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

Deep Partial Least Squares for Instrumental Variable Regression