  Propensity score matching (PSM) is the de-facto standard for estimating
causal effects in observational studies. We show that PSM and its
implementations are susceptible to several major drawbacks and illustrate these
findings using a case study with $17,427$ patients. We derive four formal
properties an optimal statistical matching algorithm should meet, and propose
Deterministic Balancing Score exact Matching (DBSeM) which meets the
aforementioned properties for an exact matching. Furthermore, we investigate
one of the main problems of PSM, that is that common PSM results in one valid
set of matched pairs or a bootstrapped PSM in a selection of possible valid
sets of matched pairs. For exact matchings we provide the mathematical proof,
that DBSeM, as a result, delivers the expected value of all valid sets of
matched pairs for the investigated dataset.
