Multivariate Matching Methods That are Monotonic Imbalance Bounding

We introduce a new ``Monotonic Imbalance Bounding'' (MIB) class of matching methods for causal inference that satisfies several important in-sample properties. MIB generalizes and extends in several new directions the only existing class, ``Equal Percent Bias Reducing'' (EPBR), which is designed to satisfy weaker properties and only in expectation. We also offer strategies to obtain specific members of the MIB class, and present a member of this class, called Coarsened Exact Matching, whose properties we analyze from this new perspective.