Robustness Against Weak or Invalid Instruments: Exploring Nonlinear Treatment Models with Machine Learning

• URL: http://arxiv.org/abs/2203.12808v4
• Date: Fri, 5 Jan 2024 04:21:55 GMT
• Title: Robustness Against Weak or Invalid Instruments: Exploring Nonlinear Treatment Models with Machine Learning
• Authors: Zijian Guo and Mengchu Zheng and Peter B\"uhlmann
• Abstract summary: We discuss causal inference for observational studies with possibly invalid instrumental variables. We propose a novel methodology called two-stage curvature identification (TSCI) by exploring the nonlinear treatment model with machine learning.
• Score: 1.3022753212679383
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We discuss causal inference for observational studies with possibly invalid instrumental variables. We propose a novel methodology called two-stage curvature identification (TSCI) by exploring the nonlinear treatment model with machine learning. {The first-stage machine learning enables improving the instrumental variable's strength and adjusting for different forms of violating the instrumental variable assumptions.} The success of TSCI requires the instrumental variable's effect on treatment to differ from its violation form. A novel bias correction step is implemented to remove bias resulting from the potentially high complexity of machine learning. Our proposed \texttt{TSCI} estimator is shown to be asymptotically unbiased and Gaussian even if the machine learning algorithm does not consistently estimate the treatment model. Furthermore, we design a data-dependent method to choose the best among several candidate violation forms. We apply TSCI to study the effect of education on earnings.

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