Primary Submission Category: Sensitivity Analysis
Identification Limits of Proximal Inference: Sharp Closed-Form Bounds
Authors: Guilherme Duarte,
Presenting Author: Guilherme Duarte*
Proximal causal inference exploits proxy variables to address unobserved confounding, but existing results largely focus on point identification under strong completeness or functional assumptions. This paper studies the identification limits of proximal inference when only a unique proxy is available and shows that, in this setting, the average treatment effect (ATE) is generally partially identified. We derive the first sharp bounds for the ATE in this class of proximal models and show that the bounds admit closed-form expressions. Sharpness is established by explicitly characterizing all observationally equivalent data-generating processes consistent with the proximal assumptions. The analysis reveals that the identified set arises from slackness in an associated cubic program, providing a transparent geometric interpretation of the failure of point identification. We further characterize the magnitude of the bias induced by adjusting for proxies rather than the latent confounder itself, thereby quantifying the limits of proxy-based adjustment. These results clarify the informational content of proximal assumptions and position partial identification as an inherent feature of proximal causal inference with limited proxy information.