Two Stage Curvature Identification with Machine Learning: Causal Inference with Possibly Invalid Instrumental Variables

Instrumental variables regression is a popular causal inference method for endogenous treatment. A significant concern in practical applications is the validity and strength of instrumental variables. This paper aims to perform causal inference when all instruments are possibly invalid. To do this, we propose a novel methodology called two stage curvature identification (TSCI) together with a generalized concept to measure the strengths of possibly invalid instruments: such invalid instruments can still be used for inference in our framework. We fit the treatment model with a general machine learning method and propose a novel bias correction method to remove the overfitting bias from machine learning methods. Among a collection of spaces of violation functions, we choose the best one by evaluating invalid instrumental variables' strength. We demonstrate our proposed TSCI methodology in a large-scale simulation study and revisit the important economics question on the effect of education on earnings.