  Uncertainty in the estimation of the causal effect in observational studies
is often due to unmeasured confounding, i.e., the presence of unobserved
covariates linking treatments and outcomes. Instrumental Variables (IV) are
commonly used to reduce the effects of unmeasured confounding. Existing methods
for IV estimation either require strong parametric assumptions, use arbitrary
distance metrics, or do not scale well to large datasets. We propose a matching
framework for IV in the presence of observed categorical confounders that
addresses these weaknesses. Our method first matches units exactly, and then
consecutively drops variables to approximately match the remaining units on as
many variables as possible. We show that our algorithm constructs better
matches than other existing methods on simulated datasets, and we produce
interesting results in an application to political canvassing.
