  Instrumental variable (IV) regression can be approached through its
formulation in terms of conditional moment restrictions (CMR). Building on
variants of the generalized method of moments, most CMR estimators are
implicitly based on approximating the population data distribution via
reweightings of the empirical sample. While for large sample sizes, in the
independent identically distributed (IID) setting, reweightings can provide
sufficient flexibility, they might fail to capture the relevant information in
presence of corrupted data or data prone to adversarial attacks. To address
these shortcomings, we propose the Sinkhorn Method of Moments, an optimal
transport-based IV estimator that takes into account the geometry of the data
manifold through data-derivative information. We provide a simple plug-and-play
implementation of our method that performs on par with related estimators in
standard settings but improves robustness against data corruption and
adversarial attacks.
