Deep Generalized Method of Moments for Instrumental Variable Analysis
This addresses a problem in causal inference for researchers and practitioners dealing with complex, high-dimensional data, offering an incremental improvement over existing methods.
The paper tackles the challenge of estimating causal effects with instrumental variable analysis when effects are complex and instruments or treatments are high-dimensional, proposing the DeepGMM algorithm that matches best-tuned methods in standard settings and works in high-dimensional scenarios where others fail.
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.