Deep Generalized Method of Moments for Instrumental Variable Analysis

TL;DR

DeepGMM introduces a scalable, efficient deep learning-based approach for instrumental variable analysis, effectively handling high-dimensional and complex causal effect estimation problems where traditional methods struggle.

Contribution

The paper presents DeepGMM, a novel variational reformulation of GMM that enables efficient control of many moment conditions and high-dimensional data in instrumental variable analysis.

Findings

Matches performance of best tuned methods in standard settings

Effective in high-dimensional scenarios where recent methods fail

Computationally tractable for large-scale datasets

Abstract

Instrumental variable analysis is a powerful tool for estimating causal effects when randomization or full control of confounders is not possible. The application of standard methods such as 2SLS, GMM, and more recent variants are significantly impeded when the causal effects are complex, the instruments are high-dimensional, and/or the treatment is high-dimensional. In this paper, we propose the DeepGMM algorithm to overcome this. Our algorithm is based on a new variational reformulation of GMM with optimal inverse-covariance weighting that allows us to efficiently control very many moment conditions. We further develop practical techniques for optimization and model selection that make it particularly successful in practice. Our algorithm is also computationally tractable and can handle large-scale datasets. Numerical results show our algorithm matches the performance of the best tuned methods in standard settings and continues to work in high-dimensional settings where even recent methods break.