  Instrumental variables (IV) regression is a popular method for the estimation
of the endogenous treatment effects. Conventional IV methods require all the
instruments are relevant and valid. However, this is impractical especially in
high-dimensional models when we consider a large set of candidate IVs. In this
paper, we propose an IV estimator robust to the existence of both the invalid
and irrelevant instruments (called R2IVE) for the estimation of endogenous
treatment effects. This paper extends the scope of Kang et al. (2016) by
considering a true high-dimensional IV model and a nonparametric reduced form
equation. It is shown that our procedure can select the relevant and valid
instruments consistently and the proposed R2IVE is root-n consistent and
asymptotically normal. Monte Carlo simulations demonstrate that the R2IVE
performs favorably compared to the existing high-dimensional IV estimators
(such as, NAIVE (Fan and Zhong, 2018) and sisVIVE (Kang et al., 2016)) when
invalid instruments exist. In the empirical study, we revisit the classic
question of trade and growth (Frankel and Romer, 1999).
