Distributional Instrumental Variable Method

Music City Center 

The instrumental variable (IV) approach is commonly used to infer causal effects in the presence of unmeasured confounding. Existing methods typically aim to estimate mean causal effects, whereas a few focus on quantile treatment effects. This work aims to estimate the entire interventional distribution, which yields classical causal estimands as functionals. We propose a method called Distributional Instrumental Variable (DIV), which leverages generative modeling in a nonlinear IV setting. We establish identifiability of the interventional distribution under general assumptions and illustrate an "under-identified" case where DIV can identify causal effects while two-stage least squares fail. Empirical results show that DIV performs well across a broad range of simulated data, outperforming existing IV approaches in identifiability and estimation error for mean or quantile treatment effects. Furthermore, we apply DIV to an economic dataset to examine the causal relationship between institutional quality and economic development, finding results that align with the original study. We also apply DIV to a single-cell dataset to assess generalizability and stability in predicting gene expression under unseen interventions.

Co-authors: Anastasiia Holovchak (ETH Zurich), Sorawit Saengkyongam (ETH Zurich), Nicolai Meinshausen (ETH Zurich)