  The finite sample variance of an inverse propensity weighted estimator is
derived in the case of discrete control variables with finite support. The
obtained expressions generally corroborate widely-cited asymptotic theory
showing that estimated propensity scores are superior to true propensity scores
in the context of inverse propensity weighting. However, similar analysis of a
modified estimator demonstrates that foreknowledge of the true propensity
function can confer a statistical advantage when estimating average treatment
effects.
