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Nonparametric Instrumental Variables Estimation Under Misspecification

Ben Deaner ()

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Abstract: 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.

Date: 2019-01, Revised 2019-11
New Economics Papers: this item is included in nep-ecm
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Handle: RePEc:arx:papers:1901.01241