Exploiting Independent Instruments: Identification and Distribution Generalization

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. Posing an independence condition, however, leads to strictly stronger identifiability results. We connect to existing literature in econometrics and provide a practical method 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 worstcase 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.

Identifying Causal Effects using Instrumental Time Series: Nuisance IV and Correcting for the Past

“…Finally, as for the i.i.d. case (Imbens and Newey, 2009;Chesher, 2003;Saengkyongam et al, 2022), considering (higher order) independence, rather than vanishing covariances may yield stronger identifiability results but may come with computational and statistical challenges.…”