Deep Partial Least Squares for Instrumental Variable Regression

TL;DR

This paper introduces a deep partial least squares method for high-dimensional nonlinear instrumental variable regression, combining dimension reduction with neural networks, and demonstrates its superior performance on synthetic and real data.

Contribution

It develops a novel deep partial least squares approach that effectively performs feature selection and dimension reduction in nonlinear instrumental variable regression.

Findings

Outperforms related methods on synthetic datasets.

Shows significant improvements in real-world application.

Provides theoretical guarantees for feature selection consistency.

Abstract

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.