On Deep Instrumental Variables Estimate

• Activity Number: 234 - New Challenges in Statistical Learning and Inference for Complex Data
• Type: Topic Contributed
• Date/Time: Tuesday, August 9, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Section for Statistical Programmers and Analysts
• Author(s): Ruiqi Liu* and Zuofeng Shang and Guang Cheng
• Companies: Texas Tech University and New Jersey Institute of Technology and Purdue University
• Keywords: Statistical Deep Learning; Instrumental Variable Regression

Abstract

The endogeneity issue is fundamentally important as many empirical applications may suffer from the omission of explanatory variables, measurement error, or simultaneous causality. Recently, \cite{hllt17} propose a "Deep Instrumental Variable (IV)" framework based on deep neural networks to address endogeneity, demonstrating superior performances to existing approaches. The aim of this paper is to theoretically understand the empirical success of the Deep IV. Specifically, we consider a two-stage estimator using deep neural networks in the linear instrumental variables model. By imposing a latent structural assumption on the reduced form equation between endogenous variables and instrumental variables, the estimator can automatically capture this latent structure and converge to the optimal instruments at the minimax optimal rate, which is free of the dimension of instrumental variables and thus mitigates the curse of dimensionality. Numerical studies on synthetic data and an application to evaluating 401(k) plans confirm our theory.