Nonparametric Additive Instrumental Variable Estimator: A Group Shrinkage Estimation Perspective

Qingliang (Michael) Fan and Wei Zhong

No 2018-052, IRTG 1792 Discussion Papers from Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series"

Abstract: In this article, we study a nonparametric approach regarding a general nonlinear reduced form equation to achieve a better approximation of the optimal instrument. Accordingly, we propose the nonparametric additive instrumental variable estimator (NAIVE) with the adaptive group Lasso.We theoretically demonstrate that the proposed estimator is root-n consistent and asymptotically normal. The adaptive group Lasso helps us select the valid instruments while the dimensionality of potential instrumental variables is allowed to be greater than the sample size. In practice, the degree and knots of B-spline series are selected by minimizing the BIC or EBIC criteria for each nonparametric additive component in the reduced form equation. In Monte Carlo simulations, we show that the NAIVE has the same performance as the linear instrumental variable (IV) estimator for the truly linear reduced form equation. On the other hand, the NAIVE performs much better in terms of bias and mean squared errors compared to other alternative estimators under the high-dimensional nonlinear reduced form equation. We further illustrate our method in an empirical study of international trade and growth. Our findings provide

Keywords: Adaptive group Lasso; Instrumental variables; Nonparametric additive model; Optimal estimator; Variable selection (search for similar items in EconPapers)
JEL-codes: C00 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

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Journal Article: Nonparametric Additive Instrumental Variable Estimator: A Group Shrinkage Estimation Perspective (2018)
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:irtgdp:2018052

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