Exploiting Independent Instruments: Identification and Distribution Generalization
This work addresses causal inference challenges for researchers and practitioners in fields like econometrics and machine learning, offering incremental improvements by leveraging independence for better identifiability and generalization.
The paper tackles the problem of identifying causal functions in instrumental variable models with unobserved confounding by exploiting independence assumptions, leading to stronger identifiability and distribution generalization. It introduces a practical method called HSIC-X, which is proven to be invariant to distributional shifts on instruments and worst-case optimal under strong shifts, even in under-identified cases.
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.