Bounding causal effects with leaky instruments

David Watson, Gecia Bravo-Hermsdorff, Lee M. Gunderson, Jordan Penn, Afsaneh Mastouri, Ricardo Silva

Keywords: Causality; instrumental variables; partial identification; optimization; uncertainty

TL;DR: We study the problem of causal effect estimation in the unidentifiable setting where candidate instrumental variables have some direct influence on treatment outcomes.

Abstract: Instrumental variables (IVs) are a popular and powerful tool for estimating causal effects in the presence of unobserved confounding. However, classical approaches rely on strong assumptions such as the $\textit{exclusion criterion}$, which states that instrumental effects must be entirely mediated by treatments. This assumption often fails in practice. When IV methods are improperly applied to data that do not meet the exclusion criterion, estimated causal effects may be badly biased. In this work, we propose a novel solution that provides $\textit{partial}$ identification in linear systems given a set of $\textit{leaky instruments}$, which are allowed to violate the exclusion criterion to some limited degree. We derive a convex optimization objective that provides provably sharp bounds on the average treatment effect under some common forms of information leakage, and implement inference procedures to quantify the uncertainty of resulting estimates. We demonstrate our method in a set of experiments with simulated data, where it performs favorably against the state of the art. An accompanying $\texttt{R}$ package, $\texttt{leakyIV}$, is available from $\texttt{CRAN}$.

List Of Authors: Watson, David and Penn, Jordan and Gunderson, Lee and Bravo-Hermsdorff, Gecia and Mastouri, Afsaneh and Silva, Ricardo

Code Url: https://github.com/dswatson/leakyIV/

Submission Number: 708