Omitted Variable Bias in Machine-Learned Causal Models

• Activity Number: 487 - Novel Causal Inference Methods for Epidemiology Studies
• Type: Contributed
• Date/Time: Wednesday, August 10, 2022 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Victor Chernozhukov and Carlos Cinelli* and Whitney Newey and Amit Sharma and Vasilis Syrgkanis
• Companies: MIT Economics and University of Washington and MIT Economics and Microsoft and Microsoft Research
• Keywords: causal inference; omitted variable bias; sensitivity analysis; bounds; debiased machine learning

Abstract

We derive general, yet simple, bounds on the size of the omitted variable bias for a broad class of causal parameters that can be identified as linear functionals of the conditional expectation function of the outcome. Such functionals encompass many of the traditional targets of investigation in causal inference studies, such as, for example, average of potential outcomes, average treatment effects, or average causal derivatives – all for general, nonparametric causal models. Our construction relies on the Riesz-Frechet representation of the target functional. Specifically, we show how the bounds depend only on the additional variation that the latent variables create both in the outcome and in the Riesz representer for the parameter of interest. Moreover, in many important cases (e.g, average treatment effects in partially linear models, or in nonseparable models with a binary treatment) the bound is shown to depend on two easily interpretable quantities: the nonparametric partial R2 of the unobserved variables with the treatment and with the outcome. Finally, we provide flexible and efficient statistical inference methods to estimate such bounds using Debiased Machine Learning.