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Nonparametric Instrumental Variables Estimation Under Misspecification

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Document pages: 57 pages

Abstract: We show that nonparametric instrumental variables (NPIV) estimators arehighly sensitive to misspecification: an arbitrarily small deviation frominstrumental validity can lead to large asymptotic bias for a broad class ofestimators. One can mitigate the problem by placing strong restrictions on thestructural function in estimation. However, if the true function does not obeythe restrictions then imposing them imparts bias. Therefore, there is atrade-off between the sensitivity to invalid instruments and bias from imposingexcessive restrictions. In light of this trade-off we propose a partialidentification approach to estimation in NPIV models. We provide a pointestimator that minimizes the worst-case asymptotic bias and error-bounds thatexplicitly account for some degree of misspecification. We apply our methods tothe empirical setting of Blundell et al. (2007) and Horowitz (2011) to estimateshape-invariant Engel curves.

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