspecification

Ben Deaner ()

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Abstract: 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.

New Economics Papers: this item is included in nep-ecm
Date: 2019-01, Revised 2019-06
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Handle: RePEc:arx:papers:1901.01241