IV-ICL: Bounding Causal Effects with Instrumental Variables via In-Context Learning

TL;DR

This paper introduces IV-ICL, a novel in-context learning approach for Bayesian inference of causal effects with instrumental variables, providing reliable bounds efficiently across diverse data scenarios.

Contribution

IV-ICL is the first amortized Bayesian in-context learning method that directly estimates the posterior distribution of causal effects and captures the entire identified set.

Findings

IV-ICL recovers the entire identified set across various data-generating processes.

It produces more valid and informative intervals than baseline methods.

Inference time is reduced by 20-500x compared to traditional approaches.

Abstract

The instrumental-variables (IV) setting is standard for partial identification of causal effects when unobserved confounding makes point identification impossible. Existing approaches face methodological bottlenecks: closed-form bound estimands are required -- e.g., Balke-Pearl equations in binary IV -- and even when available, designing accurate estimators requires manual effort tailored to each estimand. While direct Bayesian inference of the causal effects, instead of the bounds, circumvents these challenges, it is often computationally intensive and suffers from high prior sensitivity or under-dispersed posteriors. As a remedy, we introduce IV-ICL, an amortized Bayesian in-context learning method that learns the marginal posterior distribution of the causal effects directly and derives bounds as its quantiles. Unlike standard variational inference that optimizes exclusive KL divergence, amortized Bayesian inference minimizes the expected inclusive KL, a mass-covering objective. We empirically observe that optimizing inclusive KL can recover the entire identified set across diverse data-generating processes, while exclusive-KL (e.g. with variational inference) of the same Bayesian formulation collapses onto a single mode and fails to cover the identified set. We evaluate IV-ICL on synthetic and semi-synthetic IV benchmarks and show it produces intervals that are more reliably valid and more informative compared to efficient semi-parametric, Bayesian, and plug-in baselines, at 20-500x lower inference time. Beyond methodology, we propose a procedure to convert randomized controlled trials into IV benchmarks with provably preserved ground-truth causal effects that enables a more realistic evaluation of partial-identification methods.