Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instruments

Abstract

Negative control is a strategy for learning the causal relationship between treatment and outcome in the presence of unmeasured confounding. The treatment effect can nonetheless be identified if two auxiliary variables are available: a negative control treatment (which has no effect on the actual outcome), and a negative control outcome (which is not affected by the actual treatment). These auxiliary variables can also be viewed as proxies for a traditional set of control variables, and they bear resemblance to instrumental variables. I propose a family of algorithms based on kernel ridge regression for learning nonparametric treatment effects with negative controls. Examples include dose response curves, dose response curves with distribution shift, and heterogeneous treatment effects. Data may be discrete or continuous, and low, high, or infinite dimensional. I prove uniform consistency and provide finite sample rates of convergence. I estimate the dose response curve of cigarette smoking on infant birth weight adjusting for unobserved confounding due to household income, using a data set of singleton births in the state of Pennsylvania between 1989 and 1991.

References in corpus (4)

• An Introduction to Proximal Causal Learning
• Nonparametric estimation of causal heterogeneity under high-dimensional confounding
• Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach
• Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction

Cited by in corpus (3)

• Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach
• Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction
• Controlling for Unmeasured Confounding in Panel Data Using Minimal Bridge Functions: From Two-Way Fixed Effects to Factor Models