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<p>We aim to create the highest possible quality of treatment-control matches for
categorical data in the potential outcomes framework. </p><p>The method proposed in
this work aims to match units on a weighted Hamming distance, taking into account
the relative importance of the covariates; To match units on as many relevant variables
as possible, the algorithm creates a hierarchy of covariate combinations on which
to match (similar to downward closure), in the process solving an optimization problem
for each unit in order to construct the optimal matches. The algorithm uses a single
dynamic program to solve all of the units' optimization problems simultaneously. Notable
advantages of our method over existing matching procedures are its high-quality interpretable
matches, versatility in handling different data distributions that may have irrelevant
variables, and ability to handle missing data by matching on as many available covariates
as possible. We also adapt the matching framework by using instrumental variables
(IV) to the presence of observed categorical confounding that breaks the randomness
assumptions and propose an approximate algorithm which speedily generates high-quality
interpretable solutions.We show that our algorithms construct better matches than
other existing methods on simulated datasets, produce interesting results in applications
to crime intervention and political canvassing.</p>
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