On randomization inference after inexact Mahalanobis matching

In observational causal inference, matched-pairs studies are often analyzed using randomization tests. While intuitively appealing, these tests are not formally justified by the randomness in the treatment assignment process (the "design") unless all matches are exact. This paper asks whether these tests can instead be justified by the random sampling of experimental units. We find that under fairly restrictive sampling assumptions, the paired randomization test based on a regression-adjusted test statistic may be asymptotically valid despite inexact matching. We propose a new randomization test based on matching with replacement that can be justified under weaker sampling assumptions.