  In this paper, we propose deep partial least squares for the estimation of
high-dimensional nonlinear instrumental variable regression. As a precursor to
a flexible deep neural network architecture, our methodology uses partial least
squares for dimension reduction and feature selection from the set of
instruments and covariates. A central theoretical result, due to Brillinger
(2012) shows that the feature selection provided by partial least squares is
consistent and the weights are estimated up to a proportionality constant. We
illustrate our methodology with synthetic datasets with a sparse and correlated
network structure and draw applications to the effect of childbearing on the
mother's labor supply based on classic data of Angrist and Evans (1996). The
results on synthetic data as well as applications show that the deep partial
least squares method significantly outperforms other related methods. Finally,
we conclude with directions for future research.
