Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series


Nonparametric Additive Instrumental Variable Estimator: A Group Shrinkage Estimation Perspective

Qingliang Fan
Wei Zhong

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

Adaptive group Lasso; Instrumental variables; Nonparametric additive model; Optimal
estimator; Variable selection.

JEL Classification: