Kernel Single Proxy Control for Deterministic Confounding

TL;DR

This paper introduces kernel-based methods to estimate causal effects from a single proxy variable under deterministic outcome assumptions, extending causal inference to continuous treatments.

Contribution

It demonstrates that causal effects can be recovered from a single proxy with deterministic outcomes, generalizing previous methods to continuous treatments.

Findings

Both proposed methods consistently estimate causal effects.

Successful recovery of causal effects demonstrated on synthetic benchmarks.

Methods outperform existing approaches in challenging scenarios.

Abstract

We consider the problem of causal effect estimation with an unobserved confounder, where we observe a single proxy variable that is associated with the confounder. Although it has been shown that the recovery of an average causal effect is impossible in general from a single proxy variable, we show that causal recovery is possible if the outcome is generated deterministically. This generalizes existing work on causal methods with a single proxy variable to the continuous treatment setting. We propose two kernel-based methods for this setting: the first based on the two-stage regression approach, and the second based on a maximum moment restriction approach. We prove that both approaches can consistently estimate the causal effect, and we empirically demonstrate that we can successfully recover the causal effect on challenging synthetic benchmarks.