A Class of Algorithms for General Instrumental Variable Models

TL;DR

This paper introduces a new class of algorithms for bounding causal effects in general instrumental variable models, especially with continuous treatments, using gradient-based optimization to handle complex, intractable problems.

Contribution

It develops a flexible bounding method that accommodates continuous treatments and allows for a continuum of assumptions, improving over existing additive error models.

Findings

Bounds accurately capture causal effects where additive methods fail.

Method works on synthetic and real-world data, demonstrating practical utility.

Provides a range of causal effect estimates consistent with observed data.

Abstract

Causal treatment effect estimation is a key problem that arises in a variety of real-world settings, from personalized medicine to governmental policy making. There has been a flurry of recent work in machine learning on estimating causal effects when one has access to an instrument. However, to achieve identifiability, they in general require one-size-fits-all assumptions such as an additive error model for the outcome. An alternative is partial identification, which provides bounds on the causal effect. Little exists in terms of bounding methods that can deal with the most general case, where the treatment itself can be continuous. Moreover, bounding methods generally do not allow for a continuum of assumptions on the shape of the causal effect that can smoothly trade off stronger background knowledge for more informative bounds. In this work, we provide a method for causal effect bounding in continuous distributions, leveraging recent advances in gradient-based methods for the optimization of computationally intractable objective functions. We demonstrate on a set of synthetic and real-world data that our bounds capture the causal effect when additive methods fail, providing a useful range of answers compatible with observation as opposed to relying on unwarranted structural assumptions.