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.

翻译：本文提出深度偏最小二乘法，用于高维非线性工具变量回归的估计。作为灵活深度神经网络架构的前置方法，本方法利用偏最小二乘法对工具变量集合及协变量进行降维与特征选择。基于Brillinger(2012)的核心理论结果证明，偏最小二乘法提供的特征选择具有一致性，且权重估计可达到比例常数尺度。我们通过具有稀疏关联网络结构的合成数据集验证该方法，并基于Angrist与Evans (1996)的经典数据将其应用于生育对母亲劳动力供给影响的实证分析。合成数据与实证应用结果表明，深度偏最小二乘法显著优于其他相关方法。最后，我们提出未来研究方向。