Deep Partial Least Squares for IV Regression

In this paper, we propose deep partial least squares for the estimation of high-dimensional nonlinear IV regression. As a precursor to a flexible deep neural network architecture, our methodology uses partial least squares (PLS) for dimension reduction and feature selection from the set of instruments and covariates. A central theoretical result, due to Brillinger, shows that the feature selection provided by PLS 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, together with 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.