Exploiting Independent Instruments: Identification and Distribution Generalization

TL;DR

This paper introduces HSIC-X, a new method leveraging independence assumptions in instrumental variable models to improve causal identification, distributional robustness, and finite sample performance, even under weak instrument conditions.

Contribution

It proposes a practical independence-based estimator, HSIC-X, that enhances causal inference and distribution generalization in instrumental variable models, surpassing existing methods.

Findings

HSIC-X improves finite sample causal estimates.

The estimator is invariant to distribution shifts in instruments.

It remains effective even with under-identified instruments.

Abstract

Instrumental variable models allow us to identify a causal function between covariates $X$ and a response $Y$, even in the presence of unobserved confounding. Most of the existing estimators assume that the error term in the response $Y$ and the hidden confounders are uncorrelated with the instruments $Z$. This is often motivated by a graphical separation, an argument that also justifies independence. Positing an independence restriction, however, leads to strictly stronger identifiability results. We connect to the existing literature in econometrics and provide a practical method called HSIC-X for exploiting independence that can be combined with any gradient-based learning procedure. We see that even in identifiable settings, taking into account higher moments may yield better finite sample results. Furthermore, we exploit the independence for distribution generalization. We prove that the proposed estimator is invariant to distributional shifts on the instruments and worst-case optimal whenever these shifts are sufficiently strong. These results hold even in the under-identified case where the instruments are not sufficiently rich to identify the causal function.