Each week, we select a recently published Open Access article to feature. This week’s article comes from Applied Stochastic Models in Business and Industry   and proposes deep partial least squares for estimating instrumental variable regression. 

The article’s abstract is given below, with the full article available to read here.

Nareklishvili, M, Polson, N, Sokolov, V. Deep partial least squares for instrumental variable regression. Appl Stochastic Models Bus Ind. 2023; 1– 21. doi: 10.1002/asmb.2787

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) Selected Works of Daving Brillinger. 589-606, 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 Chernozhukov et al. Ann Rev Econ. (2015b):649–688. 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.