  Matching on covariates is a well-established framework for estimating causal
effects in observational studies. The principal challenge stems from the often
high-dimensional structure of the problem. Many methods have been introduced to
address this, with different advantages and drawbacks in computational and
statistical performance as well as interpretability. This article introduces a
natural optimal matching method based on multimarginal unbalanced optimal
transport that possesses many useful properties in this regard. It provides
interpretable weights based on the distance of matched individuals, can be
efficiently implemented via the iterative proportional fitting procedure, and
can match several treatment arms simultaneously. Importantly, the proposed
method only selects good matches from either group, hence is competitive with
the classical k-nearest neighbors approach in terms of bias and variance in
finite samples. Moreover, we prove a central limit theorem for the empirical
process of the potential functions of the optimal coupling in the unbalanced
optimal transport problem with a fixed penalty term. This implies a parametric
rate of convergence of the empirically obtained weights to the optimal weights
in the population for a fixed penalty term.
