Distributional Instrumental Variable Method

The instrumental variable (IV) approach is commonly used to infer causal effects in the presence of unmeasured confounding. Conventional IV models commonly make the additive noise assumption, which is hard to ensure in practice, but also typically lack flexibility if the causal effects are complex. Further, the vast majority of the existing methods aims to estimate the mean causal effects only, a few other methods focus on the quantile effects. This work aims for estimation of the entire interventional distribution. We propose a novel method called distributional instrumental variables (DIV), which leverages generative modelling in a nonlinear instrumental variable setting. We establish identifiability of the interventional distribution under general assumptions and demonstrate an `under-identified' case where DIV can identify the causal effects while two-step least squares fails to. Our empirical results show that the DIV method performs well for a broad range of simulated data, exhibiting advantages over existing IV approaches in terms of the identifiability and estimation error of the mean or quantile treatment effects. Furthermore, we apply DIV to an economic data set to examine the causal relation between institutional quality and economic development and our results that closely align with the original study. We also apply DIV to a single-cell data set, where we study the generalizability and stability in predicting gene expression under unseen interventions. The software implementations of DIV are available in R and Python.